Hidden Mass in the Asteroid Belt

The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976-1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass M_ring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived.The estimate M_ring≈(5±1)×10⁻¹⁰M_⊙ is obtained (M_⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R≈2.80 AU with 3% uncertainty. Then the total mass M_belt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: M_belt≈(18±2)×10⁻¹⁰M_⊙. The value M_belt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component M_ring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets.Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate M_belt≈18×10⁻¹⁰M_⊙ is obtained which is in excellent agreement with the dynamical finding given above.These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).     

Modern Numerical Ephemerides of Planets and the Importance of Ranging Observations for Their Creation

The JPL planetary and lunar ephemerides – DE200/LE200, DE403/LE403, DE405/LE405 and the planetary and lunar ephemerides, EPM87, EPM98, and EPM2000, constructed in the Institute of Applied Astronomy of RAS are described. Common properties and differences of the various ephemerides are given. Graphical comparisons of the DE ephemerides with each other and with the EPM ephemerides are presented. A fairly good agreement of planetary orbits is between DE403, DE405 and EPM98, EPM2000, respectively, over the interval of 120 years (1886–2006) covered by EPM98 and EPM2000. Some differences are explained by a slight disagreement in representing the orbits of Ceres, Pallas, and Vesta as they affect the planets. The accurate radar observations of planets and spacecraft make it possible not only to improve the orbital elements of planets but to determine a broad set of astronomical constants as well: km/AU, parameters of Mars rotation including its precessional rate, the masses of Jupiter, Ceres, Pallas, and Vesta, relativistic parameters of the PPN formalism, the variability of the gravitational constant G. These have been obtained in the fitting process of the DE405 and EPM2000 ephemerides to observational data, including nearly 80000 American and Russian radar observations of planets (1961–1997), ranging and doppler to the Viking and Pathfinder landers, and other miscellaneous measurements from various sources and spacecraft.     

High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants

The latest version of the planetary part of the numerical ephemerides EPM (Ephemerides of Planets and the Moon) developed at the Institute of Applied Astronomy of the Russian Academy of Sciences is presented. The ephemerides of planets and the Moon were constructed by numerical integration in the post-Newtonian metric over a 140-year interval (from 1880 to 2020). The dynamical model of EPM2004 ephemerides includes the mutual perturbations from major planets and the Moon computed in terms of General Relativity with allowance for effects due to lunar physical libration, perturbations from 301 big asteroids, and dynamic perturbations due to the solar oblateness and the massive asteroid ring with uniform mass distribution in the plane of the ecliptic. The EPM2004 ephemerides resulted from a least-squares adjustment to more than 317000 position observations (1913–2003) of various types, including radiometric measurements of planets and spacecraft, CCD astrometric observations of the outer planets and their satellites, and meridian and photographic observations. The high-precision ephemerides constructed made it possible to determine, from modern radiometric measurements, a wide range of astrometric constants, including the astronomical unit AU = (149597870.6960 ± 0.0001) km, parameters of the rotation of Mars, the masses of the biggest asteroids, the solar quadrupole moment J ₂ = (1.9 ± 0.3) × 10⁻⁷, and the parameters of the PPN formalism β and γ. Also given is a brief summary of the available state-of-the-art ephemerides with the same precision: various versions of EPM and DE ephemerides from the Jet Propulsion Laboratory (JPL) (USA) and the recent versions of these ephemerides—EPM2004 and DE410—are compared. EPM2004 ephemerides are available via FTP at ftp://qua-sar.ipa.nw.ru/incoming/EPM2004.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 202–213.Original Russian Text Copyright © 2005 by Pitjeva.     

Predictions for the frequency and orbital radii of massive extrasolar planets

We investigate the migration of massive extrasolar planets caused by gravitational interaction with a viscous protoplanetary disc. We show that a model in which planets form at 5 au at a constant rate, before migrating, leads to a predicted distribution of planets that is a steeply rising function of log( a ), where a is the orbital radius. Between 1 and 3 au, the expected number of planets per logarithmic interval in a roughly doubles. We demonstrate that, once selection effects are accounted for, this is consistent with current data, and then extrapolate the observed planet fraction to masses and radii that are inaccessible to current observations. In total, approximately 15 per cent of stars targeted by existing radial velocity searches are predicted to possess planets with masses  0.3< M _p sin( i )<10 M _J  and radii  0.1< a <5 au  . A third of these planets (around 5 per cent of the target stars) lie at the radii most amenable to detection via microlensing. A further  5–10  per cent of stars could have planets at radii of  5< a <8 au  that have migrated outwards. We discuss the probability of forming a system (akin to the Solar system) in which significant radial migration of the most massive planet does not occur. Approximately  10–15  per cent of systems with a surviving massive planet are estimated to fall into this class. Finally, we note that a smaller fraction of low-mass planets than high-mass planets is expected to survive without being consumed by the star. The initial mass function for planets is thus predicted to rise more steeply towards small masses than the observed mass function.     

Stability of the solar system

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Metallicity of the massive protoplanets around HR 8799 If formed by gravitational instability

The final composition of giant planets formed as a result of gravitational instability in the disk gas depends on their ability to capture solid material (planetesimals) during their ‘pre-collapse’ stage, when they are extended and cold, and contracting quasi-statically. The duration of the pre-collapse stage is inversely proportional roughly to the square of the planetary mass, so massive protoplanets have shorter pre-collapse timescales and therefore limited opportunity for planetesimal capture. The available accretion time for protoplanets with masses of 3, 5, 7, and 10 Jupiter masses is found to be and 5.67×10³ years, respectively. The total mass that can be captured by the protoplanets depends on the planetary mass, planetesimal size, the radial distance of the protoplanet from the parent star, and the local solid surface density. We consider three radial distances, 24, 38, and 68 AU, similar to the radial distances of the planets in the system HR 8799, and estimate the mass of heavy elements that can be accreted. We find that for the planetary masses usually adopted for the HR 8799 system, the amount of heavy elements accreted by the planets is small, leaving them with nearly stellar compositions.     

The origin of the solar system: Implications for transneptunian planets and the nature of the long-period comets

If the solar system origin is considered within the framework of the author's hypothesis on the binary stars formation as a result of rotational-exchange break-up of the rotating protostar, then difficulties involved in the usual nebular hypotheses are automatically removed (unclear aspects of the possibility of formation of the gas disc proper, the problems of the angular momentum including slow rotation of the Sun and coplanarity of the planetary orbits, of differences in planetary masses and composition, the need, for the disc remnants to be swept out, the long time of planetary formation as compared with the possible lifetime of a turbulized disc etc.).The major stages of division and evolution of the Jupiter-Sun system are described. Similarities between the massive rotating proto-Jupiter (PJ) and the classical protoplanetary discs are pointed out. The process of planetoid condensation inside PJ is discussed. The most probable site of the condensation is the region of the first Lagrangian point. The planetoids condensed were lost by PJ as a result of its fast mass decrease. A gas dynamic consideration of the motion of planetoids in PJ yields 1000–3000 yr as a time scale for the PJ's mass loss. The number of the moonlike bodies lost (the remaining Galilean satellites fixing their lower mass limit) could reach 10⁴.Evolution of such interacting bodies results in the formation beyond Neptune of a cloud (up to 10³) of moonlike (and more massive) planets.The excess concentration of the long-period comets aphelia in this area implies their genetic relation to the planets. A concept of a joint planeto-cometary cloud is introduced. A concrete hydrodynamic mechanism of ice ejection from planets into space, viz. the formation of cumulative (Monroe) jets, is pointed out.A program of further investigations is outlined and recommendations given for an experimental check on the implications of the new cosmogonic concepts.     

Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^–3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^–6 AU, 4 × 10^–6, and 5 × 10^–4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.     

Influence of the largest asteroids on the orbital motions of terrestrial planets: application to the Earth and Mars

The level of precision of modern numerical ephemeris of the Solar System necessitates taking into account the gravitational influence of the largest asteroids on the terrestrial planets. This can be done in a straightforward manner when assuming that the mass of the asteroid is well known. Nevertheless, this is rarely the case, even for the largest asteroids. In this paper, we use recent determinations of the masses of Ceres, Pallas, and Vesta to both qualitatively and quantitatively determine the action of these asteroids on the orbital parameters of the Earth and Mars. This is done by the numerical integration by comparing the orbital motions of the perturbed planet when adding or not the perturbing asteroid to the classical 9 bodies problem (the Sun + the eight planets). Some preliminary results are discussed. Published in Russian in Astronomicheskii Vestnik, 2009, Vol. 43, No. 1, pp. 83–86. The text was submitted by the autors in English.     

Photographic Observations of the Minor Planet (1) Ceres in Tashkent in 1951–1994

A procedure is described for remeasuring photographic plates with images of the minor planet (1) Ceres obtained in 1951–1994 with the Tashkent normal astrograph. To determine the observed spherical coordinates, the PPM catalog, based on the FK5 system, was used as a reference catalog. The calculation of the orbit of the minor planet (1) Ceres and the determination of the PPM zero-points and periodic errors on the basis of these observations yielded a unit weight error of 0.270. The derived coordinates and velocity components of (1) Ceres for J.D. = 2441600.5 are presented together with PPM zero-point and periodic-error-coefficient corrections. One of the results of the work is the high precision of the remeasured images, which makes it possible to use these observations, along with no less accurate observations of other selected minor planets, for determining corrections to the stellar coordinate system.     

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 10⁷ years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 10⁸ years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10⁶ years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10⁶ and 10⁸ years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10⁶ years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10⁻⁴-10⁻³ times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.     

Interferometric study of NGC 1313

The kinematics and structure of NGC 1313 are discussed on the basis of interferometric observations. Several uniformly rotating components, a total mass of 2×10¹⁰ solar masses, and deviations from pure circular movement of an amplitude of almost 20 km s^–1 are found.     

From 51 Peg to Earth-type planets

The discovery of 51 Pegasi is the result of a continuous improvement of cross-correlation spectrographs to obtain more precise radial velocities. Three generations of instruments developed over 30 years have allowed us to increase the radial-velocity precision by a factor 1000, from 250 m s^?1 in the 70s to a value close to 0.25 m s^?1 today. The statistical results gathered on exoplanet properties over the last 14 years have revealed the amazing diversity of extrasolar planetary systems. Our solar system does not appear to be a typical example of planetary systems. These discoveries have provided strong constraints for planet-formation models. At the beginning the detections were mostly focused on gaseous giant planets. Today, the best precision is achieved by the HARPS spectrograph. This makes possible the discovery of planets with masses comparable to the mass of the Earth. A new category of very low mass with minimum masses below 10 Earth masses, which may well be solid objects, has recently been revealed. This newly discovered population (apparently quite numerous) reveals specific statistical properties offering useful constraints for planet-formation models. The continuously improving precision of the radial velocity technique strengthens our hope that real Earth-type planets could be identified in the very few coming years.     

Model consideration of the bombardment event of the asteroidal belt by the planetesimals scattered from the Jupiter zone

The temporal evolutions of the planetesimals scattered from the Jupiter zone for different masses of the proto-Jupiter [(a) 0.1 and (b) 1.0 of the present mass] are investigated. Due to the combined effects of the orbital evolution of the planetesimals and the elimination of these projectiles either via impact capture or injection into escape velocity by the outer planets, the whole scattering process lasts about 10⁸ yr for case (a) and about 10⁷ yr for case (b). The longer time scale may be a good estimate for the accretion time interval of Jupiter while the shorter one (10⁷) gives the upper time limit of the late heavy-bombardment epoch of the terrestrial planets due to planetesimals scattered from the Jupiter zone. The limiting value of the encounter velocity U at the end of the scattering process is ≈0.6. Consideration of the collisional interaction of these projectiles with the asteroids indicates that the corresponding bombardment effect could be rather appreciable. Also, the asteroids on the inner edge of the main asteroid belt would have been bombarded more severely than those on the outer edge. From this point of view, the structure of the asteroidal belt could be affected significantly not only by Jupiter's gravitational perturbation effect but also by its early scattering process.     

Mid-infrared (5–100 μm) reflectance spectra and optical constants of ten phyllosilicate minerals

We have derived the real and imaginary indices of refraction for 10 phyllosilicate minerals—montmorillonite, beidellite, nontronite, hectorite, saponite, illite, illite–smectite (60/40 interlayered) kaolinite, halloysite, and serpentine—from 100–2000 cm⁻¹ (5–100 μm) at 2 cm⁻¹ spectral sampling using classical Lorentz–Lorenz dispersion theory. We present the real and imaginary indices and the oscillator parameters with which they were modeled. Use of these optical constants will aid in the modeling of thermal infrared spectra of planets, asteroids, interplanetary and interstellar dust, and protoplanetary disks around nearby stars.     

Unbound planets

Current protostellar theory has determined a lower limit to the mass of a pre-stellar gas cloud fragment of ~0.01 M. This suggests that isolated interstellar bodies in the mass range ~10 M_-710_-2 M must have originated within a planetary system. Two possible mechanisms whereby planets are lost from their parental systems to interstellar space are discussed and the abundance and distribution of such unbound planets within the Galaxy is examined. It is found that, except within the central regions of the Galaxy, unbound planets are expected to be scarce. In the solar neighbourhood for instance, the number density ratio of unbound planets to stars is estimated to range between extremes of ~4 × 10^–4–3 × 10^–2 with a most probable value of ~6 x 10^–3. The faint possibility that the hypothetical Planet X might be of extra-solar origin is also discussed.     

Motions of the perihelions of Neptune and Pluto

Five outer planets are numerically integrated over five million years in the Newtonian frame. The argument of Pluto's perihelion librates about 90 degrees with an amplitude of about 23 degrees. The period of the libration depends on the mass of Pluto: 4.0×10⁶ years forM _pluto=2.78×10^–6 M _sun and 3.8×10⁶ years forM _pluto=7.69×10^–9 M _sun, which is the newly determined mass. The motion of Neptune's perihelion is more sensitive to the mass of Pluto. ForM _pluto=7.69×10^–9 M _sun, the perihelion of Neptune does circulate counter-clockwise and forM _pluto=2.78×10^–6 M _sun, it does not circulate and the Neptune's eccentricity does not have a minimum. With the initial conditions which do not lie in the resonance region between Neptune and Pluto, a close approach between them takes place frequently and the orbit of Pluto becomes unstable and irregular.     

Planetary growth with collisional fragmentation and gas drag

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 10⁷ years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.     

Surface thermoelastic erosion of atmosphereless solar system bodies under bombardment by multicharge cosmic ray ions

The mechanism of ion-stimulated erosion of atmosphereless solar system bodies is suggested and investigated. A theoretical model for the brittle surface erosion resulting under the effect of multicharge ion cosmic rays is analyzed. It is shown that the thermoelastic waves originated in the energetic track of a very heavy ion can result in the near-surface stresses exceeding the dynamic tensile strength of the surface material for any atmosphereless solar system body. The thermoelastic wave surface arrival yields brittle erosion of the material and ejection of this latter fragments (the track-breaking process). Thus ejected dust grains have plano-oblong shape, average mass on the order of 10^–17 g and velocity up to 400 m/sec providing the surface erosion rate of 10^–1 ÷ 3 · 10² »/year (near the Earth orbit) which depends upon the surface material (rock or ice). Possible track-breaking consequences, in particular, presence of the dust fraction of ultramicron grains and their aggregates on the lunar surface are discussed. Near the bodies with the radii from 10 to 300 km predicted is the existence of extended dust cocoons consisting of ultramicron and submicron grains. Smaller objects (asteroids, comets, smallest satellites of planets, meteoroids, etc.) can serve sources of permanent dust wind of ultramicron and submicron sized grains escaping from their surfaces. The interplanetary dust yield owing to the ion-stimulated erosion of these bodies is not less than 10¹² g/year. Possible interpreting in the frames of track-breaking process some observational data and effects, including existence of dust grains with the mass of 10^–18 ÷ 10^–17 g near the Halley's comet and the nature of 2060 Chiron dust coma is discussed. To prove the theory, observational identification and investigation of dust phenomena complex related to the ion-stimulated erosion of atmosphereless bodies, suggested is employing extreme ultraviolet and far infrared/submillimeter wavelengths, as well as polarimetric methods.     

The internal activity and thermal evolution of Earth-like planets

We model the internal thermal evolution of planets with Earth-like composition and masses ranging from 0.1 to 10 Earth masses over a period of 10 billion years. We also characterize the internal activity of the planets by the velocity of putative tectonic plates, the rate at which mantle material is processed through melting zones, and the time taken to process one mantle mass. The more massive the planet the larger its processing rate (?), which scales approximately as ?∝M0.8-1.0. The processing times for all the planets increase with time as they cool and become less active. As would be expected, the surface heat flow scales with planet mass. All planets have similar declines in mantle temperature except for the largest, in which pressure effects cause a larger decline. The larger planets have higher mantle temperatures over all times. The less massive the planet, the larger the decrease in core temperature with time. The core heat flow is also found to decrease more rapidly for smaller planet masses. Finally, rough predictions are made for the time required to generate an atmosphere from estimates of the time to degas water and carbon dioxide in mantle melting zones. The degassing times depend strongly on the initial temperature of the planet, but for the temperatures used in our model all the planets degas within ∼32 Ma after their formation.