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 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 PPN-formalism. Our estimations of PPN parameters (beta and gamma?) are more stringent than previous results.Comment: Accepted by A&

Long term evolution and chaotic diffusion of the insolation quantities of Mars.

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 of 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, the 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 function of the eccentricity and obliquity are explicited with simple analytical formulas.We found an averaged eccentricity of Mars over 5 Gyr of e=0.0690 with standard deviation s_e=0.0299, while the averaged value of the obliquity is 37.62 deg with a standard deviation of 13.82 deg and a maximal value of 82.035 deg.We find that the probability for Mars obliquity to have reached more than 60 degin 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 deg, 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 for the eccentricity 0.068 and 41.80 deg for the obliquity

A long term numerical solution for the insolation quantities of the Earth

22 may 2004We 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 \etal, 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 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 405000 yr. The uncertainty of this time scale over 100 Myr should be about $0.1\%$, and $0.2\%$ over the full Mesozoic era

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

International audienceThe Peregrine breather of order eleven (P11 breather) solution to the focusing one-dimensional nonlinear Schrödinger 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

Tenth order solutions to the NLS equation with eighteen parameters

We present here new solutions of the focusing one dimensional non linear Schrödinger 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 as found for the lower orders

Observational constraint on the radius and oblateness of the lunar core-mantle boundary

International audienceLunar laser ranging (LLR) data and Apollo seismic data analyses, revealed independent evidence for the presence of a fluid lunar core. However, the size of the lunar fluid core remained uncertain by $\pm55$ km (encompassing two contrasting 2011 Apollo seismic data analyses). Here we show that a new description of the lunar interior's dynamical model provides a determination of the radius and geometry of the lunar core-mantle boundary (CMB) from the LLR observations. We compare the present-day lunar core oblateness obtained from LLR analysis with the expected hydrostatic model values, over a range of previously expected CMB radii. The findings suggest a core oblateness ($f_c=(2.2\pm0.6)\times10^{-4}$) that satisfies the assumption of hydrostatic equilibrium over a tight range of lunar CMB radii ($\mathcal{R}_{CMB}=381\pm12$ km). Our estimates of a presently-relaxed lunar CMB translates to a core mass fraction in the range of $1.59-1.77\%$ with a present-day Free Core Nutation (FCN) within $(367\pm100)$ years

Long term evolution and chaotic diffusion of the insolation quantities of Mars.

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 of 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, the 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 function of the eccentricity and obliquity are explicited with simple analytical formulas.We found an averaged eccentricity of Mars over 5 Gyr of e=0.0690 with standard deviation s_e=0.0299, while the averaged value of the obliquity is 37.62 deg with a standard deviation of 13.82 deg and a maximal value of 82.035 deg.We find that the probability for Mars obliquity to have reached more than 60 degin 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 deg, 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 for the eccentricity 0.068 and 41.80 deg for the obliquity

Impact of Infrared Lunar Laser Ranging on Lunar Dynamics

International audienceSince 2015, in addition to the traditional green (532nm), infrared (1064nm) has been the preferred wavelength for lunar laser ranging at the Calern lunar laser ranging (LLR) site in France. Due to the better atmospheric transmission of IR with respect to Green, nearly 3 times the number of normal points have been obtained in IR than in Green [ C.Courde et al 2016 ]. In our study, in addition to the historical data obtained from various other LLR sites, we include the recent IR normal points obtained from Calern over the 1 year time span (2015-2016), constituting about 4.2% of data spread over 46 years of LLR. Near even distribution of data provided by IR on both the spatial and temporal domain, helps us to improve constraints on the internal structure of the Moon modeled within the planetary ephemeris : INPOP [ Fienga et al 2015 ]. IERS recommended models have been used in the data reduction software GINS (GRGS,CNES) [ V.Viswanathan et al 2015 ]. Constraints provided by GRAIL, on the Lunar gravitational potential and Love numbers have been taken into account in the least-square fit procedure. New estimates on the dynamical parameters of the lunar core will be presented

Impact of Infrared Lunar Laser Ranging on Lunar Dynamics

International audienceSince 2015, in addition to the traditional green (532nm), infrared (1064nm) has been the preferred wavelength for lunar laser ranging at the Calern lunar laser ranging (LLR) site in France. Due to the better atmospheric transmission of IR with respect to Green, nearly 3 times the number of normal points have been obtained in IR than in Green [ C.Courde et al 2016 ]. In our study, in addition to the historical data obtained from various other LLR sites, we include the recent IR normal points obtained from Calern over the 1 year time span (2015-2016), constituting about 4.2% of data spread over 46 years of LLR. Near even distribution of data provided by IR on both the spatial and temporal domain, helps us to improve constraints on the internal structure of the Moon modeled within the planetary ephemeris : INPOP [ Fienga et al 2015 ]. IERS recommended models have been used in the data reduction software GINS (GRGS,CNES) [ V.Viswanathan et al 2015 ]. Constraints provided by GRAIL, on the Lunar gravitational potential and Love numbers have been taken into account in the least-square fit procedure. New estimates on the dynamical parameters of the lunar core will be presented