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The American Astronomical Society (AAS) , established in 1899 and based in Washington, DC, is the major organization of professional astronomers in North America. Its membership of about 7,000 individuals also includes physicists, mathematicians, geologists, engineers, and others whose research and educational interests lie within the broad spectrum of subjects comprising contemporary astronomy. The mission of the AAS is to enhance and share humanity's scientific understanding of the universe.

The Institute of Physics (IOP) is a leading scientific society promoting physics and bringing physicists together for the benefit of all. It has a worldwide membership of around 50 000 comprising physicists from all sectors, as well as those with an interest in physics. It works to advance physics research, application and education; and engages with policy makers and the public to develop awareness and understanding of physics. Its publishing company, IOP Publishing, is a world leader in professional scientific communications.

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The Planetary Science Journal is an open access journal devoted to recent developments, discoveries, and theories in planetary science. The journal welcomes all aspects of investigation of the solar system and other planetary systems.

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Paul Wiegert 2024 Planet. Sci. J. 5 184

Apophis's current trajectory takes it safely past our planet at a distance of several Earth radii on 2029 April 13. Here the possibility is considered that Apophis could collide with a small asteroid, like the ones that frequently and unpredictably strike Earth, and the resulting perturbation of its trajectory. The probability of an impact that could significantly displace Apophis relative to its keyholes is found to be less than one in 10 6 , requiring a Δ v ≳ 0.3 mm s −1 , while for an impact that could significantly displace Apophis compared to its miss distance in 2029, it is less than one in 10 9 , requiring a Δ v ≳ 5 cm s −1 . These probabilities are below the usual thresholds considered by asteroid impact warning systems. Apophis is in the daytime sky and unobservable from mid-2021 to 2027. It will be challenging to determine from single-night observations in 2027 if Apophis has moved on the target plane enough to enter a dangerous keyhole, as the deviation from the nominal ephemeris might be only a few tenths of an arcsecond. An impending Earth impact would, however, be signaled clearly in most cases by deviations of tens of arcseconds of Apophis from its nominal ephemeris in 2027. Thus, most of the impact risk could be retired by a single observation of Apophis in 2027, though a minority of cases present some ambiguity and are discussed in more detail. Charts of the on-sky position of Apophis under different scenarios are presented for quick assessment by observers.

Lauren E. Mc Keown et al 2024 Planet. Sci. J. 5 195

The Kieffer model is a widely accepted explanation for seasonal modification of the Martian surface by CO 2 ice sublimation and the formation of a "zoo" of intriguing surface features. However, the lack of in situ observations and empirical laboratory measurements of Martian winter conditions hampers model validation and refinement. We present the first experiments to investigate all three main stages of the Kieffer model within a single experiment: (i) CO 2 condensation on a thick layer of Mars regolith simulant; (ii) sublimation of CO 2 ice and plume, spot, and halo formation; and (iii) the resultant formation of surface features. We find that the full Kieffer model is supported on the laboratory scale as (i) CO 2 diffuses into the regolith pore spaces and forms a thin overlying conformal layer of translucent ice. When a buried heater is activated, (ii) a plume and dark spot develop as dust is ejected with pressurized gas, and the falling dust creates a bright halo. During plume activity, (iii) thermal stress cracks form in a network similar in morphology to certain types of spiders, dendritic troughs, furrows, and patterned ground in the Martian high south polar latitudes. These cracks appear to form owing to sublimation of CO 2 within the substrate, instead of surface scouring. We discuss the potential for this process to be an alternative formation mechanism for "cracked" spider-like morphologies on Mars. Leveraging our laboratory observations, we also provide guidance for future laboratory or in situ investigations of the three stages of the Kieffer model.

R. Wordsworth et al 2024 Planet. Sci. J. 5 67

Although the scientific principles of anthropogenic climate change are well-established, existing calculations of the warming effect of carbon dioxide rely on spectral absorption databases, which obscures the physical foundations of the climate problem. Here, we show how CO 2 radiative forcing can be expressed via a first-principles description of the molecule's key vibrational-rotational transitions. Our analysis elucidates the dependence of carbon dioxide's effectiveness as a greenhouse gas on the Fermi resonance between the symmetric stretch mode ν 1 and bending mode ν 2 . It is remarkable that an apparently accidental quantum resonance in an otherwise ordinary three-atom molecule has had such a large impact on our planet's climate over geologic time, and will also help determine its future warming due to human activity. In addition to providing a simple explanation of CO 2 radiative forcing on Earth, our results may have implications for understanding radiation and climate on other planets.

Marc W. Buie et al 2024 Planet. Sci. J. 5 196

Following the Pluto flyby of the New Horizons spacecraft, the mission provided a unique opportunity to explore the Kuiper Belt in situ. The possibility existed to fly by a Kuiper Belt object (KBO), as well as to observe additional objects at distances closer than are feasible from Earth-orbit facilities. However, at the time of launch no KBOs were known about that were accessible by the spacecraft. In this paper we present the results of 10 yr of observations and three uniquely dedicated efforts—two ground-based using the Subaru Suprime Camera, the Magellan MegaCam and IMACS Cameras, and one with the Hubble Space Telescope—to find such KBOs for study. In this paper we overview the search criteria and strategies employed in our work and detail the analysis efforts to locate and track faint objects in the Galactic plane. We also present a summary of all of the KBOs that were discovered as part of our efforts and how spacecraft targetability was assessed, including a detailed description of our astrometric analysis, which included development of an extensive secondary calibration network. Overall, these efforts resulted in the discovery of 85 KBOs, including 11 that became objects for distant observation by New Horizons and (486958) Arrokoth, which became the first post-Pluto flyby destination.

Roger N. Clark et al 2024 Planet. Sci. J. 5 198

The Moon Mineralogy Mapper (M 3 ) on the Chandrayaan-1 spacecraft provided nearly global 0.5–3 μ m imaging-spectroscopy data at 140 m pixel –1 in 85 spectral bands. Targeted locations were imaged at 70 m pixel –1 and higher spectral resolution. These data enable a detailed look at the mineralogy, hydroxyl, and water signatures exposed on the lunar surface. We find evidence for multiple processes, including probable solar wind implantation, excavation of hydroxyl-poor and water-poor material in cratering events, excavation of hydroxyl and water-rich materials from depth and global trends with rock type and latitude. Some water-rich areas display sharp boundaries with water-poor rocks but have a diffuse halo of hydroxyl surrounding the water-rich rocks indicating a weathering process of destruction of water, probably due to a regolith gardening process. Mapping for specific mineralogy shows evidence for absorptions near 2.2 μ m, probably associated with smectites, and near 1.9 μ m due to water. Lunar swirls are confirmed to be OH-poor, but we also find evidence that swirls are water-poor based on a weak 1.9 μ m water band. Some swirls show enhanced pyroxene absorption. "Diurnal" signatures are found with stable minerals. Pyroxene is shown to exhibit strong band depth changes with the diurnal cycle, which directly tracks the solar incidence angle and is consistent with changing composition and/or grain size with depth. Mapping of M 3 data for the presence of iron oxides (e.g., hematite and goethite) is found to be a false signature in the M 3 data due to scattered light in the instrument.

Derek C. Richardson et al 2024 Planet. Sci. J. 5 182

NASA's Double Asteroid Redirection Test (DART) spacecraft impacted Dimorphos, the natural satellite of (65803) Didymos, on 2022 September 26, as a first successful test of kinetic impactor technology for deflecting a potentially hazardous object in space. The experiment resulted in a small change to the dynamical state of the Didymos system consistent with expectations and Level 1 mission requirements. In the preencounter paper, predictions were put forward regarding the pre- and postimpact dynamical state of the Didymos system. Here we assess these predictions, update preliminary findings published after the impact, report on new findings related to dynamics, and provide implications for ESA's Hera mission to Didymos, scheduled for launch in 2024 October with arrival in 2026 December. Preencounter predictions tested to date are largely in line with observations, despite the unexpected, flattened appearance of Didymos compared to the radar model and the apparent preimpact oblate shape of Dimorphos (with implications for the origin of the system that remain under investigation). New findings include that Dimorphos likely became prolate due to the impact and may have entered a tumbling rotation state. A possible detection of a postimpact transient secular decrease in the binary orbital period suggests possible dynamical coupling with persistent ejecta. Timescales for damping of any tumbling and clearing of any debris are uncertain. The largest uncertainty in the momentum transfer enhancement factor of the DART impact remains the mass of Dimorphos, which will be resolved by the Hera mission.

Jean-Luc Margot et al 2024 Planet. Sci. J. 5 159

The current International Astronomical Union (IAU) definition of "planet" is problematic because it is vague and excludes exoplanets. Here, we describe aspects of quantitative planetary taxonomy and examine the results of unsupervised clustering of solar system bodies to guide the development of possible classification frameworks. Two unsurprising conclusions emerged from the clustering analysis: (1) satellites are distinct from planets and (2) dynamical dominance is a natural organizing principle for planetary taxonomy. To generalize an existing dynamical dominance criterion, we adopt a universal clearing timescale applicable to all central bodies (brown dwarfs, stars, and stellar remnants). Then, we propose two quantitative, unified frameworks to define both planets and exoplanets. The first framework is aligned with both the IAU definition of planet in the solar system and the IAU working definition of an exoplanet. The second framework is a simpler mass-based framework that avoids some of the difficulties ingrained in current IAU recommendations.

Shannon M. MacKenzie et al 2024 Planet. Sci. J. 5 176

Evidence for the beneficial role of impacts in the creation of urable or habitable environments on Earth prompts the question of whether meteorite impacts could play a similar role at other potentially urable/habitable worlds like Enceladus, Europa, and Titan. In this work, we demonstrate that to first order, impact conditions on these worlds are likely to have been consistent with the survival of organic compounds and/or sufficient for promoting synthesis in impact melt. We also calculate melt production and freezing times for crater sizes found at Enceladus, Europa, and Titan and find that even the smallest craters at these worlds offer the potential to study the evolution of chemical pathways within impact melt. These first-order calculations point to a critical need to investigate these processes at higher fidelity with lab experiments, sophisticated thermodynamic and chemical modeling, and, eventually, in situ investigations by missions.

Yoshinori Miyazaki and David J. Stevenson 2024 Planet. Sci. J. 5 192

Small planetary bodies in the solar system, including Io, Ganymede, and Callisto, may have a crust denser than their underlying mantle. Despite the inherent gravitational instability of such structures, we show that the growth timescale of the Rayleigh–Taylor (RT) instability can be as long as the age of the solar system, owing to the strong temperature dependence of viscosity. Even in cases where the instability timescale is shorter, the instability is confined to a thin layer at the base of the crust, making the foundering of the entire crust improbable in many scenarios. This study delineates the onset and aftermath of the RT instability, applying a quantitative framework to assess the stability of (i) rock-contaminated crust on icy satellites, and (ii) silicate crust floating on top of a subsurface magma ocean on Io. Notably, for Io the RT instability peels off only 10–100 m from the crust's base, and thermal diffusion rapidly recovers the crustal thickness through solidification of a magma ocean. Despite recurrent delamination of the crustal base, the initial crustal thickness is maintained by thermal diffusion, virtually stabilizing a floating dense crust. Cracking of the crust also is unlikely to result in the foundering of the crust. A dense crust on a small body is therefore difficult to be overturned, suggesting the potential ubiquity of dense surface layers throughout the solar system.

Emileigh S. Shoemaker et al 2024 Planet. Sci. J. 5 191

Perseverance traversed the eastern, northern, and western margins of the Séítah formation inlier on the rover's western fan front approach. Mapping the stratigraphy and extent of the Máaz and Séítah formations is key to understanding the depositional history and timing of crater floor resurfacing events. Perseverance's rapid progress across the Jezero crater floor between the Octavia E. Butler landing site and the western fan front resulted in limited contextual images of the deposits from the Navigation Camera and Mast Camera Zoom. By combining the limited surface images with continuous subsurface sounding by the Radar Imager for Mars' Subsurface Experiment (RIMFAX) ground-penetrating radar, Jezero crater floor stratigraphy was inferred along this rapid traverse. We produced the first subsurface map of the Máaz formation thickness and elevation of the buried Séítah formation for 2.3 km of the rapid traverse. Three distinct reflector packets were observed in RIMFAX profiles interspersed with regions of low-radar reflectivity. We interpret these reflector packets with increasing depth to be the Roubion member of the Máaz formation (covered in places with regolith), the Rochette member, and the Séítah formation. We found a median permittivity of 9.0 and bulk density of 3.2 g cm −3 from hyperbola fits to RIMFAX profiles, which suggests a mafic composition for Máaz and Séítah. The low-radar reflectivity regions within each reflector packet could indicate potential depositional hiatuses where low-density material like sediment or regolith could have accumulated between successive Máaz formation lava flows and the Séítah formation at depth.

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Jean-Pierre Williams et al 2024 Planet. Sci. J. 5 209

Faustini crater (41 km diameter) hosts a large (664 km 2 ) permanently shadowed region (PSR) with a high potential to harbor water-ice deposits. One of the 13 candidate Artemis III landing areas contains a portion of the crater rim and proximal ejecta. The ShadowCam instrument aboard the Korea Pathfinder Lunar Orbiter provides detailed images of the PSR within Faustini. We characterize the terrain and thermal environment within the Faustini PSR from ShadowCam images, Lunar Reconnaissance Orbiter thermal measurements and laser ranging, and thermal modeling. Our mapping revealed three distinct areas of the floor of Faustini based on elevations, slopes, and surface roughness. These units broadly correlate with temperatures; thus, they may be influenced by variations in volatile sublimation. Crater retention and topographic diffusion rates appear to be asymmetric across the floor, likely due to differences in maximum and average temperatures. Several irregular depressions and a pronounced lobate-rim crater are consistent with subsurface ice. However, differences in the thicknesses of deposited materials on the floor may also explain the asymmetry. Additionally, zones of elevated surface roughness across Faustini appear to result from overprinted crater ray segments, possibly from Tycho and Jackson craters. Mass wasting deposits and pitting on opposite sides of the crater wall may have resulted from the low-angle delivery of material ejected by the Shackleton crater impact event, suggesting that the Artemis III candidate landing region named "Faustini Rim A" will contain material from Shackleton.

Darren M. Williams and Michael E. Zugger 2024 Planet. Sci. J. 5 208

The number of planetary satellites around solid objects in the inner solar system is small either because they are difficult or unlikely to form or because they do not survive for astronomical timescales. Here we conduct a pilot study on the possibility of satellite capture from the process of collision-less binary exchange and show that massive satellites in the range 0.01–0.1 M ⊕ can be captured by Earth-sized terrestrial planets in a way already demonstrated for larger planets in the solar system and possibly beyond. In this process, one of the binary objects is ejected, leaving the other object as a satellite in orbit around the planet. We specifically consider satellite capture by an "Earth" in an assortment of hypothetical encounters with large terrestrial binaries at 1 au around the Sun. In addition, we examine the tidal evolution of captured objects and show that orbit circularization and long-term stability are possible for cases resembling the Earth–Moon system.

A. C. Martin et al 2024 Planet. Sci. J. 5 207

By definition, permanently shadowed regions (PSRs) never receive primary illumination from the Sun. However, most receive secondary illumination reflected from crater walls and nearby massifs. The nature of that secondary illumination, diffuse lighting that can vary significantly across small distances, complicates interpretations of geologic features. To better understand secondary illumination and aid in interpreting images of PSRs, we analyzed a collection of long-exposure Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) images of five equatorial craters collected when the crater interiors were mainly in shadow, using these as analog images for PSR illumination conditions but enabling comparisons with LROC NAC images of the same features under direct primary illumination. Using illumination models, we quantified the range of secondary photometric angles contributing to illuminating each pixel in the shadowed terrain and measured reflectance under secondary illumination. The phase angles of secondary illumination (secondary phase angles) contributing to a pixel can be well represented by the median value of contributing illumination weighted by magnitude. We show that features observed to have approximately constant albedo in primary illumination show substantial variations in reflectance across the scene in secondary illumination depending on the median secondary phase angle. Approximately 30% of craters with high-reflectance ejecta deposits are detectable in secondary illumination; only when the reflectance contrast is high (>1.3 times higher than the background reflectance in primary illumination) are a majority (>70%) of these deposits detectable in secondary illumination, meaning that small albedo differences will be hard to detect in images of PSRs.

Eloy Peña-Asensio et al 2024 Planet. Sci. J. 5 206

NASA's Double Asteroid Redirection Test (DART) and ESA's Hera missions offer a unique opportunity to investigate the delivery of impact ejecta to other celestial bodies. We performed ejecta dynamical simulations using 3 million particles categorized into three size populations (10 cm, 0.5 cm, and 30 μ m) and constrained by early postimpact LICIACube observations. The main simulation explored ejecta velocities ranging from 1 to 1000 m s −1 , while a secondary simulation focused on faster ejecta with velocities from 1 to 2 km s −1 . We identified DART ejecta orbits compatible with the delivery of meteor-producing particles to Mars and Earth. Our results indicate the possibility of ejecta reaching the Mars Hill sphere in 13 yr for launch velocities around 450 m s −1 , which is within the observed range. Some ejecta particles launched at 770 m s −1 could reach Mars's vicinity in 7 yr. Faster ejecta resulted in a higher flux delivery toward Mars and particles impacting the Earth Hill sphere above 1.5 km s −1 . The delivery process is slightly sensitive to the initial observed cone range and driven by synodic periods. The launch locations for material delivery to Mars were predominantly north of the DART impact site, while they displayed a southwestern tendency for the Earth–Moon system. Larger particles exhibit a marginally greater likelihood of reaching Mars, while smaller particles favor delivery to Earth–Moon, although this effect is insignificant. To support observational campaigns for DART-created meteors, we provide comprehensive information on the encounter characteristics (orbital elements and radiants) and quantify the orbital decoherence degree of the released meteoroids.

Yanhong Lai et al 2024 Planet. Sci. J. 5 205

On tidally locked lava planets, a magma ocean can form on the permanent dayside. The circulation of the magma ocean can be driven by stellar radiation and atmospheric winds. The strength of ocean circulation and the depth of the magma ocean depend on external forcings and the dominant balance of the momentum equation. In this study, we develop scaling laws for the magma ocean depth, oceanic current speed, and ocean heat transport convergence driven by stellar and wind forcings in three different dynamic regimes: nonrotating viscosity-dominant Regime I, nonrotating inviscid limit Regime II, and rotation-dominant Regime III. Scaling laws suggest that magma ocean depth, current speed, and ocean heat transport convergence are controlled by various parameters, including vertical diffusivity/viscosity, substellar temperature, planetary rotation rate, and wind stress. In general, scaling laws predict that magma ocean depth ranges from a few meters to a few hundred meters. For Regime I, results from scaling laws are further confirmed by numerical simulations. Considering the parameters of a typical lava super-Earth, we found that the magma ocean is most likely in the rotation-dominant Regime III.

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• 2020-present The Planetary Science Journal doi: 10.3847/issn.2632-3338 Online ISSN: 2632-3338

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Featured Article: A brief review of single silicate crystal paleointensity: rock-magnetic characteristics, mineralogical backgrounds, methods and application

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Venus: key to understanding the evolution of terrestrial planets

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• Published: 08 June 2021
• Volume 54 , pages 575–595, ( 2022 )

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• Colin F. Wilson   ORCID: orcid.org/0000-0001-5355-1533 1 ,
• Thomas Widemann 2 &
• Richard Ghail 3  

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In this paper, originally submitted in answer to ESA’s “Voyage 2050” call to shape the agency’s space science missions in the 2035–2050 timeframe, we emphasize the importance of a Venus exploration programme for the wider goal of understanding the diversity and evolution of habitable planets. Comparing the interior, surface, and atmosphere evolution of Earth, Mars, and Venus is essential to understanding what processes determined habitability of our own planet and Earth-like planets everywhere. This is particularly true in an era where we expect thousands, and then millions, of terrestrial exoplanets to be discovered. Earth and Mars have already dedicated exploration programmes, but our understanding of Venus, particularly of its geology and its history, lags behind. Multiple exploration vehicles will be needed to characterize Venus’ richly varied interior, surface, atmosphere and magnetosphere environments. Between now and 2050 we recommend that ESA launch at least two M-class missions to Venus (in order of priority): a geophysics-focussed orbiter (the currently proposed M5 EnVision orbiter – [ 1 ] – or equivalent); and an in situ atmospheric mission (such as the M3 EVE balloon mission – [ 2 ]). An in situ and orbital mission could be combined in a single L-class mission, as was argued in responses to the call for L2/L3 themes [ 3 , 4 , 5 ]. After these two missions, further priorities include a surface lander demonstrating the high-temperature technologies needed for extended surface missions; and/or a further orbiter with follow-up high-resolution surface radar imaging, and atmospheric and/or ionospheric investigations.

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Probing space to understand Earth

Venus Evolution Through Time: Key Science Questions, Selected Mission Concepts and Future Investigations

Venus, the Planet: Introduction to the Evolution of Earth’s Sister Planet

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1 Introduction

1.1 the importance of venus for comparative planetology.

One of the central goals of planetary research is to find our place in the Universe. Investigating the evolution of solar systems, planets, and of life itself, is at the heart of this quest. The three terrestrial planets in our solar system - Earth, Mars, and Venus - show a wide range of evolutionary pathways, and so represent a “key” to our understanding of planets and exoplanets.

Earth and Venus were born as twins – formed at around the same time, with apparently similar bulk composition and the same size. However, they have evolved very differently: the enormous contrast between these planets today challenge our understanding of how terrestrial planets work. The atmosphere is surprising in many ways – its 400 km/h winds on a slowly rotating planet; its enormous surface temperature, even though it absorbs less sunlight than does the Earth; its extreme aridity, with sulphuric acid as its main condensable species instead of water. The solid planet, too, is mysterious: its apparent lack of geodynamo and plate tectonics, the uncertainty of its current volcanic state, the apparent young age of much of its surface. How and why does a planet so similar to Earth end up so different?

In an era where we will soon have detected thousands of Earth-sized exoplanets, planetary science must seek to characterise these planets and to explain the diverse outcomes which may befall them. Are these exoplanets habitable? Many efforts have been made to define the edges of the ‘habitable zone’, i.e. the range of distances from a parent star at which a planet can sustain liquid water on its surface. The inner edge of the habitable zone has been estimated to lie anywhere from 0.5 AU to 0.99 AU – this latter figure, from Kopparapu et al. [ 6 ] should be a cause of concern for us Earth-dwellers! Detailed study of Venus is indispensable if we are to understand what processes determine the inner edge of the habitable zone.

The habitable zone’s boundaries will evolve over a planet’s lifetime due to the evolution of the star’s output as well as changes in the planet and its atmosphere. There are only three terrestrial planets at which we can study geophysical and evolutionary processes which govern habitability through time: Venus, Earth, and Mars. Exploration of the latter two is firmly established, while in contrast there are, at time of writing in 2019, no confirmed Venus missions after Akatsuki.

1.2 Context: The state of Venus science after Venus express and Akatsuki

ESA’s Venus Express was a very successful mission. During its science operations, from 2006 to 2014, it made a wealth of discoveries relating to the atmosphere at all altitudes from the surface up to the exosphere. It has mapped cloud motions to reveal wind velocities at different altitudes; it has measured the spatial distributions of key chemical species, and discovered new ones; it has improved our understanding of how unmagnetised Earth-like planets lose water. Despite its atmospheric focus, its most intriguing legacy may be the hints it has provided of current-day volcanic activity.

JAXA’s Akatsuki orbiter – previously known as the Venus Climate Orbiter – was launched in 2010, and has been orbiting Venus since 2015 [ 7 ]. Its scientific focus is on atmospheric dynamics; it carries a set of cameras using different wavelengths to image atmospheric motions at different altitudes. Its observations have revealed new atmospheric waves, providing ever more detailed insights into Venus’ atmospheric circulation.

In short, Venus Express and Akatsuki have provided much-needed data for atmospheric dynamics, chemistry, and radiative transfer, and for understanding of its ionosphere and induced magnetosphere. These new data are invaluable for constraining models of how Venus works today. However, the history of Venus still remains enigmatic. In this White Paper, initially submitted in response to ESA’s Voyage 2050 call, we propose a new set of investigations that focus on understanding the evolution of Venus through a combination of surface and atmospheric investigations.

Thanks to Venus Express, Europe is at the forefront of Venus research – arguably, this is a situation unmatched in the rest of the Solar System exploration programme. Research groups across Europe have participated in the construction of and analysis from the scientific payload; dozens of researchers have completed doctoral theses based on Venus Express research. Europe is thus well-placed to lead a future Venus mission. ESA can now build on this position, capitalising on investments made in the Earth Observation programme and advanced satellite technologies, to address fundamental questions about the evolution of terrestrial planets and the appearance of life.

2 Science themes

2.1 geology (interior, tectonism, volcanism, mineralogy, geomorphology).

The major unknowns in Venus geological science are associated with its resurfacing history and establishing whether it is currently geologically active.

2.1.1 Resurfacing history

The age of Venus’ surface is poorly known. Unlike Mercury, the Moon, and Mars, Venus has a thick atmosphere that effectively filters out small impactors. As a result, its crater population is limited to a few large craters; there are very few craters with diameters <20 km, and there are fewer than 1000 craters in total. The observed crater population offers poor constraints on surface ages, allowing a number of different production and resurfacing scenarios. These include catastrophic global lithospheric overturn occurring every 500–700 My [ 8 ], equilibrium resurfacing models more similar to those found on Earth [ 9 ], as well as many models in between.

The community has used the existing Magellan radar data to attempt to resolve these fundamental conflicts by applying mapping techniques to establish stratigraphic relationships among surface units and structures. NASA’s Magellan orbiter, launched in 1989, obtained global radar maps with a spatial resolution of 100–200 m. An important limitation to using radar images for geological mapping is that geological mapping requires the ability to identify distinct rock units, whose formation represent geological processes (e.g., distinct lava flows or sedimentary units). Magellan imagery provides the opportunity to identify some units; for example, it is possible to map lava flow boundaries to high precision in some terrains. But in many, many other cases, the materials being mapped have been affected by later tectonic processes; moreover, the highly deformed tessera terrain, thought to be the oldest on Venus, is characterized by overlapping structures whose relationships are ambiguous in currently available observations. Different methods for accommodating this complication have led to widely divergent mapping styles, which in turn have resulted in a range of surface evolution models, mirroring the range of interior evolution models (see e.g. reviews by [ 10 ], and [ 11 ]). Many remaining debates over, for instance, the sequence and relative timing of tectonic deformation in the complex tesserae cannot be resolved using currently available radar data, because of the limitations represented by the spatial resolution and single polarization of those data.

2.1.2 Current geological activity

Venus is thought to have similar internal heat production to Earth, but it is not clear how the internal heat is lost to space. Is heat lost solely by crustal conduction, or does volcanic activity play an important role? Is the loss rate sufficient to maintain an equilibrium or is heat building up in the interior, potentially leading to an episodic resurfacing scenario? Understanding how Venus loses its internal heat is important for understanding both Earth’s earliest history and for understanding those exoplanets larger than Earth, both of which share its problem of a buoyant lithosphere; these mechanisms at work may profoundly affect the atmosphere and climate, and prove catastrophic for life.

There are some hints of recent geological activity particularly from Venus Express data [ 12 , 13 ], but these analyses are indirect. A new radar dataset would enable not only better understanding of current surface weathering and alteration processes, which is needed in order to calculate ages for geologically recent changes such as lava flows and dune movements, but would also enable direct searching for surface change.

2.1.3 Case for next-generation radar

Because of the extreme surface conditions and opaque clouds on Venus, geological investigation requires orbital remote sensing, with techniques including interferometric synthetic aperture radar (InSAR), gravitometry, altimetry, and infrared observation using nightside infrared windows. The value of radar mapping at Venus was demonstrated by NASA’s Magellan orbiter, which obtained global radar maps with a horizontal resolution of 100–200 m and altimetry with a vertical resolution of 100 m. Advances in technology, data acquisition and processing, and satellite control and tracking, mean that the spatial resolutions in the 1–10 m range are now possible.

This high-resolution radar mapping of Venus would revolutionise geological understanding. Generations of Mars orbital imagery have seen successive order-of-magnitude improvements, as illustrated above. As imagers progressed from the 50 m resolution of Viking towards the 5 m resolution of MOC (on Mars Global Surveyor) and the higher resolutions of HRSC (on Mars Express) and HiRise (on Mars Reconnaissance Orbiter), our conception of Mars as a frozen, inactive planet was followed by hypotheses that geologically recent flow had occurred, to actual detection of current surface changes (e.g. gullies and dune movement) – as illustrated in Fig.  1 . For Venus, metre-scale imagery will enable study of Aeolian features and dunes (only two dune fields have been unambiguously identified to date on Venus); will enable more accurate stratigraphy and visibility of layering; will constrain the morphology of tesserae enough that their stress history and structural properties can be constrained; will enabled detailed study of styles of volcanism by enabling detailed mapping of volcanic vents and lava flows; and will enable direct search for surface changes due to volcanic activity and Aeolian activity. Metre-scale resolution would even enable a search for changes in rotation rate due to surface-atmosphere momentum exchange, which could constrain internal structure [ 14 ].

Images of the same region of Mars illustrate the revolutions in understanding which are enabled by increasing spatial resolution by an order of magnitude, particular for surface processes. Quoted pixel resolution is that of the displayed image used rather than the full resolution of the original. Image credits: NASA/JPL

The revolutions in radar performance go beyond just spatial resolution. Differential InSAR allows surface change detection at centimetre scale. This technique has been used to show surface deformations after earthquakes and volcanic eruptions on Earth (see Fig.  2 ); similar results on Venus could provide dramatic evidence of current volcanic or tectonic activity.

Differential InSAR revealed altimetry changes in this volcano in Kenya which previously had been thought to be dormant. [[ 15 ]; observations from Envisat ERS-1 & ERS-2]

The maturity of InSAR studies on Earth is such that data returned from Venus can confidently be understood within a solid theoretical framework developed from coupled terrestrial InSAR data and ground-truth observations, even without ground-truth data on Venus. Note that the radar spatial resolution may be high enough to permit identification of Venera and Pioneer Venus landers, which serves as some ground truth even before a new generation of landers is taken into account. Radar mapping with different polarisation states constrains surface roughness and dielectric properties; mapping at different look angles and different wavelengths will provide further new constraints on surface properties.

The proximity of Venus to Earth, the relatively calm (if extreme) surface conditions and lack of water, the absence of a large satellite and its moderately well-known geoid and topography, all help to ease the technical demands on the mission. Europe has developed a number of world-leading radar systems and could, for example, adapt a GMES Sentinel-1 or NovaSAR-S modular array antenna for use at Venus, providing higher-resolution imagery, topography, geoid, and interferometric change data that will revolutionise our understanding of surface and interior processes [ 16 ].

In addition to radar techniques, the surface can also be observed by exploiting near-infrared spectral window regions at wavelengths of 0.8–2.5 μm. On the nightside of Venus, thermal emission from the surface escapes to space in some of these spectral windows, allowing mapping of surface thermal emissivity, as demonstrated by the VIRTIS instrument on Venus Express [ 17 ]. A new instrument optimised for this observation could map mineralogy and also monitor the surface for volcanic activity [ 18 ].

2.1.4 Case for Venus in situ geological investigations

The Venera and Vega missions returned data about the composition of Venus surface materials, but their accuracy is not sufficient to permit confident interpretation. The Venera and Vega analyses of major elements (by X-ray fluorescence, XRF) did not return abundances of Na, and their data on Mg and Al are little more than detections at the 2σ level. Their analyses for K, U, and Th (by gamma rays) are imprecise, except for one (Venera 8) with extremely high K contents (~4% K 2 O) and one (Venera 9) with a non-chondritic U/Th abundance ratio. The landers did not return data on other critical trace and minor elements, like Cr and Ni. In addition, the Venera and Vega landers sampled only materials from the Venus lowlands – they did not target sites in any of the highland areas, the coronae, tesserae, nor the unique plateau construct of Ishtar Terra. Currently available instruments could provide much more precise analyses for major and minor elements, even within the engineering constraints of Venera-like landers.

A new generation of geologic instrumentation should be brought to the surface of Venus, including Raman/LIBS (Laser Induced Breakdown Spectroscopy) and XRF/XRD (X-ray diffraction); this would allow mineralogical, as well as merely elemental, composition. Such precise analyses would be welcome for basalts of Venus’ lowland plains, but would be especially desirable for the highland tesserae and for Ishtar Terra. The tesserae are thought to represent ancient crust that predates the most recent volcanic resurfacing event and so provide a geochemical look into Venus’ distant past. Ishtar Terra, too, may be composed (at least in part) of granitic rocks like Earth’s continental crust, which required abundant water to form. Coronae samples will reveal how magmatic systems evolved on Venus in the absence of water but possibly in the presence of CO 2 , SO 2 , or other volatiles. Surface geological analysis would benefit from high temperature drilling/coring and sample processing capabilities, although further investigation will be needed to assess the extent to which this can be within the scope of even an L-class mission opportunity.

Long-lived stations would provide essential seismological and meteorological data. The technological barriers to such missions are twofold: (1) the high temperature environment of the Venus surface, too hot for silicon electronics, and (2) the lack of sunlight at the surface, making solar power unviable. As has been discussed by Wilson et al. [ 19 ] and Kremic et al. [ 20 ], recent advances in high-temperature electronics have made long-duration uncooled landers a possibility which could be explored in the coming decades; this requires continued investment in the development of the electronics, in their packaging, and in their environmental qualification in Venus conditions. Power for long-duration landers on the surface could come from primary molten salt batteries, for a first generation of landers. Second-generation long-life landers could be powered by radioisotope thermoelectric generators (RTGs) or even wind power – both of which would require technology development.

Descent imaging has not yet been performed by any Venus lander. Descent imaging of any landing site would be useful, particularly so for the tessera highlands where it would reveal the morphology of the highland surfaces and yield clues as to what weathering processes have been at work in these regions. Multi-wavelength imaging in near-infrared wavelengths would yield compositional information to provide further constraints on surface processes. In particular, descent imaging can establish whether near-surface weathering or real compositional differences are the root cause for near-infrared emissivity variations seen from orbit [ 21 ] - providing important ground truth for these orbital observations.

Profiles of atmospheric composition in the near-surface atmosphere would reveal which chemical cycles are responsible for maintaining the enormously high carbon dioxide concentrations in the atmosphere, and would also reveal details about surface-atmosphere exchanges of volatiles. Several mechanisms have been invoked for buffering the observed abundance of carbon dioxide, including the carbonate [ 22 ] or pyrite-magnetite [ 23 ] buffer hypotheses. Measurements of near-surface abundances and vertical gradients of trace gases, in particular SO 2 , H 2 O, CO, and OCS, would enable discrimination between different hypotheses. Correlating these data with lander and orbiter observations will reveal how important and widespread the sources and sinks of these species might be.

Measurement of the temperature, pressure, and N 2 abundance in the lowest scale height is also essential. Only one Venus descent probe, Vega 2 in 1984, reported temperature and pressure profiles all the way down to the surface; and the gradient of its temperature profile in the lowest few km appears far more convectively unstable than is thought to be physically possible. At the altitudes where this occurs, carbon dioxide is in a supercritical fluid regime, and it has been suggested that carbon dioxide and nitrogen are separating due to exotic supercritical processes [ 24 ]. This effect would have major implications for our understanding of high pressure atmospheres everywhere, from the gas giants to exoplanets. High-accuracy measurements of pressure, temperature, and N 2 abundance down to the surface would resolve this intriguing question.

2.2 Planetary evolution as revealed by isotope geochemistry

Geology is a powerful witness to history, but it does not provide answers about evolution in the time before the formation of the oldest rocks, which on Venus are thought to have formed only about a billion years ago. For constraints on earlier evolution, we must turn to isotope geochemistry.

Radiogenic noble gas isotopes provide information about the degassing history of the planet. 40 Ar, produced from the decay of long-lived 40 K, has been continuously accumulated over >4 billion years and so its current abundance constrains the degree of volcanic/tectonic resurfacing throughout history. 129 Xe and 130 Xe are produced from the now extinct 129 I and 244 Pu respectively within the first 100 Ma of the Solar System’s history. The depletion of these isotopes in the atmospheres of Mars and Earth reveals that these two planets underwent a vigorous early degassing and blow-off, although the mechanisms of this blow-off and of subsequent deliveries of materials from comets and meteorites vary according to different scenarios. Neither the bulk Xe abundance nor the abundances of its eight isotopes have ever been measured at Venus. Measurements of these abundances would provide entirely new constraints on early degassing history. 4 He, produced in the mantle from long-lived U and Th decay, has an atmospheric lifetime of only a few hundred million years before it is lost by escape to space. Therefore its current atmospheric abundance provides constraints on recent outgassing and escape rates within the last 10 8 –10 9  years.

Non-radiogenic noble gas isotopes provide information about acquisition and loss of planet-forming material and volatiles. Venus is less depleted in Neon and Argon isotopes than are Earth and Mars, but its Xe and Kr isotopic abundances are still unknown: Xe isotopic abundances have not yet been measured, and past measurements of Kr abundance vary by an order of magnitude, providing little useful constraint. The significant fractionation of xenon on Earth and Mars can be attributed to massive blowoffs of the initial atmospheres in the period after the radiogenic creation of xenon from its parent elements, ~50–80 Myr after planet formation. However, it could also be that the fractionation is reflecting that of source material delivered late in planetary formation, perhaps from very cold comets. If Venus has the same xenon fractionation pattern as Earth and Mars, this would support the idea that a common source of fractionated xenon material was delivered to all three planets, and weaken the case that these reflect large blowoffs. If we see a pattern with less Xe fractionation then that would support the blow-off theory for Earth and Mars. Considered together with other non-radiogenic isotopic abundances, this allows determination of the relative importance of EUV, impact-related or other early loss processes. These measurements would also allow tighter constraints on how much of the gas inventory originated from the original accretion disc, how much came from the solar wind, and how much came later from planetesimals and comets. Late impacts such as the Earth’s moon-forming impact also have an effect on noble gas isotopic ratios so can also be constrained through these measurements.

Light element isotopic ratios, namely H, C, O, N, etc., provide further insights into the origin and subsequent histories of planetary atmospheres. Measurement of 20 Ne/ 21 Ne/ 22 Ne and/or of 16 O/ 17 O/ 18 O would enable determination of whether Earth, Venus, and Mars came from the same or from different parts of the protoplanetary nebula, i.e. are they are truly sibling planets of common origin. Venus’ enhanced deuterium to hydrogen ratio, 150 times greater than that found on Earth, suggests that hydrogen escape has played an important role in removing water from the atmosphere of Venus, removing more than a terrestrial ocean’s worth of water during the first few hundred million years of the planet’s evolution [ 25 ]. 14 N/ 15 N ratios have been found to vary considerably in the Solar System, with the solar wind, comets, and meteorites all exhibiting isotopic ratios different from the terrestrial values; it also is affected by preferential escape of 14 N. Measurement of the nitrogen isotopic ratio therefore helps establish whether the gas source was primarily meteoritic or cometary, and constrains the history of escape rates.

Taken together, and as illustrated in Fig. 3 , measurements of these isotopic abundances on Venus, Earth, and Mars are needed to provide a consistent picture of the formation and evolution of these planets and their atmospheres, and in particular the history of water on Venus. Early Venus would have had an atmosphere rich in carbon dioxide and water vapour, like that of Hadean Earth. Hydrodynamic escape from this early steam atmosphere would have been rapid – but would it have been rapid enough to lose all of Venus’ water before the planet had cooled enough to allow water to condense? If Venus did have a liquid water ocean, how long did this era persist before the runaway greenhouse warming ‘ran away’, with the oceans evaporating and the resulting water vapour being lost to space? The nature of early escape processes is as yet too poorly constrained to answer these questions. An early Venus with a liquid water ocean would have arguably have been more Earth-like than was early Mars and could have taken steps towards the development of life. A habitable phase for early Venus would have important consequences for our understanding of astrobiology and the habitable zones of exoplanets.

Isotopic ratios provide keys to constrain planetary origins (Ne isotopes), early atmospheric loss processes (non-radiogenic Xe, Kr, Ar), late impact scenarios, recent mantle outgassing and late resurfacing, and escape of water. Modified from [ 26 ]

This section of the paper has argued that new measurements of isotopic abundances are needed. A few isotopic ratios, notably D/H, can be measured from orbit, and indeed orbital measurements allow a comprehensive understanding of how they may vary in space and time. However, most of the isotopic abundances in question, particularly the valuable abundances of noble gases isotopes, cannot be measured remotely and require measurement in situ. Noble gas isotopes are non-reactive so will be well-mixed throughout the atmosphere; a measurement of their abundances anywhere below the homopause altitude of some 120–130 km will be representative of the whole lower atmosphere. Some isotopic abundances were measured by Venera and Pioneer Venus entry probes, but the low sensitivity of 1970s technologies used in these measurements means that many key species abundances were not measured at all, or not measured with an accuracy which provides useful constraints on Venus planetary evolution. New measurements, using modern spacecraft mass spectrometers in which European groups have considerable expertise, can be made either from a classical Venera-style descent probe, which descends to the surface within one hour or so, or from a long-lived platform dwelling for days or weeks in the cloud layer taking advantage of the benign ambient temperatures found there to make repeated measurements.

More detailed treatments of Venus isotope geochemistry goals and interpretation can be found in Chassefière et al. [ 27 ] and Baines et al. [ 26 ].

2.3 Atmospheric science (dynamics; chemistry and clouds; structure and radiative balance)

The terrestrial planets today exhibit strikingly different climates. Study of the fundamental processes at work on these three planets will lead to a deeper understanding of how atmospheres work, and of how climates evolve.

2.3.1 Dynamics and thermal structure

One of the crucial factors determining planetary habitability is the redistribution of heat around the planet. The solid planet of Venus rotates only once every 243 Earth days but the atmosphere above exhibits strong super-rotation, circling the planet some 40–50 times faster than the solid planet below. General Circulation Models (GCMs) are now able to reproduce super-rotation, but are very sensitive not only to model parameters but also to the details of how those models operate. Efforts to improve modelling of the Venus atmosphere have led to improvements in how Earth GCMs handle details like conservation of angular momentum and temperature dependent specific heat capacities [ 28 ]. Exchanges of momentum between surface and atmosphere, an important boundary condition for the atmospheric circulation, depend sensitively on the thermal structure in the lowest 10 km of the atmosphere. Many probes experienced instrument failure at these high temperatures so the atmospheric structure in the lowest parts of the atmosphere is not well known. The atmospheric circulation is driven by solar absorption in the upper cloud; most of this energy absorption is by an as-yet-unidentified UV absorber, which is spatially and temporally variable. Efforts to identify this UV absorber by remote sounding have been inconclusive, so in situ identification will be necessary.

Most of our knowledge of the wind fields on Venus has been gained by tracking imaged cloud features, or by tracking descent probes. Tracking cloud features returns information about winds at altitudes from 48 km to 70 km altitude, depending on the wavelength used. However, it is not clear at what altitude to assume that the derived cloud vectors apply; the formation mechanism for the observed contrasts is not known so it cannot be ascertained to what extent the derived velocity vectors represent true air motion rather than the product of, for example, wave activity. Furthermore, with the exception of recent observations from Akatsuki’s Longwave Infrared (LIR) Camera, observations on the day- and night-sides of Venus are obtained using different wavelengths, referring to different altitudes on day- and night-sides, so global averages of wind fields cannot be obtained by wind tracking, frustrating attempts to understand global circulation.

Direct measurement of mesospheric wind velocities (or at least their line-of-sight components) from orbit can be achieved by using Doppler sub-millimetre observations, Doppler LIDAR, or other such instruments, and this would provide invaluable constraints for circulation models. Tracking of descent probes will yield direct measurement of the vertical profile of horizontal winds in the deep atmosphere, which will provide important constraints on the mechanisms of super-rotation. Balloon elements are ideal for measuring vertical wind speeds but also provide information about wave and tidal activity at near-constant altitude.

2.3.2 Chemistry and clouds

Venus has an enormous atmosphere with many complex chemical processes at work. Processes occurring near the surface, where carbon dioxide becomes supercritical and many metals would melt, are very different from those at the mesopause where temperatures can be below −150 °C, colder than any found on Earth. A diversity of observing techniques is clearly required to understand this diversity of environments. While chemical processes in the mesosphere and lower thermosphere were studied in depth by Venus Express, processes in the clouds and below are very difficult to sound from orbit and require in situ investigation.

The dominant chemical cycles at work in Venus’s clouds are those linking sulphuric acid and sulphur dioxide: Sulphuric acid is photochemically produced at cloud-tops, has a net downwards transport through the clouds, and then evaporates and then thermal dissociates below the clouds; this is balanced by net upwards transport through the clouds of its stable chemical precursors (SO 2 and H 2 O). Infrared remote sensing observations of Venus can be matched by assuming a cloud composition entirely of sulphuric acid mixed with water, but Vega descent probe XRF measurements found also tantalising evidence of P, Cl, and even Fe in the cloud particles [ 29 ]. If confirmed these measurements would provide important clues as to exchanges with the surface: are these elements associated with volcanic, Aeolian, or other processes? The UV-blue portion of the spectrum, too, shows evidence of an as-yet-unidentified absorber in the clouds besides sulphuric acid, which could be polysulphur (S 3 , S 4 , S x ), iron chloride, or a number of other possibilities. Chemical and dynamical models of the Venus clouds have, understandably, been held back by an ignorance of the detailed composition of the clouds and hazes. An in situ chemical laboratory floating in the clouds, or multiple descent probes, is needed to address cloud composition and chemical processes.

As to lower atmosphere chemistry, it is poorly understood because the rapidly falling descent probes had time to ingest and fully analyse only a small number of atmospheric samples during their brief descent. Sub-cloud hazes were detected by several probes but their composition is unknown. Ground- and space-based observations in near-infrared window regions permit remote sounding of a few major gases, but many minor species which may play important catalytic or intermediate roles in chemical cycles are difficult or impossible to probe remotely. Mapping spatial variation of volcanically gases could be a direct way of finding active volcanism on Venus; this can be achieved using spectroscopy in nightside near-infrared, as is being developed for the EnVision M5 mission [ 30 ]. Further to this, measurement from a descent probe of near surface chemical abundances and their vertical profiles will permit determination of whether there are active surface-atmosphere exchanges taking place and of what surface reactions are buffering the atmospheric composition.

2.3.3 Thermal structure and radiative fluxes

The cloud layer of Venus is highly reflective so Venus presently absorbs less power from the Sun than does the Earth. Its high surface temperature is instead caused by its enormous greenhouse warming effect, caused by carbon dioxide, water vapour, and other gases. Its clouds, too, have a net warming effect because they prevent thermal fluxes from escaping the deep atmosphere.

1-D radiative and radiative-convective models for the determination of equilibrium climate are now widespread as researchers worldwide attempt to determine the likely climate of exoplanets. Venus offers a proving ground for these models much closer to home, one where the conditions are much better known than on exoplanets. Radiative transfer calculations on Venus are difficult: uncertainties in the radiative transfer properties of carbon dioxide at high temperatures and pressures are the main unknown, particularly in the middle- and far- infrared where there are no spectral window regions to allow empirical validation. As on Earth, clouds play an important role, reflecting away sunlight but also trapping upwelling infrared radiation. The state-of-the-art Venus radiative balance models are still mainly 1-D models representing an average over the whole planet. However, we now know that the clouds are very variable; the vertically integrated optical thickness (as measured at 0.63 μm) can vary by up to 100% [ 31 ] and the vertical structure of clouds varies strongly with latitude. In-situ measurements of cloud properties with co-located radiative flux measurements are needed to determine the diversity of cloud effects on the global radiative balance.

3 Mission elements

The long list of scientific investigations outlined above cannot all be investigated from a single spacecraft: a range of different platform types, as illustrated in Fig.  4 , can be considered.

High-priority Venus questions can be addressed by a broad range of mission concepts using surface, aerial, and orbital platforms. While many missions can be implemented in the near term using existing capabilities, investments in new technologies will enable long term surface science as well as missions that take advantage of mobility in the surface, near-surface, and atmospheric environments. Venus exploration will be undertaken by a range of international agencies; for the period 2030–2050, we recommend that ESA focus on launching at least one geophysics orbiter and one cloud-level balloon

A satellite in low, near-circular polar orbit is required for radar mapping, and for LIDAR and Doppler sub-mm measurement of wind speeds. Wide-angle cameras like the MARCI camera on Mars Reconnaissance Orbiter can be used to obtain continuous imaging coverage of UV cloud-top features. Recent examples of proposed low circular Venus orbiters include the Envision M5 radar mapper [ 1 ], VERITAS radar mapper [ 32 ], the RAVEN radar mapper [ 33 ], MuSAR radar mapper [ 34 ], and the Vesper sub-mm sounding orbiter [ 35 ].

A satellite in a highly elliptical orbit can provide synoptic views of an entire hemisphere at once. One example of this is Venus Express, whose polar apocentre allows it to study the vortex circulation of the South polar region; a second example is the nearly equatorial 40-h orbit of Japan’s Akatsuki orbiter, which allows it to dwell over low-latitude cloud features for tens of hours at a time. Furthermore, the large range of altitudes reached by satellites in such orbits is useful for in situ studies of thermosphere and ionosphere and thus for studies of solar wind interaction and escape.

Balloons are ideally suited for exploring Venus because they can operate at altitudes where pressures and temperatures are far more benign than at the surface. Deployment of two small balloons at ~55 km altitude, in the heart of the main convective cloud layer, was successfully demonstrated by the Soviet Vega mission in 1984. At this altitude, the ambient temperature is a comfortable ~20 °C and the pressure is 0.5 atm. The main environmental hazard is the concentrated sulphuric acid which makes up the cloud particles; however, the cloud abundance is relatively low (peak cloud mass loadings on the order of only 30 mg/m 3 as reported in Knollenberg and Hunten [ 36 ], similar to those found in cirrus clouds on Earth), and its chemical effects can be mitigated by choosing appropriate materials for external surfaces. Balloons at this altitude can take advantage of the fast super-rotating winds which will carry the balloon all the way around the planet in a week or less (depending on latitude and altitude). Horizontal propulsion (with motors) is not usually viable because of power requirements and the difficulty of countering the fast (250 km/h) zonal windspeed. A cloud-level balloon is an ideal platform for studying interlinked dynamical chemical and radiative cloud-level processes. It also offers a thermally stable long-lived platform from which measurements of noble gas abundances and isotopic ratios can be carefully carried out and repeated if necessary (in contrast to a descent probe, which offers one chance for making this measurement, in a rapidly changing thermal environment).

Balloons can be used to explore a range of altitudes. Operation in the convectively stable upper clouds, above 63 km, would be optimal for identification of the UV absorber, but the low atmospheric density leads to a relatively small mass fraction for scientific payload. Operation below the main cloud deck at 40 km, has been proposed by Japanese researchers, with a primary goal of establishing wind fields below the clouds. Balloons can also be used to image the surface, if they are within the lowest 1–10 km of the atmosphere, but high temperatures here require exotic designs such as metallic bellows which are beyond the scope of this paper. An intriguing possibility for revealing winds in the lower atmosphere is to use passive balloons, reflective to radio waves, which could be tracked by radar – this possibility should be studied further if a radar orbiter + entry probes architecture were to be studied further.

Descent probes provide vertical profiles of composition, radiation, chemical composition as a function of altitude, and enable access to the surface. Science goals for a descent probe include: cloud-level composition and microphysical processes; near-surface composition, winds, and temperature structure; surface composition and imaging; and noble gas abundances and isotopic ratios. If the scientific focus of the probe is measurements at cloud level then a parachute may be deployed during the initial part of the entry phase in order to slow the rate of descent during the clouds. This was carried out, for example, by the Pioneer Venus Large Probe. Alternatively, if the main focus of the probe is measurements in the lower atmosphere or surface then the probe may dispense with a parachute completely. Descent imagery of impact/landing site at visible wavelengths will be invaluable for contextualising surface results; Rayleigh scattering limits the altitudes from which useful surface imagery can be obtained to ~1 km if imaging in visible wavelengths, or to 10 km if imaging at 1 μm wavelength [ 37 ].

Landers must cope with the harsh conditions of ~450 °C at the surface of Venus. Venera-style landers use only thermal inertia and thermal insulation to keep a central electronics compartment cool, allowing operation times of only hours (see e.g. Venera-D mission, [ 38 ]). The principal science payload of a such a lander would include surface imagers and non-contact mineralogical sensors such as a Gamma spectrometer with Neutron activation, capable of measuring elemental abundances of U, Th, K, Si, Fe, Al, Ca, Mg, Mn, Cl [ 39 ], and/or Raman/LIBS [ 40 ]. Inclusion of surface sample ingestion via a drill/grinder/scoop would allow further analysis techniques (e.g. mass spectroscopy; X-ray fluorescence (XRF) spectroscopy) but would require significant technology development. Gamma- and XRF spectroscopy was performed on Venera and Vega landers, but modern equivalents of these instruments would provide much improved accuracy; also, repeating the composition analyses at a tessera region (not before sampled) would reveal whether these tessera regions are chemically differentiated from the lava plains where previous analyses have been conducted.

As discussed above, long-lived landers , using high temperature electronics so as to not require any active cooling, would not only provide key meteorological and seismic measurements, but would also serve as precursors for more capable seismometry stations (more like Insight in their capability) and eventual surface rovers – which we envisage as post-2050 developments. A recent review of the state of the art and possibilities for near-future technology demonstrators can be found in Wilson et al. [ 19 ].

4 A strawman L - class mission architecture

A Large mission to Venus should include both orbital and in situ science measurements. One possible strawman mission concept which could address this theme would be a combination of an orbiter, a cloud-level balloon platform, and (optionally) a Russian descent probe/lander. As a strawman payload, we suggest the balloon element be modelled on the 2010 EVE M3 proposal [ 2 ]. The radar-equipped orbiter may be based on EnVision M3, M4, or M5 proposals [ 1 , 41 ]. Finally, the landing probe envisaged is based on the lander component of the Venera-D mission [ 38 ].

It is very important to have multiple mission elements working together simultaneously at Venus. An orbiter is necessary both to increase vastly the volume of data returned from the in situ elements, but also to place those in situ measurements into atmospheric and geological context – including, literally, determining the position of the in situ element, which is particularly important for balloons when they are not visible from Earth. The in situ measurements are required to measure parameters, like noble gas abundances and surface mineralogy, which cannot be determined from orbit. The whole mission is greater than the sum of its parts. This has been amply demonstrated by the constellation of missions at Mars, and by the Cassini/Huygens collaboration at Titan.

Not all of these mission elements need be provided by ESA; there is ample scope for international co-operation in creating this mission architecture. In particular, Russia has unequalled heritage in providing Venus descent probes from its Venera and Vega descent probes, and will gain new heritage from its Venera-D lander, planned for the coming decade. A range of mission proposals have been developed in the USA for orbiters, balloons, and descent probes, from Discovery-class to Flagship-class, many of which could form parts of a joint NASA-ESA exploration programme should a high-level agreement be reached. Japan has an active Venus research community, with its Akatsuki (Venus Climate Orbiter) spacecraft still in flight, and has developed prototypes for a Venus sub-cloud balloon [ 42 ]. After its successful moon and Mars missions, ISRO has been developing a Venus orbiter which may launch as soon as 2023 [ 43 ] – but this, at time of writing, is still not confirmed. Israel’s TECSAR satellites enable 1-m scale radar mapping with a 300 kg satellite; in the frame of future ESA-Israel agreements, collaborations on Venus radar could be fruitful. In this time frame collaborations with China are also feasible.

These could be launched as a stack on a single launcher, or it may prove convenient to use separate launchers, for example in order to insert the orbiter into a low circular orbit before the arrival of the in situ elements for optimal data relay and contextual remote sounding for the in situ measurements.

This scenario, Orbiter + balloon + Descent Probe, was proposed to ESA in 2007 in response to the M1/M2 mission Call for Ideas as a joint European Russian mission, with a European-led orbiter and balloon, and a Russian descent probe [ 44 ]. Referred to as EVE 2007, the entire mission was to be launched on a single Soyuz launch, however subsequent studies revealed that this scenario was not consistent with a single Soyuz launcher and would be more consistent with an L-class rather than an M-class opportunity. The Venus Flagship Mission being studied by NASA in 2019–2020 provides another example of a large mission of this architecture [ 45 ].

5 Technology developments needed

Much of the technology required for Venus missions in the Voyage 2050 period already exists at a high technology readiness level, but further technology development both for spacecraft technologies and for science payload technologies would be useful to maximise science return and de-risk mission aspects, and to pave the way for future surface missions.

Many of the mission-enabling technologies required for Venus exploration are shared with other targets. Aerobraking/aerocapture would improve Δv and mass budgets for Venus orbiters. Further improvement in deep space communications, including development of Ka-band or optical communications, would provide increased data return from orbiters which would be particularly useful for the large volumes of data generated by high-resolution radar instrumentation at Venus: data rates reaching 100 Mbps or above are needed to return of Earth-like radar observations for a large fraction of the planet. High speed entry modelling, thermal protection systems, and parachute development will all be useful for Venus entry probes. Nuclear power systems are not necessary for the strawman Venus mission elements described here, but would enable longer lifetimes and increased nightside operations for the balloon element of the mission, and will be necessary for long-lived surface stations (in the even more distant future) due to the scarcity of sunlight reaching the Venus surface and long night-time duration.

Two technology areas specific to Venus exploration are balloon technology, and high-temperature (~450 °C) components. The balloons proposed in this strawman mission (based on the EVE M3 proposal) are helium superpressure balloons, which are designed to float at constant altitude. Although ESA has little familiarity with this technique, thousands of helium superpressure balloons have been launched on Earth, and two were successfully deployed on Venus in 1985 as part of the Russian Vega programme, so this is a mature technology. Air-launching of balloons – deploying them from a probe descending under parachute – was achieved by the Russian Vega balloons, was demonstrated by CNES in Vega development programmes, and demonstrated recently by JPL engineers in their own Venus balloon test programme; nevertheless, a new demonstration programme in Europe would be required to obtain recent European experience for this technology. Balloon envelope design and sulphuric acid resistance verification such as those carried at NASA/JPL [ 46 ] would also be valuable to conduct in Europe. Feasibility studies on other forms of aerial mobility, including controllable-altitude balloons, phase change fluid balloons, <5 kg microprobes and fixed wing aircraft, would also be useful for expanding the possibilities of long-term future exploration programmes. Data downlink and location determination present particular challenges for Venus balloons; addressing this with medium- or high-gain electronically steerable phased array antennae would increase the scientific return from these mission elements. A programme of investment in all of these systems, in collaboration with national agencies, would be valuable.

High temperature technologies are needed if Europe is to provide mission elements or payloads which need to operate in the lower atmosphere, below 40 km altitude. For a long-duration surface package, a full suite of subsystems will need to be developed from batteries and power distribution, to data handling, to telecommunications. The development status of these technologies is reviewed elsewhere [ 19 , 20 ].

Further investment in scientific payloads is also needed to prepare for the Voyage 2050 timeframe. Continued development of planetary radar technologies, though applicable to many planetary missions, is particularly important at Venus because Venus’ cloudy atmosphere is opaque to optical imagers. It can be argued that every Venus orbiter should carry a radar imager, just as almost every Mars orbiter has carried an optical imager, to enable follow up of geologically important targets, such as active volcanic and tectonic regions, with ever more capable imagers. Development of more capable and mass efficient radars, with ever increasing spatial and radiometric resolution, and capabilities such as polarimetry and Diffuser, will be invaluable at Venus. Leveraging the investment in Earth observing radar systems for application to Venus will be advantageous. Advanced precursors for heterodyne sub-mm and Doppler LIDAR instrumentation exist in Europe (with JUICE/SWI and MARBLL programmes, respectively, being leading examples); development of Venus versions of these instruments would enable direct measurement of mesospheric winds using Doppler velocimetry.

For atmospheric in situ measurements, a key instrument is a mass spectrometer with getters and cryotraps to isolate and precisely measure the noble gas and light element isotope abundances. These technologies have been developed for Mars (e.g. the SAM instrument on MSL/Curiosity, and the PALOMA instrument originally proposed for ExoMars), but further development to maximise the precision of the measurements and to optimise the development for the thermal environment of Venus balloons and descent probes will be needed. In situ gas chromatography–mass spectrometry characterisation of atmospheric chemistry is another mature field, but further development in particular of an aerosol collector system to allow detailed characterisation of cloud particle composition would be valuable.

Specific payload developments for a landing probe should also include surface characterisation instruments – gamma ray and neutron spectrometers, XRF/XRD, Raman instruments for mineralogical identification. High-temperature drilling and sample ingestion systems are not currently proposed for the Venera-D lander included in the strawman mission, but some feasibility studies in this area would be a useful investment. Finally, chemical, meteorological, and seismological sensors using silicon carbide or other 500 °C temperature semiconductor technology would be key elements of a long-lived lander’s payload.

In summary, most of the technologies needed for the proposed Voyage 2050 Venus mission already have high levels of heritage either from Earth or from other planetary missions, but a well-targeted development programme would de-risk mission elements and maximise the science return. Many of the development areas identified would also benefit other space missions and have spin-out potential on Earth.

6 Conclusions

As we become aware of Earth’s changing climate, and as we discover terrestrial planets in other solar systems, we gain ever more reasons to study the Earth’s nearest neighbour and closest sibling, the only Earth-sized planet besides our own that can be reached by our spacecraft.

For the scientific and programmatic reasons outlined in this document, Venus is a compelling target for exploration. The science themes important for Venus research – comparative planetology and planetary evolution – are common to all of planetary and exoplanetary science. Many of the payloads required – radar and atmospheric remote sensing, in situ mass spectrometers – are common to mission proposals for many other Solar System targets, as are mission technologies like high rate deep-space telecommunications technologies. Venus-specific technology developments meriting special attention include high-temperature systems and balloons.

Venus is an excellent proving ground for fundamental understanding of geophysical processes of terrestrial planets; an excellent proving ground for techniques of analysis of exoplanets; an indispensable part of our quest to understand the evolution of Earth-like planets. For all these reasons, Venus will be an ever more compelling theme in the coming decades, and we therefore emphatically recommend its inclusion in the Voyage 2050 plan. We suggest that ESA aim to have launched at least two M-class Venus missions by 2050, including the EnVision M5 geophysics orbiter and an in-situ element such as a cloud-level balloon; or an L-class mission combining these elements.

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Acknowledgments

This manuscript reflects two decades of inputs from the European planetary science community and colleagues across the world, coalescing around ESA’s Venus Express mission, ESA’s Venus Entry Probe mission study, the European Venus Explorer mission proposals of 2007 and 2010 (led by Eric Chassefière), the EnVision orbiter proposals (led by Richard Ghail), and the Venus Long-life Surface Platform White Paper of 2016. The authors acknowledge the scientific contributions of all the team members of these projects, the engineering contributions of the respective study teams including industrial partners, and the financial support of ESA and national space agencies which have enabled these studies. We thank Juliet Biggs for permission to reprint Fig. 2 and Kevin Baines for permission to reprint Fig. 3 . C.W. acknowledges funding from the UK Space Agency under grants ST/V001590/1 and ST/P001572/1. R.G. acknowledges funding from the UK Space Agency under grant ST/V00168X/1.

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Wilson, C.F., Widemann, T. & Ghail, R. Venus: key to understanding the evolution of terrestrial planets. Exp Astron 54 , 575–595 (2022). https://doi.org/10.1007/s10686-021-09766-0

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REVIEW article

The planetary theory of solar activity variability: a review.

• 1 Department of Earth Sciences, Environment and Georesources, Complesso Universitario di Monte S. Angelo, University of Naples Federico II, Naples, Italy
• 2 INAF, Astronomical Observatory of Padua, Padua, Italy

Commenting the 11-year sunspot cycle, Wolf (1859, MNRAS 19, 85–86) conjectured that “ the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn .” The high synchronization of our planetary system is already nicely revealed by the fact that the ratios of the planetary orbital radii are closely related to each other through a scaling-mirror symmetry equation (Bank and Scafetta, Front. Astron. Space Sci. 8, 758184, 2022). Reviewing the many planetary harmonics and the orbital invariant inequalities that characterize the planetary motions of the solar system from the monthly to the millennial time scales, we show that they are not randomly distributed but clearly tend to cluster around some specific values that also match those of the main solar activity cycles. In some cases, planetary models have even been able to predict the time-phase of the solar oscillations including the Schwabe 11-year sunspot cycle. We also stress that solar models based on the hypothesis that solar activity is regulated by its internal dynamics alone have never been able to reproduce the variety of the observed cycles. Although planetary tidal forces are weak, we review a number of mechanisms that could explain how the solar structure and the solar dynamo could get tuned to the planetary motions. In particular, we discuss how the effects of the weak tidal forces could be significantly amplified in the solar core by an induced increase in the H-burning. Mechanisms modulating the electromagnetic and gravitational large-scale structure of the planetary system are also discussed.

1 Introduction

Since antiquity, the movements of the planets of the solar system have attracted the attention of astronomers and philosophers such as Pythagoras and Kepler because the orbital periods appeared to be related to each other by simple harmonic proportions, resonances, and/or commensurabilities ( ter Haar, 1948 ; Stephenson, 1974 ). Such a philosophical concept is known as the “ Music of the Spheres ” or the “ Harmony of the Worlds ” ( Godwin, 1992 ; Scafetta, 2014a ). This property is rather common for many orbital systems ( Moons and Morbidelli, 1995 ; Scafetta, 2014a ; Aschwanden, 2018 ; Agol et al., 2021 ). Bank and Scafetta (2022) improved the Geddes and King-Hele equations describing the mirror symmetries among the orbital radii of the planets ( Geddes and King-Hele, 1983 ) and discovered their ratios obey the following scaling-mirror symmetry relation

where a planet are the semi-major axes of the orbits of the relative planets: Eris (Er), Pluto (Pl), Neptune (Ne), Uranus (Ur), Saturn (Sa), Jupiter (Ju), Mars (Ma), Earth (Ea), Venus (Ve), Mercury (Me), Vulcanoid asteroid belt (Vu), and the scattered zone surrounding the Sun (Sz). The ratio 9/8 is, musically speaking, a whole tone known as the Pythagorean epogdoon . The deviations of Eq. 1 from the actual orbital planetary ratios are within 1%.

Another intriguing aspect regarding the synchronization of the solar system is the fact that many planetary harmonics are found spectrally coherent with the solar activity cycles (e.g.: Scafetta, 2012a , 2020 , and many others). The precise physical origin of solar cycles is still poorly known and dynamo models are debated, but recent literature has strengthened the hypothesis of a correlation with planetary harmonics. Actually, a few years after the discovery of the 11-year sunspot cycle, Wolf (1859) himself conjectured that “ the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn .” Dicke (1978) noted that the sunspot cycle shows no statistical indication of being randomly generated but rather of being synchronized by a chronometer hidden deep in the Sun. Solar activity is characterized by several cycles like the Schwabe 11-year sunspot cycle ( Schwabe, 1843 ), the Hale solar magnetic 22-year cycle ( Hale, 1908 ), the Gleissberg cycle (∼85 years), the Jose cycle (∼178 years), the Suess-de Vries cycle (∼208 years), the Eddy cycle (∼1000 years), and the Bray-Hallstatt cycle (∼2300 years) ( McCracken et al., 2001 , 2013 ; Abreu et al., 2012 ; Scafetta, 2016 ). Shorter cycles are easily detected in total solar irradiance (TSI) and sunspot records, while the longer ones are detected in long-term geophysical records like the cosmogenic radionuclide ones ( 14 C and 10 Be) and in climate records ( Neff et al., 2001 ; Steinhilber et al., 2009 ). Planetary cycles have also been found in aurora records ( Scafetta, 2012c ; Scafetta and Willson, 2013a ).

Due to the evident high synchronization of planetary motions, it is worthwhile investigating the possibility that orbital frequencies could tune solar variability as well. However, although Jupiter appears to play the main role in organizing the solar system ( Bank and Scafetta, 2022 ), its orbital period (∼11.86 years) is too long to fit the Schwabe 11-year solar cycle. Thus, any possible planetary mechanism able to create this solar modulation must involve a combination of more planets. We will see that the only frequencies that could be involved in the process are the orbital periods, the synodical periods, and their beats and harmonics.

In the following sections, we review the planetary theory of solar variability and show how it is today supported by many empirical and theoretical evidences at multiple timescales. We show that appropriate planetary harmonic models correlate with the 11-year solar cycle, the secular and millennial cycles, as well as with several other major oscillations observed in solar activity, and even with the occasional occurrences of solar flares. The physics behind these results is not yet fully understood, but a number of working hypotheses will be herein briefly discussed.

2 The Solar Dynamo and Its Open Issues

The hypothesis we wish to investigate is whether the solar activity could be synchronized by harmonic planetary forcings. In principle, this could be possible because the solar structure itself is an oscillator. The solar cyclical magnetic activity can be explained as the result of a dynamo operating in the convective envelope or at the interface with the inner radiative region, where the rotational energy is converted into magnetic energy. Under certain conditions, in particular if the internal noise is sufficiently weak relative to the external forcing, an oscillating system could synchronize with a weak external periodic force, as first noted by Huygens in the 17th century ( Pikovsky et al., 2001 ).

A comprehensive review of solar dynamo models is provided by Charbonneau (2020) . In the most common α -Ω models, the magnetic field is generated by the combined effect of differential rotation and cyclonic convection. The mechanism starts with an initially poloidal magnetic field that is azimuthally stretched by the differential rotation of the convective envelope, especially at the bottom of the convective region (tachocline) where the angular velocity gradient is most steep. The continuous winding of the poloidal field lines (Ω mechanism) produces a magnetic toroidal field that accumulates in the boundary overshooting region. When the toroidal magnetic field and its magnetic pressure get strong enough, the toroidal flux ropes become buoyantly unstable and start rising through the convective envelope where they undergo helical twisting by the Coriolis forces ( α mechanism) ( Parker, 1955 ). When the twisted field lines emerge at the photosphere, they appear as bipolar magnetic regions (BMRs) that roughly coincide with the large sunspot pairs, also characterized by a dipole moment that is systematically tilted with respect to the E–W direction of the toroidal field. The turbulent decay of BMRs finally releases a N-S oriented fraction of the dipole moment that allows the formation of a global dipole field, characterized by a polarity reversal as required by the observations (Babcock–Leighton mechanism).

However, magneto-hydrodynamic simulations suggest that purely interface dynamos cannot be easily calibrated to solar observations, while flux-transport dynamos (based on the meridional circulation) are able to better simulate the 11-year solar cycle when the model parameters are calibrated to minimize the difference between observed and simulated time–latitude BMR patterns ( Dikpati and Gilman, 2007 ; Charbonneau, 2020 ). Cole and Bushby (2014) showed that by changing the parameters of the MHD α -Ω dynamo models it is possible to obtain transitions from periodic to chaotic states via multiple periodic solutions. Macario-Rojas et al. (2018) obtained a reference Schwabe cycle of 10.87 years, which was also empirically found by Scafetta (2012a) by analyzing the sunspot record. This oscillation will be discussed later in the Jupiter-Saturn model of Sections 4.2 and 6.

Full MHD dynamo models are not yet available and several crucial questions are still open such as the stochastic and nonlinear nature of the dynamo, the formation of flux ropes and sunspots, the regeneration of the poloidal field, the modulation of the amplitude and period of the solar cycles, how less massive fully convective stars with no tachocline may still show the same relationship between the rotation and magnetic activity, the role of meridional circulation, the origin of Maunder-type Grand Minima, the presence of very low-frequency Rieger-type periodicities probably connected with the presence of magneto-Rossby waves in the solar dynamo layer below the convection zone, and other issues ( Zaqarashvili et al., 2010 , 2021 ; Gurgenashvili et al., 2022 ).

3 The Solar Wobbling and Its Harmonic Organization

The complex dynamics of the planetary system can be described by a general harmonic model. Any general function of the orbits of the planets – such as their barycentric distance, speed, angular momentum, etc . – must share a common set of frequencies with those of the solar motion (e.g.: Jose, 1965 ; Bucha et al., 1985 ; Cionco and Pavlov, 2018 ; Scafetta, 2010 ). Instead, the amplitudes and phases associated with each constituent harmonic depend on the specific chosen function.

Figures 1A,B shows the positions and the velocities of the wobbling Sun with respect to the barycenter of the planetary system from BC 8002, to AD 9001 (100-day steps) calculated using the JPL’s HORIZONS Ephemeris system ( Scafetta, 2010 ; 2014a ).

FIGURE 1 . (A) The motion the wobbling Sun from 1944 to 2020 (B) The distance and the speed of the Sun relative to the barycenter of the solar system from 1800 to 2020. (C) Periodogram (red) and the maximum entropy method spectrum (blue) of the speed of the Sun from BC 8002-Dec-12, to AD 9001-Apr-24. (D) Comparison between the frequencies observed in (C) in the range 3–200 years (red) and the frequencies predicted by the harmonic model of Eq. 3 (blue). (cf. Scafetta, 2014a ).

We can analyze the main orbital frequencies of the planetary system by performing, for example, the harmonic analysis of the solar velocity alone. Its periodograms were obtained with the Fourier analysis (red) and the maximum entropy method (blue) ( Press et al., 1997 ) and are shown in Figure 1C .

Several spectral peaks can be recognized: the ∼1.092 year period of the Earth-Jupiter conjunctions; the ∼9.93 and ∼19.86 year periods of the Jupiter-Saturn spring (half synodic) and synodic cycles, respectively; the ∼11.86, ∼29.5, ∼84 and ∼165 years of the orbital periods of Jupiter, Saturn, Uranus and Neptune, respectively; the ∼60 year cycle of the Trigon of Great Conjunctions between Jupiter and Saturn; the periods corresponding to the synodic cycles between Jupiter and Neptune (∼12.8 year), Jupiter and Uranus (∼13.8 year), Saturn and Neptune (∼35.8 year), Saturn and Uranus (∼45.3) and Uranus and Neptune (∼171.4 year), as well as their spring periods.

The synodic period is defined as

where P 1 and P 2 are the orbital periods of two planets. Additional spectral peaks at ∼200–220, ∼571, ∼928 and ∼4200 years are also observed. The spring period is the half of P 12 . The observed orbital periods are listed in Table 1 .

TABLE 1 . Sidereal orbital periods of the planets of the solar system.

Some of the prominent frequencies in the power spectra appear clustered around well-known solar cycles such as in the ranges 42–48 years, 54–70 years, 82–100 years (Gleissberg cycle), 155–185 (Jose cycle), and 190–240 years (Suess-de Vries cycle) (e.g.: Ogurtsov et al., 2002 ; Scafetta and Willson, 2013a ). The sub-annual planetary harmonics and their spectral coherence with satellite total solar irradiance records will be discussed in Section 5.

The important result is that the several spectral peaks observed in the solar motion are not randomly distributed but are approximately reproduced using the following simple empirical harmonic formula

where 178 years corresponds to the period that Jose (1965) found both in the solar orbital motion and in the sunspot records (cf.: Jakubcová and Pick, 1986 ; Charvátová and Hejda, 2014 ). A comparison between the observed frequencies and those predicted by the harmonic model of Eq. 3 is shown in Figure 1D , where a strong coincidence is observed. Equation 3 suggests that the solar planetary system is highly self-organized and synchronized.

4 The Schwabe 11-year Solar Cycle

Wolf (1859) himself proposed that the ∼11-year sunspot cycle could be produced by the combined orbital motions of Venus, Earth, Jupiter and Saturn. In the following, we discuss two possible and complementary solar-planetary models made with the orbital periods of these four planets.

4.1 The Venus-Earth-Jupiter Model

The first model relates the 11-year solar cycle with the relative orbital configurations of Venus, Earth and Jupiter, which was first proposed by Bendandi (1931) as recently reminded by Battistini (2011) . Later, Bollinger (1952) , Hung (2007) and others (e.g.: Scafetta, 2012c ; Tattersall, 2013 ; Wilson, 2013 ; Stefani et al., 2016 , 2019 , 2021 ) developed more evolved models.

This model is justified by the consideration that Venus, Earth and Jupiter are the three major tidal planets ( Scafetta, 2012b ). Their alignments repeat every:

where P V = 224.701 days, P E = 365.256 days and P J = 4332.589 days are the sidereal orbital periods of Venus, Earth and Jupiter, respectively.

The calculated 22.14-year period is very close to the ∼22-year Hale solar magnetic cycle. Since the Earth–Venus–Sun–Jupiter and Sun–Venus–Earth–Jupiter configurations present equivalent tidal potentials, the tidal cycle would have a recurrence of 11.07 years. This period is very close to the average solar cycle length observed since 1750 ( Hung, 2007 ; Scafetta, 2012a ; Stefani et al., 2016 ).

Vos et al. (2004) found evidence for a stable Schwabe cycle with a dominant 11.04-year period over a 10,000-year interval which is very close to the above 11.07 periodicity, as suggested by Stefani et al. (2020a) . However, the Jupiter-Saturn model also reproduces a similar Schwabe cycle ( see Sections 4.2 and 6).

Equation 4 is an example of “orbital invariant inequality” ( Scafetta et al., 2016 ; Scafetta, 2020 ). Section 7 explains their mathematical property of being simultaneously and coherently seen by any region of a differentially rotating system like the Sun. This property should favor the synchronization of the internal solar dynamics with external forces varying with those specific frequencies.

Equation 4 can be rewritten in a vectorial formalism as

Each vector can be interpreted a frequency where the order of its components correspond to the arbitrary assumed order of the planets, in this case: (Venus, Earth, Jupiter). Thus, (3, −5, 2) ≡ 3/ P V − 5/ P E + 2/ P J , 3(1, −1, 0) ≡ 3(1/ P V − 1/ P E ) and −2(0, 1, −1) ≡ −2(1/ P E − 1/ P J ).

We observe that (1, −1, 0) indicates the frequency of the synodic cycle between Venus and Earth and (0, 1, −1) indicates the frequency of the synodic cycle between Earth and Jupiter ( Eq. 2 ). Thus, the vector (3, −5, 2) indicates the frequency of the beat created by the third harmonic of the synodic cycle between Venus and Earth and the second harmonic of the synodic cycle between Earth and Jupiter.

Equation 5 also means that the Schwabe sunspot cycle can be simulated by the function:

where t VE = 2002.8327 is the epoch of a Venus-Earth conjunction whose period is P VE = 1.59867 years; and t EJ = 2003.0887 is the epoch of an Earth-Jupiter conjunction whose period is P EJ = 1.09207 years. The 11.07-year beat is obtained by doubling the synodic frequencies given in Eq. 5 .

Figure 2A shows that the three-planet model of Eq. 6 (red) generates a beat pattern of 11.07 years reasonably in phase with the sunspot cycle (blue). More precisely, the maxima of the solar cycles tend to occur when the perturbing forcing produced by the beat is stronger, that is when the spring tides of the planets can interfere constructively somewhere in the solar structure.

FIGURE 2 . (A) The plot of Eq. 6 (red) versus the sunspot numberthe planets can interfere record (blue). ( B , Top) The sunspot number record (black) versus the alignment index I VEJ > 66%. ( B , Bottom) The sunspot number record (black) against the number of days of most alignment ( I VEJ > 95%) (red). (C , D) Power spectra of the Schwabe sunspot cycle using the Maximum Entropy Method (MEM) and the periodogram (MTM) (Press et al., 1997). (Data from: https://www.sidc.be/silso/datafiles ).

Hung (2007) and Scafetta (2012a) developed the three-planet model by introducing a three-planetary alignment index. In the case of two planets, the alignment index I ij between planet i and planet j is defined as:

where Θ ij is the angle between the positions of the two planets relative to the solar center.

Equation 7 indicates that when the two planets are aligned (Θ ij = 0 or Θ ij = π ), the alignment index has the largest value because these two positions imply a spring-tide configuration. Instead, when Θ ij = π /2, the index has the lowest value because at right angles–corresponding to a neap-tide configuration–the tides of the two planets tend to cancel each other.

In the case of the Venus-Earth-Jupiter system, there are three correspondent alignment indexes:

Then, the combined alignment index I VEJ for the three planets could be defined as:

which ranges between 0 and 2.

Figure 2B shows (in red) that the number of the most aligned days of Venus, Earth and Jupiter–estimated by Eq. 11 – presents an 11.07-year cycle. These cycles are well correlated, both in phase and frequency, with the ∼11-year sunspot cycle. Scafetta (2012a) also showed that an 11.08-year recurrence exists also in the amplitude and direction (latitude and longitude components) of the solar jerk-shock vector, which is the time-derivative of the acceleration vector. For additional details see Hung (2007) , Scafetta (2012a) , Salvador (2013) , Wilson (2013) and Tattersall (2013) .

A limitation of the Venus-Earth-Jupiter model is that it cannot explain the secular variability of the sunspot cycle which alternates prolonged low and high activity periods such as, for example, the Maunder grand solar minimum between 1645 and 1715, when very few sunspots were observed (cf. Smythe and Eddy, 1977 ). However, this problem could be solved by the Jupiter-Saturn model ( Scafetta, 2012a ) discussed below and, in general, by taking into account also the other planets ( Scafetta, 2020 ; Stefani et al., 2021 ), as discussed in Sections 6 and 7.

The 11.07-year cycle has also been extensively studied by Stefani et al. (2016) ; Stefani et al. (2018) ; Stefani et al. (2019 , 2020b , 2021) where it is claimed to be the fundamental periodicity synchronizing the solar dynamo.

4.2 The Jupiter-Saturn Model

The second model assumes that the Schwabe sunspot cycle is generated by the combined effects of the planetary motions of Jupiter and Saturn. The two planets generate two main tidal oscillations associated with the orbit of Jupiter (11.86-year period) – which is characterized by a relatively large eccentricity ( e = 0.049) – and the spring tidal oscillation generated by Jupiter and Saturn (9.93-year period) ( Brown, 1900 ; Scafetta, 2012c ). In this case, the Schwabe sunspot cycle could emerge from the synchronization of the two tides with periods of 9.93 and 11.86 years, whose average is about 11 years.

The Jupiter-Saturn model is supported by a large number of evidences. For example, Scafetta (2012a , b) showed that the sunspot cycle length, i.e. the time between two consecutive sunspot minima, is bi-modally distributed, being always characterized by two peaks at periods smaller and larger than 11 years. This suggests that there are two dynamical attractors at the periods of about 10 and 12 years forcing the sunspot cycle length to fall either between 10 and 11 years or between 11 and 12 years. Sunspot cycles with a length very close to 11 years are actually absent. In addition, Figures 2C,D show the periodograms of the monthly sunspot record since 1749. The spectral analysis of this long record reveals the presence of a broad major peak at about 10.87 years obtained by some solar dynamo models ( Macario-Rojas et al., 2018 ) which is surrounded by two minor peaks at 9.93 and 11.86 years that exactly correspond with the two main tides of the Jupiter-Saturn system.

In Section 6 we will show that the combination of these three harmonics produces a multidecadal, secular and millennial variability that is rather well correlated with the long time-scale solar variability.

5 Solar Cycles Shorter Than the Schwabe 11-year Solar Cycle

On small time scales, Bigg (1967) found an influence of Mercury on sunspots. Indeed, in addition to Jupiter, Mercury can also induce relatively large tidal cycles on the Sun because its orbit has a large eccentricity ( e = 0.206) ( Scafetta et al. 2019a ).

Rapid oscillations in the solar activity can be optimally studied using the satellite total solar irradiance (TSI) records. Since 1978, TSI data and their composites have been obtained by three main independent science teams: ACRIMSAT/ACRIM3 ( Willson and Mordvinov, 2003 ), SOHO/VIRGO ( Fröhlich, 2006 ) and SORCE/TIM ( Kopp and Lawrence, 2005a ; Kopp et al., 2005b ). Figure 3 compares the ACRIM3, VIRGO and TIM TSI from 2000 to 2014; the average irradiance is about 1361  W / m 2 .

FIGURE 3 . (A) Comparison of ACRIMSAT/ACRIM3 (black), SOHO/VIRGO (blue) and SORCE/TIM (red) TSI records versus daily sunspot number (gray). (B) Power spectrum comparison of ACRIMSAT/ACRIM3 (black), SOHO/VIRGO (blue) and SORCE/TIM (red) TSI from 2003.15 to 2011.00. The arrows at the bottom depicts the periods reported in Table 2 . ( C , Top) Periodogram of ACRIM results in W 2 / m 4 from 1992.5–2012. ( C , Bottom) Power spectra of ACRIM from 1992.5 to 2012.9) and of PMOD from 1997.75 to 2004.25. The yellow bars schematically indicate the harmonics generated by the planets as reported in Tables 2 – 4 . (D) ACRIM and PMOD TSI composites during solar maximum 23 (1998–2004). The black curve is from Eqs 7 , 8 . (E) High-pass filter of the PMOD (blue) and ACRIM (black) TSI compared against a 1.092-year harmonic Jupiter function (red). (F) ACRIM and PMOD TSI since 1978 (red) against the models of Eqs 13 , 14 . (G,H) Planetary tidal function on the Sun (blue) (see Figure 8C ) and its power spectrum (red). (I, J) Speed of the Sun relative to the solar system barycenter (blue) and its power spectrum (red). (cf. Scafetta and Willson, 2013b , c ).

5.1 The 22–40 days Time-Scale

Figure 3B shows the power spectra in the 22–40 days range of the three TSI records ( Figure 3A ) from 2003.15 to 2011.00 ( Scafetta and Willson, 2013c ). A strong spectral peak is observed at ∼27.3 days (0.075 years) ( Willson and Mordvinov, 1999 ), which corresponds to the synodic period between the Carrington solar rotation period of ∼25.38 days and the Earth’s orbital period of ∼365.25 days. The Carrington period refers to the rotation of the Sun at 26° of latitude, where most sunspots form and the solar magnetic activity emerges ( Bartels, 1934 ). The observed 27.3-day period differs from the Carrington 25.38-day period because the Sun is seen from the orbiting Earth. Thus, the 27.3-day period derives from Eq. 2 using T 1 = 25.38 days and T 2 = 365.25 days.

Figure 3B reveals additional spectral peaks at ∼ 24.8 days ( ∼ 0.068 years), ∼ 34 -35 days ( ∼ 0.093 -0.096 years), and ∼ 36 -38 days ( ∼ 0.099 -0.104 years). They fall within the range of the solar differential rotation that varies from 24.7–25.4 days near the equator ( Kotov, 2020 ) to about 38 days near the poles ( Beck, 2000 ).

However, the same periods appear to be also associated with the motion of the planets. In fact, the ∼ 24.8 -day cycle corresponds to the synodic period between the sidereal orbital period of Jupiter ( ∼ 4332.6 days) and the sidereal equatorial rotation period of the Sun ( ∼ 24.7 days) calculated using Eq. 2 . Additional synodic cycles between the rotating solar equator and the orbital motion of the terrestrial planets are calculated at ∼ 26.5 days, relative to the Earth, ∼ 27.75 days, relative to Venus, and ∼ 34.3 days, relative to Mercury ( see Table 2 ). We also notice that the major TSI spectral peak at 34.7 days is very close to the ∼ 34.3 -day Mercury-Sun synodic period, although it would require the slightly different solar rotation period of 24.89 days.

TABLE 2 . Solar equatorial (equ) and Carrington (Car) rotation cycles relative to the fixed stars and to the four major tidally active planets calculated using Eq. 2 where P 1 = 24.7 days is the sidereal equatorial solar rotation and P 2 the orbital period of a planet. Last column: color of the arrows in Figure 3B (cf. Scafetta and Willson, 2013c ).

5.2 The 0.1–1.1 year Time-Scale

Tables 3 , 4 collect the orbital periods, the synodic cycles and their harmonics among the terrestrial planets (Mercury, Venus, Earth and Mars). The tables also show the synodic cycles between the terrestrial and the Jovian planets (Jupiter, Saturn, Uranus, and Neptune). The calculated periods are numerous and clustered. If solar activity is modulated by planetary motions, these frequency clusters should be observed also in the TSI records.

TABLE 3 . Major theoretical planetary harmonics with period p < 1.6 years.

TABLE 4 . Additional expected harmonics associated with planetary orbits.

Figure 3C shows two alternative power spectra of the ACRIM and PMOD TSI records superposed to the distribution (yellow) of the planetary frequencies reported in Tables 2 – 4 . The main power spectral peaks are observed at: ∼ 0.070 , ∼ 0.097 , ∼ 0.20 , ∼ 0.25 , 0.30–0.34, ∼ 0.39 , ∼ 0.55 , 0.60–0.65, 0.7–0.9, and 1.0–1.2 years.

Figure 3C shows that all the main spectral peaks observed in the TSI records appear compatible with the clusters of the calculated orbital harmonics. For example: the Mercury-Venus spring-tidal cycle (0.20 years); the Mercury orbital cycle (0.24 years); the Venus-Jupiter spring-tidal cycle (0.32 years); the Venus-Mercury synodic cycle (0.40 years); the Venus-Jupiter synodic cycle (0.65 years); and the Venus-Earth spring tidal cycle (0.80 years). A 0.5-year cycle is also observed, which could be due to the Earth crossing the solar equatorial plane twice a year and to a latitudinal dependency of the solar luminosity. These results are also confirmed by the power spectra of the planetary tidal function on the Sun (see Figure 8C ) and of the speed of the Sun relative to the solar system barycenter ( Figures 3G-J ).

The 1.0–1.2 year band observed in the TSI records correlates well with the 1.092-year Earth-Jupiter synodic cycle. Actually, the TSI records present maxima in the proximity of the Earth-Jupiter conjunction epochs ( Scafetta and Willson, 2013b ).

Figure 3D shows the ACRIM and PMOD TSI records (red curves) plotted against the Earth-Jupiter conjunction cycles with the period of 1.092 years (black curve) from 1998 to 2004. TSI peaks are observed around the times of the conjunctions. The largest peak occurs at the beginning of 2002 when the conjunction occurred at a minimum of the angular separation between Earth and Jupiter (0°13’ 19”).

Figure 3E shows the PMOD (blue) and ACRIM (black) records band-pass filtered to highlight the 1.0–1.2 year modulation. The two curves (blue and black) are compared to the 1.092-year harmonic function (red):

where the amplitude g ( t ) was modulated according to the observed Schwabe solar cycle. The time-phase of the oscillation is chosen at t EJ = 2002 because one of the Earth-Jupiter conjunctions occurred on the 1 st of January 2002. The average Earth-Jupiter synodic period is 1.09208 years. The TSI 1.0–1.2 year oscillation is significantly attenuated during solar minima (1995–1997 and 2007–2009) and increases during solar maxima. In particular, the figure shows the maximum of solar cycle 23 and part of the maxima of cycles 22 and 24 and confirms that the TSI modulation is well correlated with the 1.092-year Earth-Jupiter conjunction cycle.

Figure 3F extends the model prediction back to 1978. Here the TSI records are empirically compared against the following equations: for ACRIM,

The blue curves are the 2-year moving averages, S A ( t ) and S P ( t ), of the ACRIM and PMOD TSI composite records, respectively. The data-model comparison confirms that the 1.092-year Earth-Jupiter conjunction cycle is present since 1978. In fact, TSI peaks are also found in coincidences with a number of Earth-Jupiter conjunction epochs like those of 1979, 1981, 1984, 1990, 1991, 1992, 1993, 1994, 1995, 1998, 2011 and 2012. The 1979 and 1990 peaks are less evident in the PMOD TSI record, likely because of the significant modifications of the published Nimbus7/ERB TSI record in 1979 and 1989–1990 proposed by the PMOD science team ( Fröhlich, 2006 ; Scafetta, 2009 ; Scafetta et al., 2011 ).

The result suggests that the side of the Sun facing Jupiter could be slightly brighter, in particular during solar maxima. Thus, when the Earth crosses the Sun-Jupiter line, it could receive an enhanced amount of radiation. This coalesces with strong hotspots observed on other stars with orbiting close giant planets ( Shkolnik et al., 2003 , 2005 ). Moreover, Kotov and Haneychuk (2020) analyzed 45 years of observations and showed that the solar photosphere, as seen from the Earth, is pulsating with two fast and relatively stable periods P 0 = 9600.606(12) s and P 1 = 9597.924(13) s. Their beatings occur with a period of 397.7(2.6) days, which coincides well with the synodic period between Earth and Jupiter (398.9 days). A hypothesis was advanced that the gravity field of Jupiter could be involved in the process.

5.3 The Solar Cycles in the 2–9 years Range

The power spectrum in Figure 2D shows peaks at 5-6 and 8.0–8.5 years. The former ones appear to be harmonics of the Schwabe 11-year solar cycle discussed in Section 3. The latter peaks are more difficult to be identified. In any case, some planetary harmonics involving Mercury, Venus, Earth, Jupiter and Saturn could explain them.

For example, the Mercury-Venus orbital combination repeats almost every 11.08 years, which is similar to the 11.07-year invariant inequality between Venus, Earth and Jupiter discussed in Section 3. In fact, P M = 0.241 years and P V = 0.615 years, therefore their closest geometrical recurrences occur after 23 orbits of Mercury (23 P M = 5.542 years) and nine orbits of Venus (9 P V = 5.535 year). Moreover, we have 46 P M = 11.086 years and 18 P V = 11.07 years. Thus, the orbital configuration of Mercury and Venus repeats every 5.54 years as well as every 11.08 years and might contribute to explain the 5–6 years spectral peak observed in Figure 2D . Moreover, eight orbits of the Earth (8 P E = 8 years) and 13 orbits of Venus (13 P V = 7.995 years) nearly coincide and this combination might have contributed to produce the spectral peak at about 8 years.

There is also the possibility that the harmonics at about 5.5 and 8–9 years could emerge from the orbital combinations of Venus, Earth, Jupiter and Saturn. In fact, we have the following orbital invariant inequalities

where the orbital periods of the four planets are given in Table 1 . Equation 15 combines the spring cycle between Venus and Jupiter with the third harmonic of the synodic cycle between Earth and Saturn. Equation 16 is the first inferior harmonic (because of the factor 2) of a combination of the synodic cycle between Venus and Saturn and the spring cycle between Earth and Jupiter. Eqs 15 , 16 express orbital invariant inequalities, whose general physical properties are discussed in Section 7.

The above results, together with those discussed in Section 4, once again suggest that the major features of solar variability at the decadal scale from 2 to 22 years could have been mostly determined by the combined effect of Venus, Earth, Jupiter and Saturn, as it was first speculated by Wolf (1859) .

6 The Multi-Decadal and Millennial Solar Cycles Predicted by the Jupiter-Saturn Model

As discussed in Section 4.1, the Jupiter-Saturn model interprets quite well two of the three main periods that characterize the sunspot number record since 1749: P S 1 = 9.93, P S 2 = 10.87 and P S 3 = 11.86 years ( Figure 2C ) ( Scafetta, 2012a ). The two side frequencies match the spring tidal period of Jupiter and Saturn (9.93 years), and the tidal sidereal period of Jupiter (11.86 years). The central peak at P S 2 = 10.87 years can be associated with a possible natural dynamo frequency that is also predicted by a flux-transport dynamo model ( Macario-Rojas et al., 2018 ). However, the same periodicity could be also interpreted as twice the invariant inequality period of Eq. 15 , which gives 10.86 years. According to the latter interpretation, the central frequency sunspot peak might derive from a dynamo synchronized by a combination of the orbital motions of Venus, Earth, Jupiter and Saturn.

The three harmonics of the Schwabe frequency band beat at P S13 = 60.95 years, P S12 = 114.78 years and P S23 = 129.95 years. Using the same vectorial formalism introduced in Section 3.1 to indicate combinations of synodical cycles, a millennial cycle, P S123 , is generated by the beat between P S12 ≡ (1, −1, 0) and P S23 ≡ (0, 1, −1) according to equation (1, −1, 0) − (0, 1, −1) = (1, −2, 1) that corresponds to the period

where we adopted the multi-digits accurate values P S 1 = 9.929656 years, P S 2 = 10.87 years and P S 3 = 11.862242 years ( Table 1 ). However, the millennial beat is very sensitive to the choice of P S 2 .

To test whether this three-frequency model actually fits solar data, Scafetta (2012a) constructed its constituent harmonic functions by setting their relative amplitudes proportional to the power of the spectral peaks of the sunspot periodogram. The three amplitudes, normalized with respect to A S 2 , are: A S 1 = 0.83, A S 2 = 1, A S 3 = 0.55.

The time-phases of the two side harmonics are referred to: t S 1 = 2000.475, which is the synodic conjunction epoch of Jupiter and Saturn (23/June/2000) relative to the Sun, when the spring tide must be stronger; and t S 3 = 1999.381, which is the perihelion date of Jupiter (20/May/1999) when its tide is stronger. The time-phase of the central harmonic was set to t S 2 = 2002.364 and was estimated by fitting the sunspot number record with the three-harmonic model keeping the other parameters fixed.

The time-phases of the beat functions are calculated using the equation

It was found t S12 = 2095.311, t S13 = 2067.044 and t S23 = 2035.043. The time-phase of the beat between P S12 and P S23 was calculated as t S123 = 2059.686. Herein, we ignore that the phases for the conjunction of Jupiter and Saturn vary by a few months from the average because the orbits are elliptic, which could imply a variation up to a few years of the time-phases of the beat functions.

The proposed three-frequency harmonic model is then given by the function

The components and the beat functions generated by the model are given by the equations

Thus, the final model becomes

To emphasize its beats we can also write

The resulting envelope functions of the beats are

Figure 4 shows the three-frequency solar model of Eq. 24 (red). Figure 4A compares it against two reconstructions of the solar activity based on 10 Be and 14 C cosmogenic isotopes (blue and black, respectively) ( Bard et al., 2000 ; Steinhilber et al., 2009 ). The millennial beat cycle is represented by the green curve. The model correctly hindcast all solar multi-decadal grand minima observed during the last 1000 years, known as the Oort, Wolf, Spörer, Maunder and Dalton grand solar minima. They approximately occurred when the three harmonics interfered destructively. Instead, the multi-decadal grand maxima occurred when the three harmonics interfere constructively generating a larger perturbation on the Sun.

FIGURE 4 . (A) Eq. 40 (red) against two reconstructions of solar activity based on 10 Be and 14 C cosmogenic isotopes ( Bard et al., 2000 ; Steinhilber et al., 2009 ). (B) . Equation 40 (red) against a Northern Hemisphere proxy temperature reconstruction by Ljungqvist (2010) . (C) The millennial oscillation predicted by the three-frequency non-linear solar model (blue) versus the TSI proxy model by Steinhilber et al. (2009) (red). (cf. Scafetta, 2012a ; 2014b ).

Figure 4B compares Eq. 24 against the Northern Hemisphere proxy temperature reconstruction of Ljungqvist (2010) (black). We notice the good time-matching between the oscillations of the model and the temperature record of both the millennial and the 115-year modulations, which is better highlighted by the smoothed filtered curves at the bottom of the figure. The Roman Warm Period (RWP), Dark Age Cold Period (DACP), Medieval Warm Period (MWP), Little Ice Age (LIA) and the Current Warm Period (CWP) are well hindcast by the three-frequency Jupiter-Saturn model.

Figure 4C shows the millennial oscillation (blue) predicted by Eq. 24 given by

The curve is well correlated with the quasi millennial solar oscillation–known as the Eddy oscillation–throughout the Holocene as revealed by the 14 C cosmogenic isotope record (red) and other geological records ( Kerr, 2001 ; Steinhilber et al., 2009 ; Scafetta, 2012a , 2014b ).

Scafetta (2012a) discussed other properties of the three-frequency solar model. For example, five 59–63 year cycles appear in the period 1850–2150, which are also well correlated with the global surface temperature maxima around about 1880, 1940 and 2000. The model also predicts a grand solar minimum around the 2030s constrained between two grand solar maxima around 2000 and 2060. The modeled solar minimum around 1970, the maximum around 2000 and the following solar activity decrease, which is predicted to last until the 2030s, are compatible with the multidecadal trends of the ACRIM TSI record ( Willson and Mordvinov, 2003 ), but not with those shown by the PMOD one ( Fröhlich, 2006 ) that uses TSI modified data ( Scafetta et al., 2019b ) and has a continuous TSI decrease since 1980. The plots of ACRIM and PMOD TSI data are shown in Figure 3F and have been extensively commented by Scafetta et al. (2019b) . Finally, the model also reproduces a rather long Schwabe solar cycle of about 15 years between 1680 and 1700. This long cycle was actually observed both in the δ 18 O isotopic concentrations found in Japanese tree rings (a proxy for temperature changes) and in 14 C records (a proxy for solar activity) ( Yamaguchia et al., 2010 ).

Scafetta (2014b) also suggested that the input of the planetary forcing could be nonlinearly processed by the internal solar dynamo mechanisms. As a consequence, the output function might be characterized by additional multi-decadal and secular harmonics. The main two frequency clusters are predicted at 57, 61, 65 years and at 103, 115, 130, and 150 years. These harmonics actually appear in the power spectra of solar activity ( Ogurtsov et al., 2002 ). In particular, Cauquoin et al. (2014) found the four secular periods (103, 115, 130, 150 years) in the 10 Be record of 325–336 kyr ago. These authors claimed that their analyzed records do not show any evidence of a planetary influence but they did not realize that their found oscillations could be derived from the beating among the harmonics of Jupiter and Saturn with the 11-year solar cycle, as demonstrated in Scafetta (2014b) .

We notice that the multi-secular and millennial hindcasts of the solar activity records made by the three-frequency Jupiter-Saturn model shown in Figure 4 are impressive because the frequencies, phases and amplitudes of the model are theoretically deduced from the orbits of Jupiter and Saturn and empirically obtained from the sunspot record from 1750 to 2010. The prolonged periods of high and low solar activity derive from the constructive and destructive interference of the three harmonics.

7 Orbital Invariant Inequality Model: The Jovian Planets and the Long Solar and Climatic Cycles

The orbital invariant inequality model was first proposed by Scafetta et al. (2016) and successively developed by Scafetta (2020) using only the orbital periods of the four Jovian planets ( Table 1 ). It successfully reconstructs the main solar multi-decadal to millennial oscillations like those observed at 55–65 years, 80–100 years (Gleissberg cycle), 155–185 years (Jose cycle), 190–240 years (Suess - de Vries cycle), 800–1200 years (Eddy cycle) and at 2100–2500 years (Bray-Hallstatt cycle) ( McCracken et al., 2001 , 2013 ; Abreu et al., 2012 ; Scafetta, 2016 ). The model predictions well agree with the solar and climate long-term oscillations discussed, for example, in Neff et al. (2001) and McCracken et al. (2013) . Let us now describe the invariant inequality model in some detail.

Given two harmonics with period P 1 and P 2 and two integers n 1 and n 2 , there is a resonance if P 1 / P 2 = n 1 / n 2 . In the real planetary motions, this identity is almost always not satisfied. Consequently, it is possible to define a new frequency f and period P using the following equation

which is called “inequality.” Clearly, f and P represent the beat frequency and the beat period between n 1 / P 1 and n 2 / P 2 . The simplest case is when n 1 = n 2 = 1, which corresponds to the synodal period between two planets defined in Eq. 2 , which is reported below for convenience:

Equation 30 indicates the average time interval between two consecutive planetary conjunctions relative to the Sun. The conjunction periods among the four Jovian planets are reported in Table 5 .

TABLE 5 . Heliocentric synodic invariant inequalities and periods with the timing of the planetary conjunctions closest to 2000 AD (cf. Scafetta, 2020 ).

Equation 29 can be further generalized for a system of n orbiting bodies with periods P i ( i = 1, 2, …, n ). This defines a generic inequality, represented by the vector ( a 1 , a 2 , …, a n ), as

where a i are positive or negative integers.

Among all the possible orbital inequalities given by Eq. 31 , there exists a small subset of them that is characterized by the condition:

This special subset of frequencies is made of the synodal planetary periods ( Eq. 30 ) and all the beats among them.

It is easy to verify that the condition imposed by Eq. 32 has a very important physical meaning: it defines a set of harmonics that are invariant with respect to any rotating system such as the Sun and the heliosphere. Given a reference system at the center of the Sun and rotating with period P o , the orbital periods, or frequencies, seen relative to it are given by

With respect to this rotating frame of reference, the orbital inequalities among more planets are given by:

If the condition of Eq. 32 is imposed, we have that f ′ = f and P ′ = P . Therefore, this specific set of orbital inequalities remains invariant regardless of the rotating frame of reference from which they are observed.

For example, the conjunction of two planets relative to the Sun is an event that is observed in the same way in all rotating systems centered in the Sun. Since the Sun is characterized by a differential rotation that depends on its latitude, this means that all solar regions simultaneously feel the same planetary beats, which can strongly favor the emergence of synchronized phenomena in the Sun. Due to this physical property, the orbital inequalities that fulfill the condition given by Eq. 32 were labeled as “invariant” inequalities.

Table 6 reports the orbital invariant inequalities generated by the large planets (Jupiter, Saturn, Uranus, and Neptune) up to some specific order. They are listed using the vectorial formalism:

where a 1 (for Jupiter), a 2 (for Saturn), a 3 (for Uranus) and a 4 (for Neptune) are positive or negative integers and their sum is zero ( Eq. 32 ).

TABLE 6 . (Left) List of invariant inequalities for periods T ≥ 40 years and M ≤ 5 for Jupiter, Saturn, Uranus, Neptune (Right).

Two order indices, M and K , can also be used. M is the maximum value among | a i | and K is defined as

Since for the invariant inequalities the condition of Eq. 32 must hold, K indicates the number of synodal frequencies between Jovian planet pairs producing a specific orbital invariant. For example, K = 1 means that the invariant inequality is made of only one synodal frequency between two planets, K = 2 indicates that the invariant inequality is made of two synodal frequencies, etc.

For example, the invariant inequality cycle (1, −3, 1, 1) has K = 3 and it is the beat obtained by combining the synodal cycles of Jupiter-Saturn, Saturn-Uranus and Saturn-Neptune because it can be decomposed into three synodal cycles like (1, −3, 1, 1) = (1, −1, 0, 0) − (0, 1, −1, 0) − (0, 1, 0, −1). In the same way, it is possible to decompose any other orbital invariant inequality. Hence, all the beats among the synodal cycles are invariant inequalities and can all be obtained using the periods and time-phases listed in Table 5 .

Table 6 lists all the invariant inequalities of the four Jovian planets up to M = 5. They can be collected into clusters or groups that recall the observed solar oscillations. The same frequencies are also shown in Figures 5A,B revealing a harmonic series characterized by clusters with a base frequency of 0.00558 1/year that corresponds to the period of 179.2 years, which is known as the Jose cycle (1965) ( Fairbridge and Shirley, 1987 ; Landscheidt, 1999 ).

FIGURE 5 . (A) The periods of the orbital invariant inequalities produced by Jupiter, Saturn, Uranus and Neptune for 1 ≤ M ≤ 5. (B) The same harmonics highlighting their base frequency ν of the Jose cycle (179.2 years). (cf. Scafetta, 2020 ). (C) Visual correlation between the INTCAL98 atmospheric Δ 14 C record ( Stuiver et al., 1998 ) and a speleothem calcite δ 18 O record (adapted from Neff et al., 2001 ). (D) Comparison between the cross-spectral analysis of the two records in C against the invariant inequalities of the solar system of Table 6 (red bars). (cf. Scafetta, 2020 ). ( E , Top) Eqs 39 , 40 that model the Hallstatt oscillation predicted by the invariant inequality (1, −3, 1, 1). ( E , Bottom) Eq. 40 (blue) against the Δ 14 C record (black) throughout the Holocene ( Reimer et al., 2004 , IntCal04.14c) and the observed Hallstatt oscillation deduced from a regression harmonic model (red). (cf. Scafetta et al., 2016 ; Scafetta, 2020 ).

The physical importance of the harmonics listed in Table 6 is shown in Figure 5C , which compares a solar activity reconstruction from a 14 C record, and the climatic reconstruction from a δ 18 O record covering the period from 9500 to 6000 years ago ( Neff et al., 2001 ): the two records are strongly correlated.

Figure 5D shows that the two records present numerous common frequencies that correspond to the cycles of Eddy (800–1200 years), Suess-de Vries (190–240 years), Jose (155–185 years), Gleissberg (80–100 years), the 55–65 year cluster, another cluster at 40–50 years, and some other features. Figure 5D also compares the common spectral peaks of the two records against the clusters of the invariant orbital inequalities (red bars) reported in Figure 5B and listed in Table 6 . The figure shows that the orbital invariant inequality model well predicts all the principal frequencies observed in solar and climatic data throughout the Holocene.

The efficiency of the model in hindcasting both the frequencies and the phases of the observed solar cycles can also be more explicitly shown. For example, the model perfectly predicts the great Bray-Hallstatt cycle (2100–2500 years) that was studied in detail by McCracken et al. (2013) and Scafetta et al. (2016) . The first step to apply the model is to determine the constituent harmonics of the invariant inequality (1, −3, 1, 1). This cycle is a combination of the orbital periods of Jupiter, Saturn, Uranus and Neptune that gives

The constituent harmonics are the synodic cycles of Jupiter-Saturn, Saturn-Uranus and Saturn-Neptune as described by the following relation

Thus, the invariant inequality (1, −3, 1, 1) is the longest beat modulation generated by the superposition of these three synodic cycles and it can be expressed as the periodic function

where P ij are the synodic periods and t ij are the correspondent time-phases listed in Table 5 .

Equation 39 is plotted in Figure 5E and shows the long beat modulation superposed to the Bray-Hallstatt period of 2318 years found in the Δ 14 C (‰) record (black) throughout the Holocene ( Reimer et al., 2004 , IntCal04.14c). This beat cycle is captured, for example, by the function:

whose period is 2318 years and the timing is fixed by the three conjunction epochs and the respective synodic periods. In fact, the argument of the above sinusoidal function is the sum of three terms that correspond to those of Eq. 38 . Equation 40 is plotted in Figure 5E as the blue curve.

Three important invariant inequalities – (1, −3, 2, 0), (0, 0, 1, −1) and (−1, 3, 0, −2) – are found within the Jose 155–185 year period band:

The long beat between Eq. 42 and Eq. 41 – that is (0, 0, 1, −1) − (−1, 3, 0, −2) = (1, −3, 1, −1) – is the great Bray–Hallstatt cycle. The fast beat between Eq. 42 and Eq. 43 – (0, 0, 1, −1) + (−1, 3, 0, −2) = (−1, 3, 1, −3) – is the Gleissberg 89-year cycle, which also corresponds to half of the Jose period of ∼178 year that regulates the harmonic structure of the wobbling of the solar motion.

Another interesting invariant inequality is (1, −2, −1, 2) = (1, 0, −1, 0) − 2(0, 1, 0, −1), which is a beat between the synodic period of Jupiter and Uranus (1,0,-1,0) and the first harmonic of the synodic period of Saturn and Neptune. The period is:

The beat oscillation is given by the equation:

that shows a 60.1-year beat oscillation. The pattern is found in both solar and climate records and could be physically relevant because the maxima of the 60-year beat occur during specific periods–the 1880s, 1940s, and 2000s–that were characterized by maxima in climatic records of global surface temperatures and in other climate records ( Agnihotri and Dutta, 2003 ; Scafetta, 2013 , 2014c ; Wyatt and Curry, 2014 ). The 60-year oscillation was even found in the records of the historical meteorite falls in China from AD 619–1943 ( Chang and Yu, 1981 ; Yu et al., 1983 ; Scafetta et al., 2019a ).

An astronomical 60-year oscillation can be obtained in several ways. In particular, Scafetta (2010) and (2012c) showed that it is also generated by three consecutive conjunctions of Jupiter and Saturn since their synodic cycle is 19.86 years and every three alignments the conjunctions occur nearly in the same constellation. The three consecutive conjunctions are different from each other because of the ellipticity of the orbits. The 60-year pattern has been known since antiquity as the Trigon of the Great Conjunctions ( Kepler, 1606 ), which also slowly rotates generating a quasi-millennial cycle known as the Great Inequality of Jupiter and Saturn ( Lovett, 1895 ; Etz, 2000 ; Scafetta, 2012c ; Wilson, 2013 ).

Both the 60-year and the quasi-millennial oscillations also characterize the evolution of the instantaneous eccentricity function of Jupiter ( Scafetta et al., 2019a ). The quasi millennial oscillation (the Heddy cycle) could be related to the two orbital invariant inequalities (0, −1, 5, −4) ≡ 772.7 years and (−1, 2, 4, −5) ≡ 1159 years. Their beat frequency being (0, −1, 5, −4) − (−1, 2, 4, −5) = (1, −3, 1, 1) ≡ 2318 years, which corresponds to the Bray–Hallstatt cycle. Their mean frequency, instead, is 0.5(0, −1, 5, −4) + 0.5(−1, 2, 4, −5) = 0.5(−1, 1, 9, −9) ≡ 927 years that reminds the Great Inequality cycle of Jupiter and Saturn suggesting that this great cycle could also be generated by the beat between the synodic period of Jupiter and Saturn, (1, −1, 0, 0) and the ninth harmonic of the synodic period of Uranus and Neptune, 9(0, 0, 1, −1).

The invariant inequality model can be extended to all the planets of the solar system ( see Tables 3 , 4 , 6 ). The ordering of the frequencies according to their physical relevance depends on the specific physical function involved (e.g. tidal forcing, angular momentum transfer, space weather modulation, etc .) and will be addressed in future work.

8 The Suess-de Vries Cycle (190–240 years)

The Suess-de Vries cycle is an important secular solar oscillation commonly found in radiocarbon records ( de Vries, 1958 ; Suess, 1965 ). Several recent studies have highlighted its importance ( Neff et al., 2001 ; Wagner et al., 2001 ; Abreu et al., 2012 ; McCracken et al., 2013 ; Lüdecke et al., 2015 ; Weiss and Tobias, 2016 ; Beer et al., 2018 ; Stefani et al., 2020b , 2021 ). Its period varies between 200 and 215 years but the literature also suggests a range between 190 and 240 years.

Stefani et al. (2021) argued that the Suess-de Vries cycle, together with the Hale and the Gleissberg-type cycles, could emerge from the synchronization between the 11.07-year periodic tidal forcing of the Venus–Earth–Jupiter system and the 19.86-year periodic motion of the Sun around the barycenter of the solar system due to Jupiter and Saturn. This model yields a Suess-de Vries-type cycle of 193 years.

Actually, the 193-year period is the orbital invariant inequality (−3, 5, −1, −1) = (0, 0, 1, −1) − (3, −5, 2, 0) where (0, 0, 1, −1) is the synodic cycle of Jupiter and Saturn (19.86 years) and (3, −5, 2, 0) is the 22.14-year orbital inequality cycle of Venus, Earth and Jupiter ( Eq. 5 ). We also notice that (0, 0, 1, −1) + (3, −5, 2, 0) = (3, −5, 3, −1) corresponds to the period of 10.47 years which is a periodicity that has been observed in astronomical and climate records ( Scafetta, 2014b ; Scafetta et al., 2020 ).

The orbital invariant inequality model discussed in Section 7 provides an alternative and/or complementary origin of the Suess-de Vries cycle. In fact, the orbital invariant inequalities among Jupiter, Saturn, Uranus and Neptune form a cluster of planetary beats with periods between 200 and 240 years. Thus, the Suess-de Vries cycle might also emerge as beat cycles among the orbital invariant inequalities with periods around 60 years and those belonging to the Gleissberg frequency band with periods around 85 years. See Table 6 . In fact, their synodic cycles would approximately be

It might also be speculated that the Suess-de Vries cycle originates from a beat between the Trigon of the Great Conjuctions of Jupiter and Saturn (3 × 19.862 = 59.6 years, which is an oscillation that mainly emerges from the synodical cycle between Jupiter and Saturn combined with the eccentricity of the orbit of Jupiter) and the orbital period of Uranus (84 years). In this case, we would have 1/(1/59.6–1/84) = 205 years.

The last two estimates coincide with the 205-year Suess-de Vries cycle found in radiocarbon records by Wagner et al. (2001) and are just slightly smaller than the 208-year cycle found in other similar recent studies ( Abreu et al., 2012 ; McCracken et al., 2013 ; Weiss and Tobias, 2016 ; Beer et al., 2018 )

We notice that the natural planetary cycles that could theoretically influence solar activity are either the orbital invariant inequality cycles (which involve the synodic cycles among the planets assumed to be moving on circular orbits) and the orbital cycles of the planets themselves because the orbits are not circular but eccentric, and their harmonics.

9 Evidences for Planetary Periods in Climatic Records

A number of solar cycles match the periods found in climatic records (see Figures 4 – 6 ) and often appear closely correlated for millennia (e.g.: Neff et al., 2001 ; Scafetta et al., 2004 ; Scafetta and West, 2006 ; Scafetta, 2009 , 2021 ; Steinhilber et al., 2012 , and many others).

FIGURE 6 . (A) Time-frequency analysis (L = 110 years) of the speed of the Sun relative to the barycenter of the solar system. (B) Time frequency analysis (L = 110 years) of the detrended HadCRUT3 temperature record. (cf. Scafetta, 2014b ). (C) Ensemble CMIP6 GCM mean simulations for different emission scenarios versus the HadCRUT global surface temperatures. (D) The same record compared with the solar-astronomical harmonic climate model Scafetta (2013) updated in Scafetta (2021) .

Evidences for a astronomical origin of the Sub-Milankovitch climate oscillations have been discussed in several studies (e.g.: Scafetta, 2010 ; 2014b , 2016 , 2018 , 2021 ). Let us now summarizes the main findings relative to the global surface temperature record from 1850 to 2010.

Figures 6A,B compare the time-frequency analyses between the speed of the Sun relative to the center of mass of the solar system ( Figure 1 ) and the HadCRUT3 global surface records ( Scafetta, 2014b ). It can be seen that the global surface temperature oscillations mimic several astronomical cycles at the decadal and multidecadal scales, as first noted in Scafetta (2010) and later confirmed by advanced spectral coherence analyses ( Scafetta, 2016 , 2018 ).

The main periods found in the speed of the Sun ( Figure 6A ) are at about 5.93, 6.62, 7.42, 9.93, 11.86, 13.8, 20 and 60 years. Most of them are related to the orbits of Jupiter and Saturn. The main periods found in the temperature record ( Figure 6B ) are at about 5.93, 6.62, 7.42, 9.1, 10.4, 13.8, 20 and 60 years. Most of these periods appear to coincide with orbital invariant inequalities ( Table 6 ) but the 9.1 and 10.4-year cycles.

Among the climate cycles, it is also found an important period of about 9.1 years, which is missing among the main planetary frequencies shown in Figure 6A . Scafetta (2010) argued that this oscillation is likely linked to a combination of the 8.85-year lunar apsidal line rotation period, the first harmonic of the 9-year Saros eclipse cycle and the 9.3-year first harmonic of the soli-lunar nodal cycle ( Cionco et al., 2021 ; Scafetta, 2012d , supplement). These three lunar cycles induce oceanic tides with an average period of about 9.1 years ( Wood, 1986 ; Keeling and Whorf, 2000 ) that could affect the climate system by modulating the atmospheric and oceanic circulation.

The 10.4-year temperature cycle is variable and appears to be the signature of the 11-year solar cycle that varies between the Jupiter-Saturn spring tidal cycle (9.93 years) and the orbital period of Jupiter (11.86 years). Note that in Figure 6B , the frequency of this temperature signal increased in time from 1900 to 2000. This agrees with the solar cycle being slightly longer (and smaller) at the beginning of the 20th century and shorter (and larger) at its end ( see Figure 2 ). We also notice that the 10.46-year period corresponds to the orbital invariant inequality (3, −5, 3, −1) among Venus, Earth, Jupiter and Saturn.

The above findings were crucial for the construction of a semi-empirical climate model based on the several astronomically identified cycles ( Scafetta, 2010 , 2013 ). The model included the 9.1-year solar-lunar cycle, the astronomical-solar cycles at 10.5, 20, 60 and, in addition, two longer cycles with periods of 115 years (using Eq. 25 ) and a millennial cycle here characterized by an asymmetric 981-year cycle with a minimum around 1700 (the Maunder Minimum) and two maxima in 1080 and 2060 (using Eq. 28 ). The model was completed by adding the volcano and the anthropogenic components deduced from the ensemble average prediction of the CMIP5 global circulation models assuming an equilibrium climate sensitivity (ECS) of about 1.5°C that is half of that of the model average, which is about 3°C. This operation was necessary because the identified natural oscillations already account for at least 50% of the warming observed from 1970 to 2000. Recently, Scafetta (2021) upgraded the model by adding some higher frequency cycles.

Figure 6C shows the HadCRUT4.6 global surface temperature record ( Morice et al., 2012 ) against the ensemble average simulations produced by the CMIP6 global circulation models (GCMs) using historical forcings (1850–2014) extended with three different shared socioeconomic pathway (SSP) scenarios (2015–2100) ( Eyring et al., 2016 ). Figure 6D shows the same temperature record against the proposed semi-empirical astronomical harmonic model under the same forcing conditions. The comparison between panels C and D shows that the semi-empirical harmonic model performs significantly better than the classical GCMs in hindcasting the 1850–2020 temperature record. It also predicts moderate warming for the future decades, as explained in detail by Scafetta (2013 , 2021) .

10 Possible Physical Mechanisms

Many authors suggest that solar cycles revealed in sunspot and cosmogenic records could derive from a deterministic non-linear chaotic dynamo ( Weiss and Tobias, 2016 ; Charbonneau, 2020 , 2022 ). However, the assumption that solar activity is only regulated by dynamical and stochastic processes inside the Sun has never been validated mainly because these models have a poor hindcasting capability.

We have seen how the several main planetary harmonics and orbital invariant inequalities tend to cluster towards specific frequencies that characterize the observed solar activity cycles. This suggests that the strong synchronization among the planetary orbits could be further extended to the physical processes that are responsible for the observed solar variability.

The physical mechanisms that could explain how the planets may directly or indirectly influence the Sun are currently unclear. It can be conjectured that the solar dynamo might have been synchronized to some planetary periods under the action of harmonic forcings acting on it for several hundred million or even billion years. In fact, as pointed out by Huygens in the 17th century, synchronization can occur even if the harmonic forcing is very weak but lasts long enough ( Pikovsky et al., 2001 ).

There may be two basic types of mechanisms referred to how and where in the Sun the planetary forcing is acting. In particular, we distinguish between the mechanisms that interact with the outer regions of the Sun and those that act in its interior.

1. Planetary tides can perturb the surface magnetic activity of the Sun, the solar corona, and thus the solar wind. The solar wind, driven by the rotating twisted magnetic field lines ( Parker, 1958 ; Tattersall, 2013 ), can reconnect with the magnetic fields of the planets when they get closer during conjunctions. This would modulate the solar magnetic wind density distribution and the screening efficiency of the whole heliosphere on the incoming cosmic rays. The effect would be a modulation of the cosmogenic records which then also act on the cloud cover. It is also possible that the planets can focus and modulate by gravitational lensing the flux of interstellar and interplanetary matter–perhaps even of dark matter–towards the Sun and the Earth stimulating solar activity ( Bertolucci et al., 2017 ; Scafetta, 2020 ; Zioutas et al., 2022 ) and, again, contributing to clouds formation on Earth which alters the climate.

2. Gravitational planetary tides and torques could reach the interior of the Sun and synchronize the solar dynamo by forcing its tachocline ( Abreu et al., 2012 ; Stefani et al., 2016 , 2019 , 2021 ) or even modulate the nuclear activity in the core ( Wolff and Patrone, 2010 ; Scafetta, 2012b ).

Scafetta and Willson (2013b) argued that these two basic mechanisms could well complement each other. In principle, it might also be possible that the physical solar dynamo is characterized by a number of natural frequencies that could resonate with the external periodic forcings yielding some type of synchronization. Let us briefly analyze several cases.

10.1 Mechanisms Associated With Planetary Alignments

The frequencies associated with planetary alignments and, in particular, those of the Jovian planets, were found to reproduce the main observed cycles in solar and climatic data. Scafetta (2020) showed examples of gravitational field configurations produced by a toy-model made of four equal masses orbiting around a 10 times more massive central body.

The Sun could feel planetary conjunctions because at least twenty-five out of thirty-eight largest solar flares were observed to start when one or more planets among Mercury, Venus, Earth, and Jupiter were either nearly above the position of the flare (within 10° longitude) or on the opposite side of the Sun ( Hung, 2007 ). For example, Mörner et al. (2015) showed that, on 7 January 2014, a giant solar flare of class X1.2 was emitted from the giant sunspot active region AR 1944 ( NASA, 2014 ), and that the flare pointed directly toward the Earth when Venus, Earth and Jupiter were exactly aligned in a triple conjunction and the planetary tidal index calculated by Scafetta (2012b) peaked at the same time.

Hung (2007) estimated that the probability for this to happen at random was 0.039%, and concluded that “ the force or momentum balance (between the solar atmospheric pressure, the gravity field, and magnetic field) on plasma in the looping magnetic field lines in solar corona could be disturbed by tides, resulting in magnetic field reconnection, solar flares, and solar storms. ” Comparable results and confirmations that solar flares could be linked to planetary alignments were recently discussed in Bertolucci et al. (2017) and Petrakou (2021) .

10.2 Mechanisms Associated With the Solar Wobbling

The movement of the planets and, in particular, of the Jovian ones, are reflected in the solar wobbling. Charvátová (2000) and Charvátová and Hejda (2014) showed that the solar wobbling around the center of mass of the solar system forms two kinds of complex trajectories: an ordered one, where the orbits appear more symmetric and circular, and a disordered type, where the orbits appear more eccentric and randomly distributed. These authors found that the alternation between these two states presents periodicities related, for example, to the Jose (∼178 years) and Bray–Hallstatt (∼2300 years) cycles.

Figure 7A compares the Bray–Hallstatt cycle found in the Δ 14 C (‰) record (black) throughout the Holocene ( Reimer et al., 2004 , IntCal04.14c) with two orbital records representing the periods of the pericycle and apocycle orbital arcs of the solar trajectories as extensively discussed by Scafetta et al. (2016) . Figure 7B shows the solar wobbling for about 6000 years where the alternation of ordered and disordered orbital patterns typically occurs according to the Bray–Hallstatt cycle of 2318 years ( Scafetta et al., 2016 ).

FIGURE 7 . (A) The Hallstatt oscillation (2318 years) found in Δ 14 C (‰) record and in the eccentricity function of the barycenter of the planets relative to the Sun. (B) Ordered and disordered orbits of the barycenter of the planets relative to the Sun. (C , D) The Hallstatt oscillation found in Δ 14 C (‰) record and in the apocycles and pericycles of the orbits of the center of mass of the planets relative to the Sun. (cf. Scafetta et al., 2016 ).

In particular, the astronomical records show that the Jose cycle is modulated by the Bray–Hallstatt cycle. Figures 7C,D show examples of how planetary configurations can reproduce the Bray–Hallstatt cycle: see details in Scafetta et al. (2016) . The fast oscillations correspond to the orbital invariant inequalities with periods of 159, 171.4 and 185 years while the long beat oscillation corresponds to the orbital invariant inequality with a period of 2318 years, which perfectly fits the Bray–Hallstatt cycle as estimated in McCracken et al. (2013) ( see Table 6 ). It is possible that the pulsing dynamics of the heliosphere can periodically modulate the solar wind termination shock layer and, therefore, the incoming interstellar dust and cosmic ray fluxes.

10.3 Mechanisms Associated With Planetary Tides and Tidal Torques

Discussing the tidal interactions between early-type binaries, Goldreich and Nicholson (1989) demonstrated that the tidal action and torques can produce important effects in the thin overshooting region between the radiative and the convective zone, which is very close to the tachocline. This would translate both in tidal torques and in the onset of g-waves moving throughout the radiative region. A similar mechanism should also take place in late-type stars like the Sun ( Goodman and Dickson, 1998 ).

Abreu et al. (2012) found an excellent agreement between the long-term solar cycles and the periodicities in the planetary tidal torques. These authors assumed that the solar interior is characterized by a non-spherical tachocline. Under such a condition, the planetary gravitational forces exert a torque on the tachocline itself that would then vary with the distribution of the planets around the Sun. These authors showed that the torque function is characterized by some specific planetary frequencies that match those observed in cosmogenic radionuclide proxies of solar activity. The authors highlighted spectral coherence at the following periods: 88, 104, 150, 208 and 506 years. The first four periods were discussed above using alternative planetary functions; the last period could be a harmonic of the millennial solar cycle also discussed above and found in the same solar record ( Scafetta, 2012a ; 2014b ).

Abreu et al. (2012) observed that the tachocline approximately coincides with the layer at the bottom of the convection zone where the storage and amplification of the magnetic flux tubes occur. These are the flux tubes that eventually erupt at the solar photosphere to form active regions. The tachocline layer is in a critical state because it is very sensitive to small perturbations being between the radiative zone characterized by stable stratification ( δ < 0) and the convective zone characterized by unstable stratification ( δ > 0). The proposed hypothesis is that the planetary tides could influence the magnetic storage capacity of the tachocline region by modifying its entropy stratification and the superadiabaticity parameter δ , thereby altering the maximum field strength of the magnetic flux tubes that regulate the solar dynamo.

However, Abreu et al. (2012) also acknowledged that their hypothesis could not explain how the tiny tidal modification of the entropy stratification could produce an observable effect although they conjectured the presence of a resonance mediated by gravity waves.

The planetary tidal influence on the solar dynamo has been rather controversial because the tidal accelerations at the tachocline layer are about 1000 times smaller than the accelerations of the convective cells ( de Jager and Versteegh, 2005 ). Scafetta (2012b) calculated that the gravitational tidal amplitudes produced by all the planets on the solar chromosphere are of the order of 1 mm or smaller ( see Table 7 ). More recently, Charbonneau (2022) critiqued Stefani et al. (2019 , 2021) by observing that also the planetary tidal forcings of Jupiter and Venus could only exert a “homeopathic” influence on the solar tachocline concluding that they should be unable to synchronize the dynamo. Charbonneau (2022) also observed that even angular momentum transport by convective overshoot into the tachocline would be inefficient and concluded that synchronization could only be readily achieved in presence of high forcing amplitudes, stressing the critical need for a powerful amplification mechanism.

TABLE 7 . Mean tidal elongations at the solar surface produced by all planets.

While it is certainly true that the precise underlying mechanism is not completely understood, the rough energetic estimate that 1 mm tidal height corresponds to 1 m/s velocity at the tachocline level might still entail sufficient capacity for synchronization by changing the (sensitive) field storage capacity ( Abreu et al., 2012 ) or by synchronizing that part of α that is connected with the Tayler instability or by the onset of magneto-Rossby waves at the tachocline ( Dikpati et al., 2017 ; Zaqarashvili, 2018 ). In all cases, it could be possible that only a few high-frequency planetary forcing (e.g. the 11.07-year Venus-Earth-Jupiter tidal model) are able to efficiently synchronize the solar dynamo ( Stefani et al., 2016 ; Stefani et al., 2018 ; Stefani et al., 2019 ). At the same time, additional and longer solar cycles could emerge when some feature of the dynamo is also modulated by the angular momentum exchange associated with the solar wobbling ( Stefani et al., 2021 ). Finally, Albert et al. (2021) proposed that stochastic resonance could explain the multi-secular variability of the Schwabe cycle by letting the dynamo switch between two distinct operating modes as the solution moves back and forth from the attraction basin of one to the other.

Alternatively, the problem of the tidal “homeopathic” influence on the tachocline could be solved by observing that tides could play some more observable role in the large solar corona where the solar wind originates, or in the wind itself at larger distances from the Sun where the tides are stronger, or even in the solar core where they could actually trigger a powerful response from nuclear fusion processes. Let us discuss the latter hypothesis.

10.4 A Possible Solar Amplification of the Planetary Tidal Forcing

A possible amplification mechanism of the effects of the tidal forcing was introduced by Wolff and Patrone (2010) and Scafetta (2012b) .

Wolff and Patrone (2010) proposed that tidal forcing could act inside the solar core inducing waves in the plasma by mixing the material and carrying fresh fuel to the deeper and hotter regions. This mechanism would make solar-type stars with a planetary system slightly brighter because their fuel would burn more quickly.

Scafetta (2012b) further developed this approach and introduced a physical mechanism inspired by the mass-luminosity relation of main-sequence stars. The basic idea is that the luminosity of the core of the Sun can be written as

where L ⊙ is the baseline luminosity of the star without planets and Δ L tidal ( t ) = A ⋅ Ω ̇ tidal ( t ) is the small luminosity increase induced by planetary tides inside the Sun. Ω ̇ tidal ( t ) is the rate of the gravitational tidal energy which is continuously dissipated in the core and A is the amplification factor related to the triggered luminosity production via H-burning.

To calculate the magnitude of the amplification factor A we start by considering the Hertzsprung-Russell mass-luminosity relation , which establishes that, if the mass of a star increases, its luminosity L, increases as well. In the case of a G-type main-sequence star, with luminosity L and mass M = M ⊙ + Δ M , the mass-luminosity relation approximately gives

where L ⊙ is the solar luminosity and M ⊙ is the mass of the Sun ( Duric, 2004 ). By relating the luminosity of a star to its mass, the Hertzsprung-Russell relation suggests a link between the luminosity and the gravitational power continuously dissipated inside the star.

The total solar luminosity is

where 1 AU = 1.496 ⋅ 10 11  m is the average Sun-Earth distance, and TSI is the total solar irradiance 1360.94  W / m 2 at 1 AU. Every second, the core of the Sun transforms into luminosity a certain amount of mass according to the Einstein equation E = mc 2 . If dL ( r ) is the luminosity produced inside the shell between r and r + dr ( Bahcall et al., 2001 , 2005 ), the mass transformed into light every second in the shell is

where c = 2.998 ⋅ 10 8   m / s is the speed of the light and r is the distance from the center of the Sun.

The transformed material can be associated with a correspondent loss of gravitational energy of the star per time unit U ̇ ⊙ , which can be calculated using Eq. 50 as

where the initial factor 1/2 is due to the virial theorem, m ⊙ ( r ) is the solar mass within the radius r ≤ R S and L ( r ) is the luminosity profile function derived by the standard solar model ( Bahcall et al., 2001 , 2005 ).

The gravitational forces will do the work necessary to compensate for such a loss of energy to restore the conditions for the H-burning. In fact, the solar luminosity would decrease if the Sun’s gravity did not fill the vacuum created by the H-burning, which reduces the number of particles by four (4 H → 1 He ). At the same time, the nucleus of He slowly sinks releasing additional potential energy. All this corresponds to a gravitational work in the core per time unit, Ω ̇ ⊙ that is associated with light production.

The basic analogy made by Scafetta (2012b) is that Ω ̇ ⊙ should be of the same order of magnitude as the rate of the gravitational energy loss due to H-fusion ( Ω ̇ ⊙ ≈ U ̇ ⊙ ) . Moreover, the energy produced by the dissipation of the tidal forces in the core should be indistinguishable from the energy produced by the other gravitational forces in the Sun. Thus, it is as if tides added some gravitational power that becomes Ω ̇ ⊙ + Ω ̇ tidal .

For small perturbations, since light production is directly related both to the solar mass and to the gravitational power dissipated inside the core, Scafetta (2012b) assumed the equivalence

where Ω ̇ tidal is the tidal perturbing power dissipated inside the Sun and Ω ̇ ⊙ ≡ U ̇ ⊙ is the rate of the gravitational energy lost by the Sun through H-burning. Thus, from Eqs 47 , 48 we get

where the amplification factor is calculated as

Equation 54 means that any little amount of gravitational power dissipated in the core (like that induced by planetary tidal forcing) could be amplified by a factor of the order of one million by nuclear fusion. This could be equivalent to having gravitational tidal amplitudes amplified from 1 mm to 1 km at the tachocline. This amplification could solve the problem of the “homeopathic” gravitational tidal energy contribution highlighted by Charbonneau (2022) .

By using such a large amplification factor and the estimated gravitational power Ω ̇ tidal dissipated inside the solar core, Scafetta (2012b) calculated the tidally-induced TSI produced by each of the planets ( Figures 8A,B ), as well as that of all the planets together ( Figure 8C ). The sequence of the relative tidal relevance of the planets is Jupiter, Venus, Earth, Mercury, Saturn, Mars, Uranus and Neptune. The mean enhancement of their overall tidally-induced TSI is of the order of 0.3–0.8  W / m 2 , depending on the specific Love number of the tides ( see Figure 8C ). However, on shorter time scales the tides could produce TSI fluctuations up to 0.6–1.6  W / m 2 in absence of dampening mechanisms. In particular, on a decadal time scale, the TSI fluctuations due to Jupiter and Saturn could reach amplitudes of 0.08–0.20  W / m 2 ( see the black curve in Figure 8C ).

FIGURE 8 . (A , B) Theoretical TSI enhancement induced by the tides of each planet on the Sun obtained using Scafetta (2012b) amplification hypothesis; the Love numbers are 3/2 (left axis) and 15/4 (right axis). (C) The same as produced by the tides of all the planets. (D) Lomb-periodogram spectral analysis of the sunspot number record (red) and of the tidal function (black) produced by all the planets.

If the luminosity flux reaching the tachocline from the radiative zone is modulated by the contribution of tidally-induced luminosity oscillations with a TSI amplitude of the order of 0.01-0.10  W / m 2 , the perturbation could be sufficiently energetic to tune the solar dynamo with the planetary frequencies. The dynamo would then further amplify the luminosity signal received at the tachocline up to ∼ 1 W / m 2 amplitudes as observed in TSI cycles ( Willson and Mordvinov, 2003 ).

Figure 8D compares the periodograms of the sunspot number record and of the planetary luminosity signal shown in Figure 8C . The two side frequency peaks at about 10 years (J/S-spring tide) and 11.86 years (J-tide) perfectly coincide in the two spectral analyses. The central frequency peak at about 10.87 years shown only by sunspot numbers could be directly generated by the solar dynamo excited by the two tidal frequencies ( Scafetta, 2012a ) or other mechanisms connected with the dynamo as discussed above.

An obvious objection to the above approach is that the Kelvin-Helmholtz time-scale ( Mitalas and Sills, 1992 ; Stix, 2003 ) predicts that the light journey from the core to the convective zone requires 10 4 –10 8 years. Therefore, the luminosity fluctuations produced inside the core could be hardly detectable because they would be smeared out before reaching the convective zone. At most, there could exist only a slightly enhanced solar luminosity related to the overall tidally-induced TSI mean enhancement of the order of 0.3–0.8  W / m 2 as shown in Figure 8C .

However, several different mechanisms may be at work. In fact, the harmonic tidal forcing acts simultaneously throughout the core and in the radiative zone, and simultaneously produces everywhere a synchronized energy oscillation that can be amplified in the core as discussed above. This would can give rise to modulated seismic waves (g and p-mode oscillations ) that can propagate from the core up to the tachocline region in a few hours because the sound speed inside the Sun is a few hundred kilometers per second ( Hartlep and Mansour, 2005 ; Barker and Ogilvie, 2010 ; Ahuir et al., 2021 ). These waves might also couple with the g-waves produced in the tachocline ( Goodman and Dickson, 1998 ) producing a perturbation in the tachocline region sufficiently strong to synchronize the solar dynamo with the planetary tidal frequencies.

11 Conclusion

Many empirical evidences suggest that planetary systems can self-organize in synchronized structures although some of the physical mechanisms involved are still debated.

We have shown that the high synchronization of our own planetary system is nicely revealed by the fact that the ratios of the orbital radii of adjacent planets, when raised to the 2/3rd power, express the simple ratios found in harmonic musical consonances while those of the mirrored ones follow the simple, elegant, and highly precise scaling-mirror symmetry Eq. 1 ( Bank and Scafetta, 2022 ).

The solar system is made of synchronized coupled oscillators because it is characterized by a set of frequencies that are linked to each other by the harmonic Eq. 3 , which are easily detected in the solar wobbling. Thus, it is then reasonable to hypothesize that the solar activity could be also tuned to planetary frequencies.

We corroborated this hypothesis by reviewing the many planetary harmonics and orbital invariant inequalities that characterize the planetary motions and observing that often their frequencies correspond to those of solar variability.

It may be objected that, since the identified planetary frequencies are so numerous, it could be easy to occasionally find that some of them roughly correspond to those of the solar cycles. However, the fact is that the planetary frequencies of the solar system, from the monthly to the millennial time scales, are not randomly distributed but tend to cluster around some specific values that quite well match those of the main solar activity cycles.

Thus, it is rather unlikely that the results shown in Figures 2 – 6 are just occasional. In some cases, our proposed planetary models have even been able to predict the time-phase of the solar oscillations like that of the Schwabe 11-year sunspot cycle throughout the last three centuries, as well as those of the secular and millennial modulations throughout the Holocene. The two main planetary models that could explain the Schwabe 11-year cycle and its secular and millennial variation involve the planets Venus, Earth, Jupiter and Saturn, as it was initially suggested by Wolf (1859) . We further suggest that the Venus-Earth-Jupiter model and the Jupiter-Saturn model could be working complementary to each other.

The alternative hypothesis that the solar activity is regulated by an unforced internal dynamics alone (i.e. by an externally unperturbed solar dynamo) has never been able to reproduce the variety of the observed oscillations. In fact, standard MHD dynamo models are not self-consistent and do not even directly explain the well-known 11-year solar cycle nor they are able to predict its timing without assuming a number of calibrated parameters ( Tobias, 2002 ; Jiang et al., 2007 ).

There have been several objections to a planetary theory of solar variability. For example, Smythe and Eddy (1977) claimed that planetary cycles and conjunctions could not predict the timing of grand solar minima like the Maunder Minimum of the 17th century. However, Scafetta (2012a) developed a solar-planetary model able to predict all the grand solar maxima and minima of the last millennium ( Figure 4 ).

Other authors reasonably claimed that planetary gravitational tides are too weak to modulate solar activity ( Charbonneau, 2002 ; de Jager and Versteegh, 2005 ; Charbonneau, 2022 ); yet, several empirical evidences support the importance of their role ( Wolff and Patrone, 2010 ; Abreu et al., 2012 ; Scafetta, 2012b ; Stefani et al., 2016 , 2019 ). Stefani et al. (2016 , 2021) proposed that the Sun could be at least synchronized by the tides of Venus, Earth and Jupiter, producing an 11.07-year cycle that reasonably matches the Schwabe cycle. Longer cycles could be produced by a dynamo excited by angular momentum transfer from Jupiter and Saturn. Instead, Scafetta (2012b) proposed that, in the solar core, the effects of the weak tidal forces could be amplified one million times or more due to an induced increase in the H-burning, thus providing a sufficiently strong forcing to synchronize and modulate the solar dynamo with planetary harmonics at multiple time scales.

Objections to the latter hypothesis, based on the slow light propagation inside the radiative zone according to the Kelvin–Helmholtz timescale ( Mitalas and Sills, 1992 ; Stix, 2003 ), could be probably solved. In fact, tidal forces are believed to favor the onset of g-waves moving back and forth throughout the radiative region of the Sun ( Barker and Ogilvie, 2010 ; Ahuir et al., 2021 ). Thus, g-waves themselves could be amplified and modulated in the core by the tidally induced H-burning enhancement ( Scafetta, 2012b ). Then, both tidal torques and g-waves could cyclically affect the tachocline region at the bottom of the convective zone and synchronize the solar dynamo.

Alternatively, planetary alignments can also modify the large-scale electromagnetic and gravitational structure of the planetary system altering the space weather in the solar system. For example, in coincidence of planetary alignments, an increase of solar flares has been observed ( Hung, 2007 ; Bertolucci et al., 2017 ; Petrakou, 2021 ). The solar wobbling, which reflects the motion of the barycenter of the planets, changing from more regular to more chaotic trajectories, correlates well with some long climate cycles like the Bray-Hallstatt cycle (2100–2500 years) ( Charvátová, 2000 ; Charvátová and Hejda, 2014 ; Scafetta et al., 2016 ). Finally, Scafetta et al. (2020) showed that the infalling meteorite flux on the Earth presents a 60-year oscillation coherent with the variation of the eccentricity of Jupiter’s orbit induced by Saturn. The falling flux of meteorites and interplanetary dust would then contribute to modulate cloud formation.

In conclusion, many empirical evidences suggest that planetary oscillations should be able to modulate the solar activity and even the Earth’s climate, although several open physical issues remain open. These results stress the importance of identifying the relevant planetary harmonics, the solar activity cycles and the climate oscillations as phenomena that, in many cases, are interconnected. This approach could be useful to predict both solar and climate variability using harmonic constituent models as it is currently done for oceanic tides. We think that the theory of a planetary modulation of solar activity should be further developed because no clear alternative theory exists to date capable to explain the observed planetary-solar interconnected periodicities.

Author Contributions

NS wrote a first draft of the paper. NS and AB have discussed in more details all the topics and together prepared the final manuscript.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: planetary systems, orbital synchronization, solar cycles, tidal forces, mechanisms of solar variability

Citation: Scafetta N and Bianchini A (2022) The Planetary Theory of Solar Activity Variability: A Review. Front. Astron. Space Sci. 9:937930. doi: 10.3389/fspas.2022.937930

Received: 06 May 2022; Accepted: 16 June 2022; Published: 04 August 2022.

Reviewed by:

Copyright © 2022 Scafetta and Bianchini. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Antonio Bianchini, [email protected] ; Nicola Scafetta, [email protected]

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• Bruno C. Quint   ORCID: orcid.org/0000-0002-1557-3560 51 ,
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• Letizia Stanghellini   ORCID: orcid.org/0000-0003-4047-0309 58 ,
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• Albert A. Zijlstra   ORCID: orcid.org/0000-0002-3171-5469 37  

Nature Astronomy volume  6 ,  pages 1421–1432 ( 2022 ) Cite this article

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• Astrophysical disks
• Astrophysical dust
• Stellar evolution

An Author Correction to this article was published on 03 January 2023

This article has been updated

Planetary nebulae—the ejected envelopes of red giant stars—provide us with a history of the last, mass-losing phases of 90% of stars initially more massive than the Sun. Here we analyse images of the planetary nebula NGC 3132 from the James Webb Space Telescope (JWST) Early Release Observations. A structured, extended hydrogen halo surrounding an ionized central bubble is imprinted with spiral structures, probably shaped by a low-mass companion orbiting the central star at about 40–60 au. The images also reveal a mid-infrared excess at the central star, interpreted as a dusty disk, which is indicative of an interaction with another closer companion. Including the previously known A-type visual companion, the progenitor of the NGC 3132 planetary nebula must have been at least a stellar quartet. The JWST images allow us to generate a model of the illumination, ionization and hydrodynamics of the molecular halo, demonstrating the power of JWST to investigate complex stellar outflows. Furthermore, new measurements of the A-type visual companion allow us to derive the value for the mass of the progenitor of a central star with excellent precision: 2.86 ± 0.06  M ⊙ . These results serve as pathfinders for future JWST observations of planetary nebulae, providing unique insight into fundamental astrophysical processes including colliding winds and binary star interactions, with implications for supernovae and gravitational-wave systems.

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An infrared transient from a star engulfing a planet

JWST/NIRCam detections of dusty subsolar-mass young stellar objects in the Small Magellanic Cloud

Direct images and spectroscopy of a giant protoplanet driving spiral arms in MWC 758

Data availability.

HST data are available at HST Legacy Archive ( https://hla.stsci.edu ). JWST data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute ( https://archive.stsci.edu/ ). MUSE data were collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile (ESO Programme 60.A-9100), presented in ref. 74 , and are available at the ESO Archive ( http://archive.eso.org ). San Pedro de Martir data are available at http://kincatpn.astrosen.unam.mx .

Code availability

The code MOCASSIN is available at https://mocassin.nebulousresearch.org/ . ZEUS3-D is available at the Laboratory for Computational Astrophysics 84 ). The compiled version of Shape is available at http://www.astrosen.unam.mx/shape .

Change history

03 january 2023.

A Correction to this paper has been published: https://doi.org/10.1038/s41550-022-01884-9

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Acknowledgements

We acknowledge the International Astronomical Union that oversees the work of Commission H3 on Planetary Nebulae. It is through the coordinating activity of this committee that this paper came together. S.A. acknowledges support under the grant 5077 financed by IAASARS/NOA. J.A. and V.B. acknowledge support from the EVENTs/Nebulae-Web research programme, Spanish AEI grant PID2019-105203GB-C21. I.A. acknowledges the support of CAPES, Brazil (Finance Code 001). E.D.B. acknowledges financial support from the Swedish National Space Agency. E.G.B. acknowledges NSF grants AST-1813298 and PHY-2020249. J.C. and E.P. acknowledge support from an NSERC Discovery Grant. G.G.-S. thanks M. L. Norman and the Laboratory for Computational Astrophysics for the use of ZEUS-3D. D.A.G.-H. and A.M. acknowledge support from the ACIISI, Gobierno de Canarias and the European Regional Development Fund (ERDF) under grant with reference PROID2020010051 as well as from the State Research Agency (AEI) of the Spanish Ministry of Science and Innovation (MICINN) under grant PID2020-115758GB-I00. J.G.-R. acknowledges support from Spanish AEI under Severo Ochoa Centres of Excellence Programme 2020-2023 (CEX2019-000920-S). J.G.-R. and V.G.-L. acknowledge support from ACIISI and ERDF under grant ProID2021010074. D.R.G. acknowledges the CNPq grant 313016/2020-8. M.A.G. acknowledges support of grant PGC2018-102184-B-I00 of the Ministerio de Educación, Innovación y Universidades cofunded with FEDER funds and from the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). D.J. acknowledges support from the Erasmus+ programme of the European Union under grant number 2020-1-CZ01-KA203-078200. A.I.K. and Z.O. were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. This research is/was supported by an Australian Government Research Training Program (RTP) Scholarship. M.M. and R.W. acknowledge support from STFC Consolidated grant (2422911). C.M. acknowledges support from UNAM/DGAPA/PAPIIT under grant IN101220. S.S.M. acknowledges funding from UMiami, the South African National Research Foundation and the University of Cape Town VC2030 Future Leaders Award. J.N. acknowledges support from NSF grant AST-2009713. C.M.d.O. acknowledges funding from FAPESP through projects 2017/50277-0, 2019/11910-4 e 2019/26492-3 and CNPq, process number 309209/2019-6. J.H.K. and P.M.B. acknowledge support from NSF grant AST-2206033 and a NRAO Student Observing Support grant to Rochester Institute of Technology. M.O. was supported by JSPS Grants-in-Aid for Scientific Research(C) (JP19K03914 and 22K03675). Q.A.P. acknowledges support from the HKSAR Research grants council. Vera C. Rubin Observatory is a Federal project jointly funded by the National Science Foundation (NSF) and the Department of Energy (DOE) Office of Science, with early construction funding received from private donations through the LSST Corporation. The NSF-funded LSST (now Rubin Observatory) Project Office for construction was established as an operating centre under the management of the Association of Universities for Research in Astronomy (AURA). The DOE-funded effort to build the Rubin Observatory LSST Camera (LSSTCam) is managed by SLAC National Accelerator Laboratory (SLAC). A.J.R. was supported by the Australian Research Council through award number FT170100243. L.S. acknowledges support from PAPIIT UNAM grant IN110122. C.S.C.’s work is part of I+D+i project PID2019-105203GB-C22 funded by the Spanish MCIN/AEI/10.13039/501100011033. M.S.-G. acknowledges support by the Spanish Ministry of Science and Innovation (MICINN) through projects AxIN (grant AYA2016-78994-P) and EVENTs/Nebulae-Web (grant PID2019-105203GB-C21). R.S.’s contribution to the research described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. J.A.T. thanks the Marcos Moshisnky Fundation (Mexico) and UNAM PAPIIT project IA101622. E.V. acknowledges support from the ‘On the rocks II project’ funded by the Spanish Ministerio de Ciencia, Innovación y Universidades under grant PGC2018-101950-B-I00. A.A.Z. acknowledges support from STFC under grant ST/T000414/1. This research made use of Photutils, an Astropy package for detection and photometry of astronomical sources 83 , of the Spanish Virtual Observatory ( https://svo.cab.inta-csic.es ) project funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00 and of the computing facilities available at the Laboratory of Computational Astrophysics of the Universidade Federal de Itajubá (LAC-UNIFEI, which is maintained with grants from CAPES, CNPq and FAPEMIG). Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESAC/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). The JWST Early Release Observations and associated materials were developed, executed and compiled by the ERO production team: H. Braun, C. Blome, M. Brown, M. Carruthers, D. Coe, J. DePasquale, N. Espinoza, M. Garcia Marin, K.Gordon, A. Henry, L. Hustak, A. James, A. Jenkins, A. Koekemoer, S. LaMassa, D. Law, A. Lockwood, A. Moro-Martin, S. Mullally, A. Pagan, D. Player, K. Pontoppidan, C. Proffitt, C. Pulliam, L. Ramsay, S. Ravindranath, N. Reid, M. Robberto, E. Sabbi, L. Ubeda. The EROs were also made possible by the foundational efforts and support from the JWST instruments, STScI planning and scheduling, and Data Management teams. Finally, this work would not have been possible without the collaborative platforms Slack (slack.com) and Overleaf (overleaf.com).

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School of Mathematical and Physical Sciences, Macquarie University, Sydney, New South Wales, Australia

Orsola De Marco

Astronomy, Astrophysics and Astrophotonics Research Centre, Macquarie University, Sydney, New South Wales, Australia

Department of Physics, Technion, Haifa, Israel

Muhammad Akashi & Noam Soker

Kinneret College on the Sea of Galilee, Samakh, Israel

Muhammad Akashi

Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Penteli, Greece

Stavros Akras & Panos Boumis

Observatorio Astronómico Nacional (OAN/IGN), Madrid, Spain

Javier Alcolea, Valentin Bujarrabal & Miguel Santander-García

Instituto de Física e Química, Universidade Federal de Itajubá, Itajubá, Brazil

Isabel Aleman & Hektor Monteiro

Aix-Marseille Université, CNRS, CNES, LAM (Laboratoire d’Astrophysique de Marseille), Marseille, France

Philippe Amram

Astronomy Department, University of Washington, Seattle, WA, USA

Bruce Balick

Department of Space, Earth and Environment, Chalmers University of Technology, Gothenburg, Sweden

Elvire De Beck

Department of Physics and Astronomy, University of Rochester, Rochester, NY, USA

Eric G. Blackman & Adam Frank

Laboratory for Laser Energetics, University of Rochester, Rochester, NY, USA

Eric G. Blackman

European Southern Observatory, Garching, Germany

Henri M. J. Boffin & Jeremy R. Walsh

Green Bank Observatory, Green Bank, WV, USA

Jesse Bublitz

INAF - Osservatorio Astrofisico di Torino, Pino Torinese, Italy

Beatrice Bucciarelli

Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada

Jan Cami & Els Peeters

Institute for Earth and Space Exploration, University of Western Ontario, London, Ontario, Canada

SETI Institute, Mountain View, CA, USA

Institute of Astronomy, University of Cambridge, Cambridge, UK

Nicholas Chornay

Institute of Astronomy and Astrophysics, Academia Sinica (ASIAA), Taipei, Taiwan

You-Hua Chu

GRANTECAN, La Palma, Spain

Romano L. M. Corradi

Instituto de Astrofísica de Canarias, La Laguna, Spain

Romano L. M. Corradi, D. A. García-Hernández, Jorge García-Rojas, Veronica Gómez-Llanos, David Jones & Arturo Manchado

Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Spain

D. A. García-Hernández, Jorge García-Rojas, Veronica Gómez-Llanos, David Jones & Arturo Manchado

Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada, Mexico

Guillermo García-Segura, Christophe Morisset & Laurence Sabin

Observatório do Valongo, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

Denise R. Gonçalves

Instituto de Astrofísica de Andalucía, IAA-CSIC, Glorieta de la Astronomía, Granada, Spain

Martín A. Guerrero

School of Physics and Astronomy, Monash University, Clayton, Victoria, Australia

Amanda I. Karakas & Zara Osborn

ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Canberra, Australian Capital Territory, Australia

Center for Imaging Science, Rochester Institute of Technology, Rochester, NY, USA

Joel H. Kastner

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Consejo Superior de Investigaciones Científicas, Madrid, Spain

Arturo Manchado

School of Physics and Astronomy, Cardiff University, Cardiff, UK

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Department of Physical Sciences, The Open University, Milton Keynes, UK

Iain McDonald

Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester, UK

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Australian Astronomical Optics, Faculty of Science and Engineering, Macquarie University, North Ryde, New South Wales, Australia

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Department of Physics, University of Miami, Coral Gables, FL, USA

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South African Astronomical Observatory, Cape Town, South Africa

Astronomy Department, University of Cape Town, Rondebosch, South Africa

NITheCS National Institute for Theoretical and Computational Sciences, Stellenbosch, South Africa

Leiden Observatory, Leiden University, Leiden, the Netherlands

Ana Monreal-Ibero

Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

Rodolfo Montez Jr

Center for Computational Relativity and Gravitation, Rochester Institute of Technology, Rochester, NY, USA

Jason Nordhaus

National Technical Institute for the Deaf, Rochester Institute of Technology, Rochester, NY, USA

Departamento de Astronomia, Instituto de Astronomia, Geofísica e Ciências Atmosféricas da USP, Cidade Universitária, São Paulo, Brazil

Claudia Mendes de Oliveira

Okayama Observatory, Kyoto University, Asakuchi, Japan

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Department of Physics, The University of Hong Kong, Hong Kong SAR, China

Quentin A. Parker

Laboratory for Space Research, Hong Kong SAR, China

Rubin Observatory Project Office, Tucson, AZ, USA

Bruno C. Quint

Department of Molecular Astrophysics, IFF-CSIC, Madrid, Spain

Guillermo Quintana-Lacaci

Centre for Astronomy, School of Physics, National University of Ireland Galway, Galway, Ireland

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University of New South Wales, Australian Defence Force Academy, Canberra, Australian Capital Territory, Australia

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Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

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Centro de Astrobiología (CAB), CSIC-INTA, Madrid, Spain

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Contributions

The following authors have contributed majorly to multiple aspects of the work that lead to this paper, the writing and the formatting of figures: O.D. (writing, structure, interpretation and synthesis), I.A. (H 2 interpretation), B.B. (processing and interpreting images), G.G.-S. (2D hydro modelling), J.H.K. (writing, H 2 measurements and interpretation), M.M. (imaging, photometry and H 2 interpretation), B.M. (stellar photometry), S.S.M. (hydrodynamics of binaries), A.M.-I. (MUSE data analysis), H.M. (photoionization and morpho-kinematic models), P.M.B. (JWST image production), C.M. (photoionization modelling), R.S. (disk model and comparative interpretation), N.S. (hydro modelling and interpretation), L. Stanghellini (distances and abundance interpretation), W.S. (morpho-kinematic models), J.R.W. (spatially resolved spectroscopy), A.A.Z. (disk model, H 2 measurements, writing and interpretation). The following authors have contributed key expertise to aspects of this paper: M.A. (hydrodynamic modelling and jet interpretation), J.A. (CO observations), S.A. (H 2 interpretation), P.A. (space-resolved spectroscopy), E.G.B. (hydrodynamics), J.B. (HST and radio images of fast evolving PN), B. Bucciarelli (Gaia data), V.B. (radio observations, disk observation and interpretation, and comparative studies), Y.-H.C. (disk interpretation), J.C. (molecular formation), R.L.M.C. (final review and interpretation), D.A.G.-H. (IR dust/PAH features and abundances), J.G.-R. (photoionization modelling), V.G.-L. (photoionization modelling), D.R.G. (comparative analysis), M.A.G. (X-ray imaging), D.J. (close binaries), A.I.K. (final review and stellar nucleosynthesis), A.M. (nebular morphology and H 2 interpretation), I.M. (photometry modelling), R.M. (X-ray and ultraviolet imaging), Z.O. (binary nucleosynthesis), M.O. (IR imaging), Q.A.P. (morphology), E.P. (nebular spectroscopy and PAHs), A.J.R. (binary populations), L. Sabin (abundances), C.S.C. (radio), M.S.-G. (nebular evolution), I.S. (star and star nebula association), A.K.S. (dust), J.A.T. (morphology), T.U. (nebular imaging), G.V.d.S. (IR observations), P.V. (AGB evolution model). The following authors contributed by commenting on some aspects of the analysis and manuscript: E.D.B., H.M.J.B., P.B., N.C., A.F., S.K., F.L., J.N., C.M.d.O., B.C.Q., G.Q.-L., M.R., E.V., W.V., R.W. and H.V.W.

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Correspondence to Orsola De Marco .

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Supplementary Text, Tables 1 and 2, Figs. 1–8 and References.

Supplementary Video 1

A fly-through video of the morpho-kinematic reconstruction of the ionized cavity of PN NGC 3132 shown in Fig. 3.

Supplementary Video 2

A fly-through video of the illumination model of the H2 halo of PN NGC 3132 shown in Fig. 5.

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De Marco, O., Akashi, M., Akras, S. et al. The messy death of a multiple star system and the resulting planetary nebula as observed by JWST. Nat Astron 6 , 1421–1432 (2022). https://doi.org/10.1038/s41550-022-01845-2

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