Cosmic ray impact on extrasolar earth-like planets in close-in habitable zones

Because of their different origins, cosmic rays can be subdivided into galactic cosmic rays and solar/stellar cosmic rays. The flux of cosmic rays to planetary surfaces is mainly determined by two planetary parameters: the atmospheric density and the strength of the internal magnetic moment. If a planet exhibits an extended magnetosphere, its surface will be protected from high-energy cosmic ray particles. We show that close-in extrasolar planets in the habitable zone of M stars are synchronously rotating with their host star because of the tidal interaction. For gravitationally locked planets the rotation period is equal to the orbital period, which is much longer than the rotation period expected for planets not subject to tidal locking. This results in a relatively small magnetic moment. We found that an Earth-like extrasolar planet, tidally locked in an orbit of 0.2 AU around an M star of 0.5 solar masses, has a rotation rate of 2% of that of the Earth. This results in a magnetic moment of less than 15% of the Earth's current magnetic moment. Therefore, close-in extrasolar planets seem not to be protected by extended Earth-like magnetospheres, and cosmic rays can reach almost the whole surface area of the upper atmosphere. Primary cosmic ray particles that interact with the atmosphere generate secondary energetic particles, a so-called cosmic ray shower. Some of the secondary particles can reach the surface of terrestrial planets when the surface pressure of the atmosphere is on the order of 1 bar or less. We propose that, depending on atmospheric pressure, biological systems on the surface of Earth-like extrasolar planets at close-in orbital distances can be strongly influenced by secondary cosmic rays.     

M stars as targets for terrestrial exoplanet searches and biosignature detection

The changing view of planets orbiting low mass stars, M stars, as potentially hospitable worlds for life and its remote detection was motivated by several factors, including the demonstration of viable atmospheres and oceans on tidally locked planets, normal incidence of dust disks, including debris disks, detection of planets with masses in the 5-20 M() range, and predictions of unusually strong spectral biosignatures. We present a critical discussion of M star properties that are relevant for the long- and short-term thermal, dynamical, geological, and environmental stability of conventional liquid water habitable zone (HZ) M star planets, and the advantages and disadvantages of M stars as targets in searches for terrestrial HZ planets using various detection techniques. Biological viability seems supported by unmatched very long-term stability conferred by tidal locking, small HZ size, an apparent short-fall of gas giant planet perturbers, immunity to large astrosphere compressions, and several other factors, assuming incidence and evolutionary rate of life benefit from lack of variability. Tectonic regulation of climate and dynamo generation of a protective magnetic field, especially for a planet in synchronous rotation, are important unresolved questions that must await improved geodynamic models, though they both probably impose constraints on the planet mass. M star HZ terrestrial planets must survive a number of early trials in order to enjoy their many Gyr of stability. Their formation may be jeopardized by an insufficient initial disk supply of solids, resulting in the formation of objects too small and/or dry for habitability. The small empirical gas giant fraction for M stars reduces the risk of formation suppression or orbit disruption from either migrating or nonmigrating giant planets, but effects of perturbations from lower mass planets in these systems are uncertain. During the first approximately 1 Gyr, atmospheric retention is at peril because of intense and frequent stellar flares and sporadic energetic particle events, and impact erosion, both enhanced, the former dramatically, for M star HZ semimajor axes. Loss of atmosphere by interactions with energetic particles is likely unless the planetary magnetic moment is sufficiently large. For the smallest stellar masses a period of high planetary surface temperature, while the parent star approaches the main sequence, must be endured. The formation and retention of a thick atmosphere and a strong magnetic field as buffers for a sufficiently massive planet emerge as prerequisites for an M star planet to enter a long period of stability with its habitability intact. However, the star will then be subjected to short-term fluctuations with consequences including frequent unpredictable variation in atmospheric chemistry and surficial radiation field. After a review of evidence concerning disks and planets associated with M stars, we evaluate M stars as targets for future HZ planet search programs. Strong advantages of M stars for most approaches to HZ detection are offset by their faintness, leading to severe constraints due to accessible sample size, stellar crowding (transits), or angular size of the HZ (direct imaging). Gravitational lensing is unlikely to detect HZ M star planets because the HZ size decreases with mass faster than the Einstein ring size to which the method is sensitive. M star Earth-twin planets are predicted to exhibit surprisingly strong bands of nitrous oxide, methyl chloride, and methane, and work on signatures for other climate categories is summarized. The rest of the paper is devoted to an examination of evidence and implications of the unusual radiation and particle environments for atmospheric chemistry and surface radiation doses, and is summarized in the Synopsis. We conclude that attempts at remote sensing of biosignatures and nonbiological markers from M star planets are important, not as tests of any quantitative theories or rational arguments, but instead because they offer an inspection of the residues from a Gyr-long biochemistry experiment in the presence of extreme environmental fluctuations. A detection or repeated nondetections could provide a unique opportunity to partially answer a fundamental and recurrent question about the relation between stability and complexity, one that is not addressed by remote detection from a planet orbiting a solar-like star, and can only be studied on Earth using restricted microbial systems in serial evolution experiments or in artificial life simulations. This proposal requires a planet that has retained its atmosphere and a water supply. The discussion given here suggests that observations of M star exoplanets can decide this latter question with only slight modifications to plans already in place for direct imaging terrestrial exoplanet missions.     

An estimate of the prevalence of biocompatible and habitable planets

A Monte Carlo computer model of extra-solar planetary formation and evolution, which includes the planetary geochemical carbon cycle, is presented. The results of a run of one million galactic disc stars are shown where the aim was to assess the possible abundance of both biocompatible and habitable planets. (Biocompatible planets are defined as worlds where the long-term presence of surface liquid water provides environmental conditions suitable for the origin and evolution of life. Habitable planets are those worlds with more specifically Earthlike conditions). The model gives an estimate of 1 biocompatible planet per 39 stars, with the subset of habitable planets being much rarer at 1 such planet per 413 stars. The nearest biocompatible planet may thus lie approximately 14 LY distant and the nearest habitable planet approximately 31 LY away. If planets form in multiple star systems then the above planet/star ratios may be more than doubled. By applying the results to stars in the solar neighbourhood, it is possible to identify 28 stars at distances of < 22 LY with a non-zero probability of possessing a biocompatible planet.     

Taxonomy of the extrasolar planet

When a star is described as a spectral class G2V, we know that the star is similar to our Sun. We know its approximate mass, temperature, age, and size. When working with an extrasolar planet database, it is very useful to have a taxonomy scale (classification) such as, for example, the Harvard classification for stars. The taxonomy has to be easily interpreted and present the most relevant information about extrasolar planets. I propose an extrasolar planet taxonomy scale with four parameters. The first parameter concerns the mass of an extrasolar planet in the form of units of the mass of other known planets, where M represents the mass of Mercury, E that of Earth, N Neptune, and J Jupiter. The second parameter is the planet's distance from its parent star (semimajor axis) described in a logarithm with base 10. The third parameter is the mean Dyson temperature of the extrasolar planet, for which I established four main temperature classes: F represents the Freezing class, W the Water class, G the Gaseous class, and R the Roasters class. I devised one additional class, however: P, the Pulsar class, which concerns extrasolar planets orbiting pulsar stars. The fourth parameter is eccentricity. If the attributes of the surface of the extrasolar planet are known, we are able to establish this additional parameter where t represents a terrestrial planet, g a gaseous planet, and i an ice planet. According to this taxonomy scale, for example, Earth is 1E0W0t, Neptune is 1N1.5F0i, and extrasolar planet 55 Cnc e is 9E-1.8R1.     

Tides and the evolution of planetary habitability

Tides raised on a planet by the gravity of its host star can reduce the planet's orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars ( less or similar to 0.35 M(circle)). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, approximately 5 M(circle) planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.     

A reappraisal of the habitability of planets around M dwarf stars

Stable, hydrogen-burning, M dwarf stars make up about 75% of all stars in the Galaxy. They are extremely long-lived, and because they are much smaller in mass than the Sun (between 0.5 and 0.08 M(Sun)), their temperature and stellar luminosity are low and peaked in the red. We have re-examined what is known at present about the potential for a terrestrial planet forming within, or migrating into, the classic liquid-surface-water habitable zone close to an M dwarf star. Observations of protoplanetary disks suggest that planet-building materials are common around M dwarfs, but N-body simulations differ in their estimations of the likelihood of potentially habitable, wet planets that reside within their habitable zones, which are only about one-fifth to 1/50th of the width of that for a G star. Particularly in light of the claimed detection of the planets with masses as small as 5.5 and 7.5 M(Earth) orbiting M stars, there seems no reason to exclude the possibility of terrestrial planets. Tidally locked synchronous rotation within the narrow habitable zone does not necessarily lead to atmospheric collapse, and active stellar flaring may not be as much of an evolutionarily disadvantageous factor as has previously been supposed. We conclude that M dwarf stars may indeed be viable hosts for planets on which the origin and evolution of life can occur. A number of planetary processes such as cessation of geothermal activity or thermal and nonthermal atmospheric loss processes may limit the duration of planetary habitability to periods far shorter than the extreme lifetime of the M dwarf star. Nevertheless, it makes sense to include M dwarf stars in programs that seek to find habitable worlds and evidence of life. This paper presents the summary conclusions of an interdisciplinary workshop (http://mstars.seti.org) sponsored by the NASA Astrobiology Institute and convened at the SETI Institute.     

Is the presence of oxygen on an exoplanet a reliable biosignature?

We revisit the validity of the presence of O(2) or O(3) in the atmosphere of a rocky planet as being a biosignature. Up to now, the false positive that has been identified applies to a planet during a hot greenhouse runaway, which is restricted to planets outside the habitable zone (HZ) of the star that are closer to the star. In this paper, we explore a new possibility based on abiotic photogeneration of O(2) at the surface of a planet that could occur inside the HZ. The search for such a process is an active field of laboratory investigation that has resulted from an ongoing interest in finding efficient systems with the capacity to harvest solar energy on Earth. Although such a process is energetically viable, we find it to be a very unlikely explanation for the observation of O(2) or O(3) in the atmosphere of a telluric exoplanet in the HZ. It requires an efficient photocatalyst to be present and abundant under natural planetary conditions, which appears unlikely according to our discussion of known mineral photochemical processes. In contrast, a biological system that synthesizes its constituents from abundant raw materials and energy has the inherent adaptation advantage to become widespread and dominant (Darwinist argument). Thus, O(2) appears to continue to be a good biosignature.     

Exchange of meteorites (and life?) between stellar systems

It is now generally accepted that meteorite-size fragments of rock can be ejected from planetary bodies. Numerical studies of the orbital evolution of such planetary ejecta are consistent with the observed cosmic ray exposure times and infall rates of these meteorites. All of these numerical studies agree that a substantial fraction (up to one-third) of the ejecta from any planet in our Solar System is eventually thrown out of the Solar System during encounters with the giant planets Jupiter and Saturn. In this paper I examine the probability that such interstellar meteorites might be captured into a distant solar system and fall onto a terrestrial planet in that system within a given interval of time. The overall conclusion is that it is very unlikely that even a single meteorite originating on a terrestrial planet in our solar system has fallen onto a terrestrial planet in another stellar system, over the entire period of our Solar System's existence. Although viable microorganisms may be readily exchanged between planets in our solar system through the interplanetary transfer of meteoritic material, it seems that the origin of life on Earth must be sought within the confines of the Solar System, not abroad in the galaxy.     

High-resolution simulations of the final assembly of Earth-like planets. 2. Water delivery and planetary habitability

The water content and habitability of terrestrial planets are determined during their final assembly, from perhaps 100 1,000-km "planetary embryos " and a swarm of billions of 1-10-km "planetesimals. " During this process, we assume that water-rich material is accreted by terrestrial planets via impacts of water-rich bodies that originate in the outer asteroid region. We present analysis of water delivery and planetary habitability in five high-resolution simulations containing about 10 times more particles than in previous simulations. These simulations formed 15 terrestrial planets from 0.4 to 2.6 Earth masses, including five planets in the habitable zone. Every planet from each simulation accreted at least the Earth's current water budget; most accreted several times that amount (assuming no impact depletion). Each planet accreted at least five water-rich embryos and planetesimals from the past 2.5 astronomical units; most accreted 10-20 water-rich bodies. We present a new model for water delivery to terrestrial planets in dynamically calm systems, with low-eccentricity or low-mass giant planets-such systems may be very common in the Galaxy. We suggest that water is accreted in comparable amounts from a few planetary embryos in a " hit or miss " way and from millions of planetesimals in a statistically robust process. Variations in water content are likely to be caused by fluctuations in the number of water-rich embryos accreted, as well as from systematic effects, such as planetary mass and location, and giant planet properties.     

Spectral signatures of photosynthesis. II. Coevolution with other stars and the atmosphere on extrasolar worlds

As photosynthesis on Earth produces the primary signatures of life that can be detected astronomically at the global scale, a strong focus of the search for extrasolar life will be photosynthesis, particularly photosynthesis that has evolved with a different parent star. We take previously simulated planetary atmospheric compositions for Earth-like planets around observed F2V and K2V, modeled M1V and M5V stars, and around the active M4.5V star AD Leo; our scenarios use Earth's atmospheric composition as well as very low O2 content in case anoxygenic photosynthesis dominates. With a line-by-line radiative transfer model, we calculate the incident spectral photon flux densities at the surface of the planet and under water. We identify bands of available photosynthetically relevant radiation and find that photosynthetic pigments on planets around F2V stars may peak in absorbance in the blue, K2V in the red-orange, and M stars in the near-infrared, in bands at 0.93-1.1 microm, 1.1-1.4 microm, 1.5-1.8 microm, and 1.8-2.5 microm. However, underwater organisms will be restricted to wavelengths shorter than 1.4 microm and more likely below 1.1 microm. M star planets without oxygenic photosynthesis will have photon fluxes above 1.6 microm curtailed by methane. Longer-wavelength, multi-photo-system series would reduce the quantum yield but could allow for oxygenic photosystems at longer wavelengths. A wavelength of 1.1 microm is a possible upper cutoff for electronic transitions versus only vibrational energy; however, this cutoff is not strict, since such energetics depend on molecular configuration. M star planets could be a half to a tenth as productive as Earth in the visible, but exceed Earth if useful photons extend to 1.1 microm for anoxygenic photosynthesis. Under water, organisms would still be able to survive ultraviolet flares from young M stars and acquire adequate light for growth.     

Looking for planetary moons in the spectra of distant Jupiters

More than 100 nearby stars are known to have at least one Jupiter-sized planet. Whether any of these giant gaseous planets has moons is unknown, but here we suggest a possible way of detecting Earth-sized moons with future technology. The planned Terrestrial Planet Finder observatory, for example, will be able to detect objects comparable in size to Earth. Such Earth-sized objects might orbit their stars either as isolated planets or as moons to giant planets. Moons of Jovian-sized planets near the habitable zones of main-sequence stars should be noticeably brighter than their host planets in the near-infrared (1-4 microm) if their atmospheres contain methane, water, and water vapor, because of efficient absorption of starlight by these atmospheric components. By taking advantage of this spectral contrast, future space observatories will be able to discern which extrasolar giant planets have Earth-like moons capable of supporting life.     

The search for companions to Epsilon Eridani

The authors review efforts to examine the star Epsilon Eridani and determine the possibility for the existence of an Earth-like planet. Early data indicated that there must be a habitable ecosphere about 82.5 million Km from the primary. Research into the existence of another planetary system determined that Epsilon Eridani was a binary star with an Oort cloud system, indicating the possibility of planet formation. A review of the evidence suggests that the presence of the small red Dwarf companion star precludes the existence of a planetary system surrounding Epsilon Eridani. It is suggested that observations continue to provide further data about the formation of binary systems.     

Circumstellar habitable zones: an overview

We review aspects of circumstellar habitable zones based on results reported at the First International Conference on Circumstellar Habitable Zones (held in 1994 at NASA Ames Research Center). Recent advances in atmospheric radiative transfer modeling have shown that circumstellar habitable zones are wider than previously thought. New considerations may allow a much shorter time scale both for the origin as well as the evolution of biological forms. The most abundant M dwarf stars, contrary to previous views, appear to be able to support the necessary conditions for a habitable zone around them. New planet formation models indicate that at least one planet should form within the circumstellar habitable zone of single dwarf stars regardless of mass. Biogenic materials also appear to be widespread and delivery to terrestrial planets via cometary impacts may be a viable mechanism. Finally, biology will modify a planet and provide positive feedback, in general, to increase the habitability of a planet. Overall, new astronomical, planetary, and biological considerations each seem to indicate that habitable zones around other stars may be both more widespread and more stable than previous research had indicated.     

Ozone concentrations and ultraviolet fluxes on Earth-like planets around other stars

Coupled radiative-convective/photochemical modeling was performed for Earth-like planets orbiting different types of stars (the Sun as a G2V, an F2V, and a K2V star). O(2) concentrations between 1 and 10(-5) times the present atmospheric level (PAL) were simulated. The results were used to calculate visible/near-IR and thermal-IR spectra, along with surface UV fluxes and relative dose rates for erythema and DNA damage. For the spectral resolution and sensitivity currently planned for the first generation of terrestrial planet detection and characterization missions, we find that O(2) should be observable remotely in the visible for atmospheres containing at least 10(-2) PAL of O(2). O(3) should be visible in the thermal-IR for atmospheres containing at least 10(-3) PAL of O(2). CH(4) is not expected to be observable in 1 PAL O(2) atmospheres like that of modern Earth, but it might be observable at thermal-IR wavelengths in "mid-Proterozoic-type" atmospheres containing approximately 10(-1) PAL of O(2). Thus, the simultaneous detection of both O(3) and CH(4) - considered to be a reliable indication of life - is within the realm of possibility. High-O(2) planets orbiting K2V and F2V stars are both better protected from surface UV radiation than is modern Earth. For the F2V case the high intrinsic UV luminosity of the star is more than offset by the much thicker ozone layer. At O(2) levels below approximately 10(-2) PAL, planets around all three types of stars are subject to high surface UV fluxes, with the F2V planet exhibiting the most biologically dangerous radiation environment. Thus, while advanced life is theoretically possible on high-O(2) planets around F stars, it is not obvious that it would evolve as it did on Earth.     

Planet populations in the Milky Way and beyond

Only about 15 years ago, speculations probably as old as mankind itself about the existence of planets orbiting stars other than the Sun turned into evidence. Recent technological advances make it now possible to find planets at separations from their host star that we consider suitable for life to form and evolve. However, we neither know the necessary nor the sufficient conditions. Even the detection of another planet teeming with life would signpost a beginning rather than an end. It would not answer the deeper questions of the origin and (maybe more importantly) future of our existence. In order to understand our own role in the cosmos, we need to investigate our context, which not only contains habitable planets similar to ours, but comprises the full amazing diversity of the planetary zoo. A comprehensive picture will only arise from complementary evidence provided by several applied planet detection techniques. The most curious effect of gravitational microlensing plays a special role with its capability for inferring a census of planets within the Milky Way, involving different stellar populations, with a sensitivity reaching down to the mass of the Moon, and even in neighbouring galaxies such as M31.     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

Role of the ionosphere for the atmospheric evolution of planets

We have synthesized current understanding, mainly observations, with regard to ion escape mechanisms to space from the ionosphere and exosphere of Titan and Earth-type planets, with the intent to provide an improved input for models of atmospheric evolution on early Earth and Earth-type planets and exoplanets. We focus on the role of the ionosphere and its non-linear response to solar parameters, all of which have been underestimated in current models of ancient atmospheric escape (4 billion years ago). Factors that have been overlooked include the following: (1) Much larger variation of O(+) outflow than H(+) outflow from the terrestrial ionosphere, depending on solar and geomagnetic activities (an important consideration when attempting to determine the oxidized state of the atmosphere of early Earth); (2) magnetization of the ionopause, which keeps ionospheric ions from escaping and controls many other escape processes; (3) extra ionization by, for example, the critical ionization velocity mechanism, which expands the ionosphere to greater altitudes than current models predict; and (4) the large escape of cold ions from the dense, expanded ionosphere of Titan. Here we offer, as a guideline for quantitative simulations, a qualitative diagnosis of increases or decreases of non-thermal escape related to the ionosphere for magnetized and unmagnetized planets in response to changes in solar parameters (i.e., solar EUV/FUV flux, solar wind dynamic pressure, and interplanetary magnetic field).     

Climate model studies of synchronously rotating planets

M stars constitute 75% of main sequence stars though, until recently, their star systems have not been considered suitable places for habitable planets to exist. In this study the climate of a synchronously rotating planet around an M dwarf star is evaluated using a three-dimensional global atmospheric circulation model. The presence of clouds and evaporative cooling at the surface of the planet result in a cooler surface temperature at the subsolar point. Water ice forms at the polar regions and on the dark side, where the minimum temperature lies between -30 degrees C and 0 degrees C. As expected, rainfall is extremely high on the starlit side and extremely low on the dark side. The presence of a dry continent causes higher temperatures on the dayside, and allows accumulation of snow on the nightside. The absence of any oceans leads to higher day-night temperature differences, consistent with previous work. The present study reinforces recent conclusions that synchronously rotating planets within the circumstellar habitable zones of M dwarf stars should be habitable, and therefore M dwarf systems should not be excluded in future searches for exoplanets.     

Detecting tree-like multicellular life on extrasolar planets

Over the next two decades, NASA and ESA are planning a series of space-based observatories to find Earth-like planets and determine whether life exists on these planets. Previous studies have assessed the likelihood of detecting life through signs of biogenic gases in the atmosphere or a red edge. Biogenic gases and the red edge could be signs of either single-celled or multicellular life. In this study, we propose a technique with which to determine whether tree-like multicellular life exists on extrasolar planets. For multicellular photosynthetic organisms on Earth, competition for light and the need to transport water and nutrients has led to a tree-like body plan characterized by hierarchical branching networks. This design results in a distinct bidirectional reflectance distribution function (BRDF) that causes differing reflectance at different sun/view geometries. BRDF arises from the changing visibility of the shadows cast by objects, and the presence of tree-like structures is clearly distinguishable from flat ground with the same reflectance spectrum. We examined whether the BRDF could detect the existence of tree-like structures on an extrasolar planet by using changes in planetary albedo as a planet orbits its star. We used a semi-empirical BRDF model to simulate vegetation reflectance at different planetary phase angles and both simulated and real cloud cover to calculate disk and rotation-averaged planetary albedo for a vegetated and non-vegetated planet with abundant liquid water. We found that even if the entire planetary albedo were rendered to a single pixel, the rate of increase of albedo as a planet approaches full illumination would be comparatively greater on a vegetated planet than on a non-vegetated planet. Depending on how accurately planetary cloud cover can be resolved and the capabilities of the coronagraph to resolve exoplanets, this technique could theoretically detect tree-like multicellular life on exoplanets in 50 stellar systems.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).