New ephemeris of Phobos and Mars Express close flybys V. Lainey (1), V. Dehant (1), P. Rosenblatt (1), T. Andert (2) and M. Pätzold (2) Several close flybys of Mars Express at the moon Phobos will occur in Such events are the opportunity for an improved estimate of Phobos gravity field. To achieve this goal, an ephemeris of Phobos at high precision is required. We present a new dynamical model of the motion of Phobos, fitted on observations from spacecraft and the latest Earth-based observations. Observations database of the Martian satellites (N.Emelianov) F.Colas, pic du midi Conclusion: We developed numerical ephemerides of the Martian system. In particular, tidal effects have been introduced by a rigorous formulation. This will provide after fit an estimation of k 2 and Q parameters. The fit of our model to the complete set of observations is still processing but will be finished soon. A routine will be available on request. Introduction: Discovered in 1877 by A.Hall, Phobos is particularly well known today for its secular acceleration, which may be the easiest observable one in the Solar system. Estimated for the first time in 1945 to deg/yr 2 by Sharpless, this value is today better constrained around deg/yr 2. This secular acceleration implies a decrease of the semi-major axis. Hence, Phobos is slowly evolving toward Mars, with a lifetime estimated to 30 million years. The modeling: Our ephemerides are the first completely numerical ephemerides of the Martian moons. Indeed, so far only analytical or semi-analytical ephemerides have been developped. The lack of orbital resonances among this system and the small masses of the satellites allowed a high precision for anaytical treatments. Even the tides raised by the satellites on Mars could have been modeled efficiently using a t 2 term in the satellites longitudes. However, the improvements and the increasing number of the observations (Earth-ground based and the spacecrafts ones) allow the introduction of a higher level of modeling. Among one of them, the spin/revolution coupling of both moons, become relevant in this context. The Observations: We have benefited of the astrometric database of N.Emelianov. It includes most of the Martian moons observations (including Morley’s catalogue, Viking and Phobos 2 observations). We included to this consistent set of observations some new observations made with MOLA (B.Bills, private communication). (1) Royal Observatory of Belgium, 3 Avenue Circulaire, B1180 Bruxelles (2) Institut für Geophysik und Meteorologie Zülpicherstr. 49 a Koeln References: Chapront-Touzé, M., A&A, v.240, 1990 Jacobson, R.A., Synnott, S.P., Campbell, J.K., A&A, v.225, 1989 Lemoine, F.G., Smith, D.E., Rowlands,D.D., Zuber, M.T., Neumann,G.A., Chinn,D.S., Pavlis,D.E., JGR, v.106, 2001 Mignard, F., MNRAS, v.194, 1981 Morley,T., A&A, v.228, 1990 Morley,T. A&AS, v.77, 1989 Neumann, G.A., Bills, B.G., Smith,D.E., Zuber,M.T., LPI, 2004 Sinclair, A.T., A&A,v.220, 1989 Sharpless, B.P., Astron.J. v51, 1945 We used of software called NOE (Numerical Orbit Elaboration) to modeled the motion of the satellites. NOE computations include the partial derivatives of the solutions with respect to the initial conditions (positions and velocities) but also to some physical parameters like the masses, the orientation of the northern pole of the bodies. More, the tides have been introduced by a physical tidal bulge on the planet, allowing us to compute partial derivatives with respect to the Martian Love number k 2 and the dissipation function Q. This work is supported by PRODEX and the MAGE network (Mars Geophysical European network). The Mars-Express Radio Science Experiment MaRS is funded by DLR Bonn under grant 50QP9909 The use of 196 Ground based observations made by D.Pascu (private communication) between 30 th August and 3 rd September 2003 will greatly increase the low number of observations (mainly by MGS) available these last ten years. The ephemerides representation: Chebychev polynomials are often used in ephemerides numerical solution because of their convenience. However the fast revolution motion of the Martian moons makes this solution not appropriate. Hence, we will apply a Fourier analysis treatment on the elliptical elements, for the representation of our solution. Because of the spacecraft needs (mainly Viking and Phobos 2 missions), many ephemerides of the Martian satellites have been elaborated at the end of the 80s. Most of them benefited from the spacecraft observations which are several kilometers accurate. -The tides raised by the moons on Mars -The gravitational perturbation of the Sun, the Earth, the Moon, Jupiter and Saturn (using DE406) -The precession of Mars -The oblateness of the Martian moons and their spin-orbit resonance However the strong acceleration makes the satellite orbit slowly drifting from its predicted one. Today, Phobos ephemerides are shifted of more than 12 kilometers. New ephemerides are necessary. Our modeling of the Martian introduces: -The Martian Cnp, Snp oblateness coefficients with a truncation at the 12 th order (using GMM-2B potential)