Can the mass of Martian Moons be measured by Gaia?

1. Previous determinations of Phobos and Deimos mass: Authors GM Phobos (10-3km3s-2) GM Deimos (10-3km3s-2) Hildebrand, 1979 - 0.12 Williams et al. 1988 0.85+/-0.07 0.12+/-0.01 Kolyuka et al. 1990 0.722+/-0.005 - Smith et al. 1995 0.587+/-0.033 0.091+/-0.055 Can the mass of Martian Moons be measured by Gaia? V. Lainey(1,2), P. Tanga (3) (1) Royal Observatory of Belgium, 3 Avenue Circulaire, B1180 Bruxelles (2) IMCCE/Paris Observatory, UMR8028 du CNRS, 77 Avenue Denfert-Rochereau F-75014 Paris, France (3) Observatoire de la Côte d’Azur, BP 4229, 06304 Nice, France The Gaia mission will operate over five years, nominally starting from 2011. Several tens of accurate astrometric and photometric measurements of each of the Solar System bodies will be available. In this work we focus on the specific case of the moons of Mars, whose positions will be known with an uncertainty better than ~0.1 mas, never reached by ground or space-based observatories. So far, the mass of the Martian moons have been only deduced by Viking and Phobos 2 flybys. On the other hand, the mutual perturbations of one moon on the other have never been detected up to now. We investigate this question again, in order to derive the expected residuals in the current orbit solution due to mutual perturbations. This study represents a first step in our understanding of the role of Gaia for dynamical studies of the natural planetary satellites. Numerical results We first performed two numerical simulations, one including the mass of the Martian moons (Williams et al. 1988 for Phobos and Smith et al. 1995 for Deimos) and one putting the mass values to zero. Let us recall that the introduction of the satellite masses induce mutual perturbations and also secular acceleration (tidal effects). Below are the differences on the satellite distances between the two integrations using the 60 simulated Gaia observations. As expected, mainly secular terms arise here (see plots below). The moons of Mars, today 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. This acceleration is still the only way to deduce the dissipation inside Mars with an estimation for the dissipation function of Q=100+/-50 (Smith and Born, 1976; Yoder, 1982). However, such determination assumes that the mass of Phobos is known, which is still controversial and need further measurements (see Andert et al. 2004). Moreover, the density of the Martian moons is a crucial point to understand their internal structure and past history in regards to impact (Stickney crater) and capture scenarios. A low density will indicate some rubble pile configuration while a high density will indicate an asteroid capture. km Phobos km Deimos t (yr) t (yr) A more detailed analysis revealed that these drifts are induced essentially by mutual perturbations (tides do not appear clearly at this scale). In a second step we adjusted the zero-mass model trying to reproduce the simulated observations obtained when including the satellite masses, by an adjustement of initial conditions (initial positions and velocities). The best-fit yields a new serie of “residuals” representing the effect of mutual perturbations and tides which cannot vanish during the elaboration of ephemeris. This step is necessary to test the observability of the effects due to Martian moon masses. During the fit procedure, no weight was assigned, and the same 60 epochs were used. The observations by Gaia The Gaia satellite will play an important role in Solar System science, thanks to the extremely high accuracy of its astrometry, and to the wealth of spectro-photometric data (see also the poster by Cellino et al. 2005). Gaia will observe Mars ~60 times by its astrometric instrument, over 5 years. In order to study the observations of Phobos and Deimos, we simulated a whole sequence of detections of Mars by Gaia. We assume in the following that the same number of observations – at the same epochs - are available for its satellites. The statistics will not be affected by this choice. When observed by Gaia, the Mars system will be at an average phase angle of 33°. The corresponding magnitude for Phobos and Deimos will be around V=12.8 and V=13.4, respectively. At that brightness, the expected astrometric accuracy (for each observation, G2V star) is ~60 marcsec (mas), corresponding to 70 meters at the distance of Mars (1.58 AU on average for observations by Gaia). Such accuracy may allow the detection of tidal accelerations (induced by the action of the moons on the planet surface) and mutual perturbations of the Martian moons and so to fit their masses during ephemerides procedure. To emphasize the magnitude of such perturbations induced by the Martian moon masses in the ephemerides residuals, we have used numerical integration. Phobos Deimos km km t (yr) t (yr) Secular drifts have vanished and the residuals reach in this case a few hundreds meters on Phobos positions because of the tidal effects (induced by Phobos mass) and ~10 meters on Deimos position because of mutual perturbations (induced by Phobos mass). Given the accuracy of Gaia observations (60 mas, or 70 meters), the perturbations due to the mass of Phobos will be easily measured. A part of the observations occurs at lower distance (~1 AU or less) thus increasing the possibility of obtaining independent measurements of Phobos mass. The model We used a software called NOE (Numerical Orbit Elaboration) to model the motion of the satellites. NOE computations include the partial derivatives of the solutions with respect both to the initial conditions (positions and velocities) and to some physical parameters of the bodies (notably the mass and the orientation of the rotation axis). The tides have been introduced by a physical tidal bulge on the planet, following Mignard (1981). Our final modeling of the Martian moons include: -Martian Cnp, Snp oblateness coefficients with a truncation at the 12th order (using GMM-2B potential) -Tides raised by the moons on Mars -Gravitational perturbations of the Sun, the Earth, the Moon and Jupiter (using DE406) -The precession of Mars -The satellite mutual perturbations Conclusion We have proved that Martian moon masses may be detectable by Gaia. The accuracy of mass measurements will be highly dependent from GAIA’s distance to Mars at each epoch of observations. The precise evaluation of accuracies will require futher analysis. However, since the amplitude of the induced perturbations should be about linear, the mass of Phobos could be measured at a 10% level of accuracy, much better than other recent determinations. References: Cellino et al., DPS poster… Hildebrand C, Born G.H. and Duxburry T.C.Univ. texas press, 1979. Kolyuka Yu.F., Efimov A.E., Kudryavstev S.M., Margorin O.K., Tarasov V.P. and Tikhonov V.F., Sov. Astron. Lett. 16, 168-170, 1990. 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 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 Neumann G.A., Bills B.G., Smith D.E., Zuber M.T., 35th Lunar and Planetary Science Conference, 2004. Sharpless, B.P., Astron.J. v.51, 1945 Smith D.E., Lemoine G., Zuber M.T. Geophys. Res., 22, 2171-2174, 1995. Williams B.G., Duxbury T.C. and Hildebrand C.E., Lunar Planet. Sci Conf., XIX, 1274, 1988. Smith, J.C., Born, G.H., Icarus, v.27, 1976 Yoder, C., Icarus, v.49, 1982 This work benefited from the support of the European Community's Improving Human Potential Programme under contract RTN2-2001-00414, MAGE