M. Gastineau

INPOP06: a new numerical planetary ephemeris

INPOP06 is the new numerical planetary ephemeris developed at the IMCCE-Observatoire de Paris. INPOP (Integrateur Numerique Planetaire 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).

Strong chaos induced by close encounters with Ceres and Vesta

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.

Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity

The current knowledge of Mercury orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made by Mariner 10 in the 70s, and MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired dur- ing 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 PPN- formalism. Our estimations of PPN parameters ( and ) are more stringent than previous results.

Constraints on the location of a possible 9th planet derived from the Cassini data

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° .

Electron density distribution and solar plasma correction of radio signals using MGS, MEX, and VEX spacecraft navigation data and its application to planetary ephemerides

The Mars Global Surveyor (MGS), Mars Express (MEX), and Venus Express (VEX) experienced several superior solar conjunctions. These conjunctions cause severe degradations of radio signals when the line of sight between the Earth and the spacecraft passes near to the solar corona region. The primary objective of this work is to deduce a solar corona model from the spacecraft navigation data acquired at the time of solar conjunctions and to estimate its average electron density. The corrected or improved data are then used to fit the dynamical modeling of the planet motions, called planetary ephemerides. We analyzed the radio science raw data of the MGS spacecraft using the orbit determination software GINS. The range bias, obtained from GINS and provided by ESA for MEX and VEX, are then used to derive the electron density profile. These profiles are obtained for different intervals of solar distances:

Tests of GR with INPOP15a planetary ephemerides: estimations of possible supplementary advances of perihelia for Mercury and Saturn

Planetary ephemerides are a good tool for studying general relativity at the scale of our solar system. We present here new evaluations of advances of perihelia for Mercury and Saturn.

Parallel operations of sparse polynomials on multicores: I. multiplication and Poisson bracket

The multiplication of the sparse multivariate polynomials using the recursive representations is revisited to take advantage on the multicore processors. We take care of the memory management and load-balancing in order to obtain linear speedup. The widely used Poisson bracket during the studies of the dynamical systems had been parallelized on these computers. Benchmarks are presented, comparing our implementation to the other computer algebra systems.

Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

The Peregrine breather of order eleven (P11 breather) solution to the focusing one-dimensional nonlinear Schrodinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P11 breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.

18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation

We present here new solutions of the focusing one-dimensional nonlinear Schrodinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.

Twenty Two Parameter Deformations of the Twelfth Peregrine Breather Solutions to the NLS Equation

The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schrodinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation in terms of explicit quotients of polynomials of degree 156 in x and t by a product of an exponential depending on t are obtained. The patterns of the modulus of these solutions in the