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.
We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in Laskar (2000, Phys. Rev. Lett., 84, 3240). Since then, the AMD has been ...revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database for which the orbital elements are sufficiently well known.
ABSTRACT
Eccentricity is a parameter of particular interest as it is an informative indicator of the past of planetary systems. It is however not always clear whether the eccentricity fitted on ...radial velocity data is real or if it is an artefact of an inappropriate modelling. In this work, we address this question in two steps: we first assume that the model used for inference is correct and present interesting features of classical estimators. Secondly, we study whether the eccentricity estimates are to be trusted when the data contain incorrectly modelled signals, such as missed planetary companions, non-Gaussian noises, correlated noises with unknown covariance, etc. Our main conclusion is that data analysis via posterior distributions, with a model including a free error term gives reliable results provided two conditions. First, convergence of the numerical methods needs to be ascertained. Secondly, the noise power spectrum should not have a particularly strong peak at the semiperiod of the planet of interest. As a consequence, it is difficult to determine if the signal of an apparently eccentric planet might be due to another inner companion in 2:1 mean motion resonance. We study the use of Bayes factors to disentangle these cases. Finally, we suggest methods to check if there are hints of an incorrect model in the residuals. We show on simulated data the performance of our methods and comment on the eccentricities of Proxima b and 55 Cnc f.
The discovery of the chaotic behavior of the planetary orbits in the Solar System Laskar, J., 1989. Nature 338, 237–238; Laskar, J., 1990. Icarus 88, 266–291 was obtained using numerical integration ...of averaged equations. In Laskar, J., 1994. Astron. Astrophys. 287, L9–L12, these same equations are integrated over several Gyr and show the evidence of very large possible increase of the eccentricity of Mercury through chaotic diffusion. On the other hand, in the direct numerical integration of Ito and Tanikawa Ito, T., Tanikawa, K., 2002. Mon. Not. R. Astron. Soc. 336, 483–500 performed without general relativity over
±
4
Gyr
, the eccentricity of Mercury presented some chaotic diffusion, but with a maximal excursion smaller than about 0.35. In the present work, a statistical analysis is performed over more than 1001 different integrations of the secular equations over 5 Gyr. This allows to obtain for each planet, the probability for the eccentricity to reach large values. In particular, we obtain that the probability of the eccentricity of Mercury to increase beyond 0.6 in 5 Gyr is about 1 to 2%, which is relatively large. In order to compare with Ito and Tanikawa Ito, T., Tanikawa, K., 2002. Mon. Not. R. Astron. Soc. 336, 483–500, we have performed the same analysis without general relativity, and obtained even more orbits of large eccentricity for Mercury. In order to clarify these differences, we have performed as well a direct integration of the planetary orbits, without averaging, for a dynamical model that do not include the Moon or general relativity with 10 very close initial conditions over 3 Gyr. The statistics obtained with this reduced set are comparable to the statistics of the secular equations, and in particular we obtain two trajectories for which the eccentricity of Mercury increases beyond 0.8 in less than 1.3 and 2.8 Gyr, respectively. These strong instabilities in the orbital motion of Mercury results from secular resonance between the perihelion of Jupiter and Mercury that are facilitated by the absence of general relativity. The statistical analysis of the 1001 orbits of the secular equations also provides probability density functions (PDF) for the eccentricity and inclination of the terrestrial planets (Mercury, Venus, the Earth and Mars) that are very well approximated by Rice PDF. This provides a very simple representation of the planetary PDF over 5 Gyr. On this time-scale the evolution of the PDF of the terrestrial planets is found to be similar to the one of a diffusive process. As shown in Laskar Laskar, J., 1994. Astron. Astrophys. 287, L9–L12, the outer planets orbital elements do not present significant diffusion, and the PDFs of their eccentricities and inclinations are well represented by the PDF of quasiperiodic motions with a few periodic terms.
To explain the unusual distribution of Kuiper belt objects, several authors have advocated the existence of a super-Earth planet in the outer solar system. It has recently been proposed that a 10 M⊕ ...object with an orbit of 700 AU semi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper belt objects around Sedna. Here we use the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. We test the possibility of adding the proposed planet without increasing the residuals of the planetary ephemerides, fitted over the whole INPOP planetary data sample. We demonstrate that the presence of such an object is not compatible with the most sensitive data set, the Cassini radio ranging data, if its true anomaly is in the intervals −130°: −100° or −65°:85° . Moreover, we find that the addition of this object can reduce the Cassini residuals, with a most probable position given by a true anomaly v = 117.8°+11°-10° .
Abstract
We present here the new INPOP lunar ephemeris, INPOP17a. This ephemeris is obtained through the numerical integration of the equations of motion and of rotation of the Moon, fitted over 48 ...yr of lunar laser ranging (LLR) data. We also include the 2 yr of infrared LLR data acquired at the Grasse station between 2015 and 2017. Tests of the universality of free-fall are performed. We find no violation of the principle of equivalence at the (−3.8 ± 7.1) × 10−14 level. A new interpretation in the frame of dilaton theories is also proposed.
The current knowledge of Mercury’s orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER ...made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform general relativity tests of the parametrized post-Newtonian (PPN) formalism. Our estimations of PPN parameters (γ and β) are more stringent than previous results.
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 ∼3.34 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth.
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. CITE) 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. CITE), 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. CITE). 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.
The angular momentum deficit (AMD)-stability criterion allows to discriminate between a priori stable planetary systems and systems for which the stability is not granted and needs further ...investigations. AMD-stability is based on the conservation of the AMD in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first-order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first-order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first-order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopædia.
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