A planetary system with an escaping Mars

The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ _E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ _E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

The atmospheric composition and structure of Jupiter and Saturn from ISO observations: a preliminary review

Infrared spectra of Jupiter and Saturn have been recorded with the two spectrometers of the Infrared Space Observatory (ISO) in 1995–1998, in the 2.3–180 μm range. Both the grating modes (R=150–2000) and the Fabry-Pérot modes (R=8000–30,000) of the two instruments were used. The main results of these observations are (1) the detection of water vapour in the deep troposphere of Saturn; (2) the detection of new hydrocarbons (CH₃C₂H, C₄H₂, C₆H₆, CH₃) in Saturn’s stratosphere; (3) the detection of water vapour and carbon dioxide in the stratospheres of Jupiter and Saturn; (4) a new determination of the D/H ratio from the detection of HD rotational lines. The origin of the external oxygen source on Jupiter and Saturn (also found in the other giant planets and Titan in comparable amounts) may be either interplanetary (micrometeoritic flux) or local (rings and/or satellites). The D/H determination in Jupiter, comparable to Saturn’s result, is in agreement with the recent measurement by the Galileo probe (Mahaffy, P.R., Donahue, T.M., Atreya, S.K., Owen, T.C., Niemann, H.B., 1998. Galileo probe measurements of D/H and ³He/⁴He in Jupiters atmosphere. Space Science Rev. 84 251–263); the D/H values on Uranus and Neptune are significantly higher, as expected from current models of planetary formation.     

Models of Jupiter and Saturn after Galileo mission

New models of Jupiter are based on observational data provided by the Galileo spaceprobe, which considerably improved previously existing estimates of the helium abundance in the atmosphere of Jupiter. These data yield for Jupiter’s atmosphere 20% of the solar oxygen abundance and do not agree with the results of the analysis of the collision of comet Shoemaker-Levy 9 with Jupiter (10 times the solar value). Therefore, both the models of Jupiter with water-depleted and water-enriched atmosphere are considered. By analogy with Jupiter, trial models of Saturn with a water-depleted external envelope are also developed. The molecular-metallic phase transition pressure of hydrogen P_m was taken to be 1.5, 2 and 3 Mbar. Since Saturn’s internal molecular envelope is noticeably enriched in the IR-component (its weight concentration, 0.25–0.30, being by a factor of 3–4 higher than in Jupiter), the phase transition pressure in Saturn can be lower than in Jupiter. In the constructed models, the IR-core masses are 3–3.5 M_⊕ for Jupiter and 3–5.5 M_⊕ for Saturn. Jupiter’s and Saturn’s IR-cores can be considered embryos onto which the accretion of the gas occurred during the formation of the planets. The mass of the hydrogen–helium component dispersed in the zone of planetary formation constitutes ≈2–5 planetary masses for Jupiter and ≈11–14 planetary masses for Saturn.     

Resonant structures in the solar system

The resonance theory is discussed with respect to the Solar System with a view to show that every triad of successive planets in the Solar System follows Laplace's resonance relation. With rings now known to exist around three of the four major planets, scientists have begun to speculate about the possible existence of ring structure and one or two small planets going around the Sun itself. It is also believed that the ring systems may exist around the planets Neptune and Mars. In this paper an attempt is made to provide a basis to these beliefs using Laplace's resonance relation. The triads of successive innermost objects (rings and/or satellites) in the satellite — systems of Jupiter, Saturn and Uranus are also shown to follow Laplace's resonance relation.     

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus’ equilateral equilibrium points is investigated with respect to the inclination of the asteroid’s orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L ₄ and L ₅, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 × 10⁹ years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 ≤ a ≤ 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids’ orbit was varied in the range 0° < i < 60° and the semimajor axes were fixed. It turned out that only four ‘windows’ of stable orbits survive: these are the orbits for the initial inclinations 0° < i < 7°, 9° < i < 13°, 31° < i < 36° and 38° < i < 50°. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.     

Dynamical evolution of NEAs: Close encounters, secular perturbations and resonances

We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v ₆ (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some “fast-track” dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits.     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.     

Could CoRoT-7b and Kepler-10b be remnants of evaporated gas or ice giants?

We present thermal mass loss calculations over evolutionary time scales for the investigation if the smallest transiting rocky exoplanets CoRoT-7b (∼1.68R_Earth) and Kepler-10b (∼1.416R_Earth) could be remnants of an initially more massive hydrogen-rich gas giant or a hot Neptune-class exoplanet. We apply a thermal mass loss formula which yields results that are comparable to hydrodynamic loss models. Our approach considers the effect of the Roche lobe, realistic heating efficiencies and a radius scaling law derived from observations of hot Jupiters. We study the influence of the mean planetary density on the thermal mass loss by placing hypothetical exoplanets with the characteristics of Jupiter, Saturn, Neptune, and Uranus to the orbital location of CoRoT-7b at 0.017 AU and Kepler-10b at 0.01684 AU and assuming that these planets orbit a K- or G-type host star. Our findings indicate that hydrogen-rich gas giants within the mass domain of Saturn or Jupiter cannot thermally lose such an amount of mass that CoRoT-7b and Kepler-10b would result in a rocky residue. Moreover, our calculations show that the present time mass of both rocky exoplanets can be neither a result of evaporation of a hydrogen envelope of a “Hot Neptune” nor a “Hot Uranus”-class object. Depending on the initial density and mass, these planets most likely were always rocky planets which could lose a thin hydrogen envelope, but not cores of thermally evaporated initially much more massive and larger objects.     

Capture of dust grains in exterior resonances with planets

The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 Μm the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 10⁵ years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e ₀ ~ 0.48 of libration point for this resonance.     

Making other earths: dynamical simulations of terrestrial planet formation and water delivery

We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals, assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter's mass, position and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1-4 terrestrial planets inside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11 “habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100+oceans of water (1 ocean=1.5×10²⁴ g), and vary in mass between 0.23M_⊕ and 3.85M_⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1-2M_⊕ protoplanets which can serve as the accretion seeds for 2+M_⊕ planets with large water contents.     

Building the terrestrial planets: Constrained accretion in the inner Solar System

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.     

Structure of the Earth’s circumsolar dust ring

Interplanetary dust particles from comets and asteroids pervade the Solar System and become temporarily trapped into orbital resonances with Earth, leading to a circumsolar dust ring. Using the unique vantage point of the Spitzer Space Telescope from its Earth-trailing solar orbit, we have measured for the first time the azimuthal structure of the Earth’s resonant dust ring. There is a relative paucity of particles within 0.1 AU of the Earth, followed by an enhancement in a cloud that is centered 0.2 AU behind Earth with a width of 0.08 AU along the Earth’s orbit. The North ecliptic pole is ∼3% brighter at 8 μm wavelength when viewed from inside the enhancement. The presence of azimuthal asymmetries in debris disks around other stars is considered strong evidence for planets. By measuring the properties of the Earth’s resonant ring, we can provide “ground truth” to models for interactions of planets and debris disks, possibly leading to improved predictions for detectability of life-bearing planets. The low amplitude of the azimuthal asymmetry in the Earth’s circumsolar ring suggests significant contributions to the zodiacal light from particles that are large (>30 μm) or have large orbital eccentricity that makes capture into mean motion resonances inefficient.     

On the origin of the unusual orbit of Comet 2P/Encke

The orbit of Comet 2P/Encke is difficult to understand because it is decoupled from Jupiter—its aphelion distance is only 4.1 AU. We present a series of orbital integrations designed to determine whether the orbit of Comet 2P/Encke can simply be the result of gravitational interactions between Jupiter-family comets and the terrestrial planets. To accomplish this, we integrated the orbits of a large number of objects from the trans-neptunian region, through the realm of the giant planets, and into the inner Solar System. We find that at any one time, our model predicts that there should be roughly 12 objects in Encke-like orbits. However, it takes roughly 200 times longer to evolve onto an orbit like this than the typical cometary physical lifetime. Thus, we suggest that (i) 2P/Encke became dormant soon after it was kicked inward by Jupiter, (ii) it spent a significant amount of time inactive while rattling around the inner Solar System, and (iii) it only became active again as the ν₆ secular resonance drove down its perihelion distance.     

Planet X and the origins of the shower and steady state flux of short-period comets

In the planet X model periodic comet showers are associated with passages of the planet's perihelion and aphelion points through a primordial disk of comets believed to lie beyond the orbit of Neptune. A strong feature of this model is that the required orbital elements and mass of planet X are consistent with independently predicted values based on the residuals in the motions of Uranus and Neptune. Here we present a more extensive analysis of the model taking into account the fact that only those comets scattered directly into the zones of influence of Saturn and Jupiter can contribute to a shower whose duration is consistent with observation (≲ 15 myr). These requirements impose a minimum planetary inclination of ≈25°, which in turn restricts the semimajor axis to be ≲100 AU. A fraction of the comets scattered directly into the zones of influence of Uranus and Neptune will evolve on time scales of ∼10⁸ years into the steady state flux of short-period comets. We find that the absolute numbers of shower and steady state are comparable and compatible with the known terrestrial cratering rate, assuming the existence of long-lived extinct comet cores. Canonical planet X model parameters, deduced in part from the scattering dynamics analysis, are: semimajor axis ≈80 AU, eccentricity ≈0.3, inclination ≈45°, and mass ≈5m_⊕. An analysis is given which suggests that planet X, in its present orbit, can create the requisite density gradient of comets near perihelion and aphelion during the lifetime of the Solar System. The required inclination of planet X's orbit (≳25°) may explain the failure of previous surveys to discover the planet as its present latitude is not likely to be near the ecliptic. It it exists, the best immediate hope of finding planet X is the ongoing IRAS search in the 100-μm band and the full sky optical survey by Shoemaker and Shoemaker. Independent of the question of periodic comet showers, the existence of planet X and the comet disk can readily explain the origin of the steady state flux of short-period comets over a wide range of parameters.     

Far-infrared and submillimeter observations of the planets

New broadband observations in several passbands between 30 and 500 μm of Mercury, Venus, Mars, Jupiter, Saturn, and Uranus are presented. The best agreement between the data and various thermal models of Mars, Jupiter, and Uranus is obtained with a slightly cooler absolute temperature scale than that previously adopted by Armstrong et al. (1972). The effective temperature of Uranus is 58 ± 2°K, which is in agreement with its solar equilibrium temperature. The existence of an internal energy source of Saturn has been reconfirmed and must lie within the range of 0.9 to 3.2 times the absorbed solar flux. A depression exists in the spectra of Jupiter, Saturn, and Uranus between 80 and 300 μm, which may be a result of NH₃ opacity.     

Odyssey: a solar system mission

The Solar System Odyssey mission uses modern-day high-precision experimental techniques to test the laws of fundamental physics which determine dynamics in the solar system. It could lead to major discoveries by using demonstrated technologies and could be flown within the Cosmic Vision time frame. The mission proposes to perform a set of precision gravitation experiments from the vicinity of Earth to the outer Solar System. Its scientific objectives can be summarized as follows: (1) test of the gravity force law in the Solar System up to and beyond the orbit of Saturn; (2) precise investigation of navigation anomalies at the fly-bys; (3) measurement of Eddington’s parameter at occultations; (4) mapping of gravity field in the outer solar system and study of the Kuiper belt. To this aim, the Odyssey mission is built up on a main spacecraft, designed to fly up to 13 AU, with the following components: (a) a high-precision accelerometer, with bias-rejection system, measuring the deviation of the trajectory from the geodesics, that is also giving gravitational forces; (b) Ka-band transponders, as for Cassini, for a precise range and Doppler measurement up to 13 AU, with additional VLBI equipment; (c) optional laser equipment, which would allow one to improve the range and Doppler measurement, resulting in particular in an improved measurement (with respect to Cassini) of the Eddington’s parameter. In this baseline concept, the main spacecraft is designed to operate beyond the Saturn orbit, up to 13 AU. It experiences multiple planetary fly-bys at Earth, Mars or Venus, and Jupiter. The cruise and fly-by phases allow the mission to achieve its baseline scientific objectives [(1) to (3) in the above list]. In addition to this baseline concept, the Odyssey mission proposes the release of the Enigma radio-beacon at Saturn, allowing one to extend the deep space gravity test up to at least 50 AU, while achieving the scientific objective of a mapping of gravity field in the outer Solar System [(4) in the above list].