Abstract. We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from −250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar et al. 1993) by using a direct integration of the gravitational equations for the orbital motion, and by improving the dissipative contributions, in particular in the evolution of the Earth-Moon System. The orbital solution has been used for the calibration of the Neogene period (Lourens et al. 2004), and is expected to be used for age calibrations of paleoclimatic data over 40 to 50 Myr, eventually over the full Palaeogene period (65 Myr) with caution. Beyond this time span, the chaotic evolution of the orbits prevents a precise determination of the Earth's motion. However, the most regular components of the orbital solution could still be used over a much longer time span, which is why we provide here the solution over 250 Myr. Over this time interval, the most striking feature of the obliquity solution, apart from a secular global increase due to tidal dissipation, is a strong decrease of about 0.38 degree in the next few millions of years, due to the crossing of the s 6 + g 5 − g 6 resonance (Laskar et al. 1993). For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we propose to use the term of largest amplitude in the eccentricity, related to g 2 − g 5 , with a fixed frequency of 3.200 /yr, corresponding to a period of 405 000 yr. The uncertainty of this time scale over 100 Myr should be about 0.1%, and 0.2% over the full Mesozoic era.

As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, we provide here a precise solution for the evolution of Mars' spin over 10 to 20 Myr. Over 250 Myr, we present a statistical study of its possible evolution, when considering the uncertainties in the present rotational state. Over much longer time span, reaching 5 Gyr, chaotic diffusion prevails, and we have performed an extensive statistical analysis of the orbital and rotational evolution of Mars, relying on Laskar's secular solution of the Solar System, based on more than 600 orbital and 200 000 obliquity solutions over 5 Gyr. The density functions of the eccentricity and obliquity are specified with simple analytical formulas. We found an averaged eccentricity of Mars over 5 Gyr of 0.0690 with standard deviation 0.0299, while the averaged value of the obliquity is 37.62 • with a standard deviation of 13.82 • , and a maximal value of 82.035 •. We find that the probability for Mars' obliquity to have reached more than 60 • in the past 1 Gyr is 63.0%, and 89.3% in 3 Gyr. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62 • , with the addition of a random noise allowing a slow diffusion beyond this limit. We can also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80 • for the obliquity.

We present here a new solution for the astronomical computation of the orbital motion of the Earth spanning from 0 to −250 Myr. The main improvement with respect to our previous numerical solution La2004 is an improved adjustment of the parameters and initial conditions through a fit over 1 Myr to a special version of the highly accurate numerical ephemeris INPOP08 (Intégration Numérique Planétaire de l'Observatoire de Paris). The precession equations have also been entirely revised and are no longer averaged over the orbital motion of the Earth and Moon. This new orbital solution is now valid over more than 50 Myr in the past or into the future with proper phases of the eccentricity variations. Owing to the chaotic behavior, the precision of the solution decreases rapidly beyond this time span, and we discuss the behavior of various solutions beyond 50 Myr. For paleoclimate calibrations, we provide several different solutions that are all compatible with the most precise planetary ephemeris. We have thus reached the time where geological data are now required to discriminate between planetary orbital solutions beyond 50 Myr.

International audienceCompared to the previous INPOP versions, the INPOP10a planetary and lunar ephemeris has several improvements. For the planets of our solar system, no big change was brought in the dynamics but improvements were implemented in the fitting process, the data sets used in the fit and in the selection of fitted parameters. We report here the main characteristics of the planetary part of INPOP10a like the fit of the product of the Solar mass with the gravitational constant (GM$_{\odot}$) instead of the astronomical unit. Determinations of PPN parameters as well as adjustments of the Sun J2 and of asteroid masses are also presented. New advances of nodes and perihelia of planets were also estimated and are given here. As for INPOP08, INPOP10a provides to the user, positions and velocities of the planets, the moon, the rotation angles of the Earth and the Moon as well as TT-TDB chebychev polynomials at http://www.imcce.fr/inpo

It has been established that, owing to the proximity of a resonance with Jupiter, Mercury's eccentricity can be pumped to values large enough to allow collision with Venus within 5 Gyr (refs 1-3). This conclusion, however, was established either with averaged equations that are not appropriate near the collisions or with non-relativistic models in which the resonance effect is greatly enhanced by a decrease of the perihelion velocity of Mercury. In these previous studies, the Earth's orbit was essentially unaffected. Here we report numerical simulations of the evolution of the Solar System over 5 Gyr, including contributions from the Moon and general relativity. In a set of 2,501 orbits with initial conditions that are in agreement with our present knowledge of the parameters of the Solar System, we found, as in previous studies, that one per cent of the solutions lead to a large increase in Mercury's eccentricity-an increase large enough to allow collisions with Venus or the Sun. More surprisingly, in one of these high-eccentricity solutions, a subsequent decrease in Mercury's eccentricity induces a transfer of angular momentum from the giant planets that destabilizes all the terrestrial planets approximately 3.34 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth.

We consider the full Solar System including (1) Ceres and some of the main asteroids, (2) Pallas, (4) Vesta, (7) Iris, and (324) Bamberga. We show that close encounters among these small bodies induce strong chaotic behavior in their orbits and in those of many asteroids that are much more chaotic than previously thought. Even if space missions will allow very precise measurements of the positions of Ceres and Vesta, their motion will be unpredictable over 400 kyr. As a result, it will never be possible to recover the precise evolution of the Earth's eccentricity beyond 60 Myr. Ceres and Vesta thus appear to be the main limiting factors for any precise reconstruction of the Earth orbit, which is fundamental for the astronomical calibration of geological timescales. Moreover, collisions of Ceres and Vesta are possible, with a collision probability of 0.2% per Gyr.

INPOP06 is the new numerical planetary ephemeris developed at the IMCCE-Observatoire de Paris. INPOP (Intégrateur Numérique Planétaire de l'Observatoire de Paris) is a numerical integration of the motion of the nine planets and the Moon fitted to the most accurate available planetary observations. It also integrates the motion of 300 perturbing main belt asteroids, the rotation of the Earth and the Moon libration. We used more than 55 000 observations including the latest tracking data of the Mars Global Surveyor (MGS) and Mars Odyssey (Odyssey) missions. The accuracy obtained with INPOP06 is comparable to the accuracy of recent versions of the JPL DE ephemerides (DE414, Standish 2003, JPL IOM, 312N, 03; Konopliv et al. 2006, Icarus, 182, 23) and of the EPM ephemerides (EPM2004, Pitjeva 2005, Sol. Syst. Res., 39, 176).Key words. celestial mechanics -ephemerides -astrometry IntroductionThe launch by NASA of the first interplanetary missions is a part of a considerable and continuous effort to develop and improve planetary ephemerides. The Jet Propulsion Laboratory (JPL) was entrusted with this task and produced many ephemerides combining the best theories and the most recent observational techniques, such as range measurements or VLBI tracking. Major improvements in observational accuracy (Lunar Laser Ranging, range and VLBI spacecraft tracking) permitted by modern technology, and in response to more demanding needs, have led to comparable improvements in the accuracy of the planetary and lunar ephemerides. Based on some first versions of the numerical integration of planetary motions (see for instance Devine & Dunham 1966;Ash et al. 1971), the DE96 JPL ephemerides (Standish et al. 1976) were among the first of the known and widely distributed accurate numerical ephemerides fitted to observations developed by JPL. These were followed by DE200 (Standish 1990), DE403 (Standish et al. 1995) and DE405 (Standish 1998). All these ephemerides are numerically integrated with a variable step-size, variable-order, Adams method. Their dynamical model includes point-mass interactions between the nine planets, the Sun and asteroids, relativistic PPN effects (Moyer 1971(Moyer , 2000, figure effects, Earth tides and lunar librations (Newhall et al. 1983). Since DE96, some improvements have been added to the DE ephemerides, and new ephemerides such as DE409 (Standish 2004), DE410 (Standish 2005) and DE414 (Standish 2003;Konopliv et al. 2006) were constructed and fitted on increasingly dense sets of space mission tracking data. Numerical solutions have also being developed at the Institute of Applied Astronomy of the Russian Academy of Sciences (IAA RAS). They are based on a dynamical model very similar to the JPL one. These ephemerides, EPM, are also fitted to optical, radar and space tracking data and have an accuracy comparable to the JPL ephemerides (Krasinsky et al. 1982;1986;1993;Pitjeva 2001Pitjeva , 2005.For many years, the accurate planetary ephemerides built at the JPL have been the only source of numerical ep...

The latest version of the planetary ephemerides developed at the Paris Observatory and at the Besançon Observatory is presented. INPOP08 is a 4-dimension ephemeris since it provides positions and velocities of planets and the relation between Terrestrial Time and Barycentric Dynamical Time. Investigations to improve the modeling of asteroids are described as well as the new sets of observations used for the fit of INPOP08. New observations provided by the European Space Agency deduced from the tracking of the Mars Express and Venus Express missions are presented as well as the normal point deduced from the Cassini mission. We show importance of these observations in the fit of INPOP08, especially in terms of Venus, Saturn and Earth-Moon barycenter orbits.