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INPOP08, a 4-D Planetary Ephemeris: from Asteroid and Time-Scale Computations to ESA Mars Express and Venus Express Contributions

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INPOP08, a 4-D Planetary Ephemeris: from Asteroid and Time-Scale Computations to ESA Mars Express and Venus Express Contributions Astronomy & Astrophysics manuscript no. inpop08.2.v3c June 10, 2009 (DOI: will be inserted by hand later) INPOP08, a 4-D planetary ephemeris: From asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. A. Fienga1;2, J. Laskar1, T. Morley3, H. Manche1, P. Kuchynka1, C. Le Poncin-Lafitte4, F. Budnik3, M. Gastineau1, and L. Somenzi1;2 1 Astronomie et Syst`emesDynamiques, IMCCE-CNRS UMR8028, 77 Av. Denfert-Rochereau, 75014 Paris, France 2 Observatoire de Besan¸con,CNRS UMR6213, 41bis Av. de l'Observatoire, 25000 Besan¸con,France 3 ESOC, Robert-Bosch-Str. 5, Darmstadt, D-64293 Germany 4 SYRTE, CNRS UMR8630, Observatoire de Paris, 77 Av. Denfert-Rochereau, 75014 Paris, France June 10, 2009 Abstract. The latest version of the planetary ephemerides developed at the Paris Observatory and at the Besan¸conObservatory is presented here. INPOP08 is a 4-dimension ephemeris since it provides to users positions and velocities of planets and the relation between TT and TDB. Investigations leading 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 (ESA) deduced from the tracking of the Mars Express (MEX) and Venus Express (VEX) missions are presented as well as the normal point deduced from the Cassini mission. We show the huge impact brought by these observations in the fit of INPOP08, especially in terms of Venus, Saturn and Earth-Moon barycenter orbits. Key words. celestial mechanics - ephemerides 1. Introduction ephemeris. The basic idea is to provide to users po- sitions and velocities of Solar System celestial objects, Since the first release, INPOP06, of the plane- and also, time ephemerides relating the Terrestrial time- tary ephemerides developed at Paris and Besan¸con scale, TT, and the time argument of INPOP, the so-called Observatories, (Fienga et al. 2008, www.imcce.fr/inpop), Barycentric Dynamical Time TDB, based on the defini- several improvements have been conducted on the dynam- tion adopted by the International Astronomical Union in ical modeling of the INPOP ephemeris. The observation 2006. Such a release of planet and time ephemerides dataset has also been substantially increased, especially enable us to go towards four-dimensional plane- with the addition of ranging data from the ESA space mis- tary ephemerides. Section 2 describes the INPOP pro- sions Mars Express and Venus Express. Moreover, the per- cedure for the computation of the TT-TDB relation. spective of highly accurate astrometric space missions like GAIA or highly accurate pulsar timing astrometry, Section 3 is devoted to a brief account of the new con- led to increase the consistency of the ephemeris reference straints and modeling implemented in INPOP for the as- frames by adopting time-scales that are in agreement with teroid perturbations. As in INPOP06, 300 asteroids are the definitions adopted by the International Astronomical included in the dynamical equations of INPOP08, and the Union in 2006. The resulting new version of INPOP plan- remaining ones are modelized as a ring. With respect to etary ephemerides, INPOP08, is presented here with the INPOP06, the ring model and the asteroid selection have description of its new features. The INPOP08 ephemeris been improved, and the precise description of these ad- has also been fitted to all available Lunar Laser Ranging vances are made in (Kuchynka et al, 2009). data (Manche et al., 2007). An important part of the new observations used for One of the novelties present in INPOP08 is the ad- the INPOP08 fit consists in the tracking data provided by dition, in the distribution of the ephemeris, of a time the ESA space missions Mars Express and Venus Express scale transformation TT-TDB that is coherent with the (Morley 2006a, 2007a, 2007b). These datasets are the first radio ranging data provided by ESA, and their acquisi- Send offprint requests to: A. Fienga, fi[email protected] tion and reduction process is described in section 4. VEX 2 Fienga et al: INPOP08, a 4-D planetary ephemeris observations bring a very important set of infor- based on (Damour,Soffel and Xu 1991) formal- mations on Venus orbit. It is especially of interest ism including spin/spin, mass/mass and mass/spin since this orbit is much less perturbed by aster- couplings. However, each fundamental reference system oids than Mars and therefore has greater potential has its own time-scale: TCB for the BCRS and TCG for for precise ephemeris motion, fundamental physics the GCRS. The relation between TCB and TCG can be testing and reference frame establishment. derived, but time transformations are only determined for The section 5 deals with the INPOP fit obtained by specified space-time events (one coordinate time and three comparisons between the dynamical modeling and the ob- spatial positions) so, at the geocenter, the transformation servations. In this process, 34 asteroid masses were fit- reads (Damour, Soffel and Xu 1991, Soffel et al. ted against only 5 in INPOP06. Comparisons are made 2003): between obtained asteroid masses and other published masses. Values for the fitted Earth-Moon barycenter and dT CG 1 1 1 Sun oblateness J are also given. We have also fitted the = 1 + α(TCB) + β(TCB) + O (1) 2 dT CB c2 c4 c5 AU and comparisons are provided with the latest deter- minations of DE414 (Standish 2006; Konopliv et al. 2006) c being the speed of light in a vacuum and where and DE421 (Folkner 2008). In addition, we have performed as well a second 1 GM fit, where the AU is given the IERS Conventions 2 X A α(TCB) = − vE − ; (2) 2 rEA 2003 value (IERS03), and the Solar GM is de- A6=E duced. 2 32 On several occasions, for planned high precision ob- 1 4 1 X GMA β(TCB) = − vE + 4 5 servations, we had some enquiries about the real accu- 8 2 rEA A6=E racy of the position or velocities given by the plane- ( tary ephemerides. This is actually a difficult question X GMA 3 2 2 + 4vA:vE − vE − 2vA to answer, but we have tried in section 6 to provide rEA 2 some estimates of these uncertainties, by comparison with A6=E 2 INPOP06 and DE421. The last section is devoted to the 1 1 vA:rEA + aA:rEA + conclusions and perspectives. 2 2 rEA ) X GMB + : (3) rAB 2. INPOP as a 4-D planetary ephemeris B6=A With INPOP08, we aim to produce planetary ephemerides as fully compatible as possible with the relativistic back- Capital latin subscripts A and B enumerate massive bod- ground recently adopted by the astronomical community ies, E corresponds to the Earth, MA is the mass of body and summarized by the IAU2000 and IAU2006 conven- A, rEA = xE − xA, rEA = jrEAj, vA = x_ A, aA = v_ A, tions (Soffel el al., 2003). This leads to the production of a dot signifying time derivative with respect to TCB and an ephemeris in TDB, and to the construction of a TT- xA being the BCRS position of body A. TDB transformation. The following subsections describe Eqs. (1), (2) and (3) exhibit that the time transfor- the various steps involved in this process and the impact mation between TCB and TCG is explicitly related to for the ephemeris users. the positions and velocities of Solar System bodies, so to the planetary ephemeris itself. As stressed by Klioner (2008), if we are distributing a time transformation to- 2.1. The TCB-TCG transformation gether with positions and velocities, we are building a Two reference systems are defined: a global one, the four-dimensional planetary ephemeris. This time transfor- Barycentric Celestial Reference System (BCRS), covering mation will be called in the following time ephemeris to the whole Solar System and a local one, the Geocentric be close to the terminology of Irwin and Fukushima Celestial Reference System (GCRS), which is physically (1999). suitable for the modeling of processes in the vicinity of An issue remains. The use of TCB in planetary the Earth. BCRS is particularly useful when one wants ephemerides should induce important changes in numer- to model the light propagation or motion of celestial ob- ical values of planet masses, initial conditions and astro- jects in the Solar System. We can then, in the mass- nomical unit commonly adopted by users. monopoles approximation, write the equation of mo- Therefore, even if a TCB-based ephemeris and tion of bodies as well as the conservation laws satis- a TDB-based ephemeris are related linearly, cau- fied by the Solar System barycenter (see Damour and tion has to be taken when one wants to shift from Vokrouhlick´y1995); all these features being already im- one ephemeris to an other as it will induce large plemented in INPOP06. (Damour and Vokrouhlick´y changes for all users. For a more complete discus- 1995) gives the complete conservation equations sion, see for instance (Klioner 2008). Fienga et al: INPOP08, a 4-D planetary ephemeris 3 2.2. The TT-TCG transformation B3 of IAU2006 which made TDB a fixed linear function of TCB as follows: The IAU time realization is done by the International Atomic Time (TAI) with a service running since 1958 and T DB = TCB − LB(JD − T0) × 86400 + T DB0; (9) attempting to match the rate of proper time on the geoid −8 where T0 = 2443144:5003725, LB = 1:550519768 × 10 , by using an ensemble of atomic clocks spread over the T DB = −6:55 × 10−5s and JD is the TCB Julian date. surface and low orbital space of the Earth. TAI is con- 0 TCB value (like TT and TCG ones) is T0 for the event ventionally related to the Terrestrial Time (TT) and the 1977 January 1 00h 00m 00s TAI at the geocenter.
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