Phobos interior from librations determination using Doppler and star tracker measurements

Numerical simulations have been performed to assess the precision that can be obtained on Phobos libration angles by using two types of data acquired by a probe landed on the Martian moon: (1) Direct-To-Earth (DTE) Doppler data and (2) Star-Tracker (ST) data. Compared to independent estimates, combination of DTE and ST data provides the more precise estimates of Phobos libration angles at the 10 − 3 − 10 − 5 degree level. Short period libration amplitudes are functions of the relative moments of inertia. Thus their determination would provide constraints on mass distributions inside Phobos. We show that the longitudinal libration amplitude at the orbital period, while being clearly distinct from the resonance period, is the most interesting signal for that purpose, because it leads to the best precision on ( B − A ) / C ( 10 − 5 after only 10 weeks of operation). Nevertheless, we showed that inferring the individual moments of inertia A, B and C with a precision sufficient ( < 1 % ) to distinguish the rotational behavior of an homogenous from that of an heterogenous body requires the determination of one of the degree-two gravity field coefficient at the percent level. ition, we stress that ST and DTE data combination allows de-correlating librational motion from orbital motion since ST measurements are sensitive to the moonʹs rotation and do not depend on its ephemeris, whereas DTE Doppler data are sensitive to both motions as well as to Phobosʹ surface displacement due to the tides raised by Mars. Furthermore, the ephemeris of Phobos has to be known at the centimeter level to allow measuring the tidal surface displacement with enough precision to conclude on the nature of Phobosʹ interior (rubble pile versus monolithic) as one step toward constraining its origin and evolution.