Abstract
Effects of spherically asymmetric terms of the Phobos gravity en trajectories for Phobos exploration in close proximity such as hovering close to the surface of Phobos, horizontal movement in hovering condition, and trajectories connecting the L1 and L2 points of the Mars-Phobos system are analyzed in this paper. Harmonic coefficients of the gravitational potential of Phobos obtained by Chao et al. are used in this analysis. The required velocity increment ΔV through the hovering of 7.66 hours, which is the period of Phobos orbit around the Mars, is obtained over the whole regions of Phobos. The minimum value of ΔV was about 82 m/s at the sub-Mars and the anti-sub-Mars points in the point-mass approximation. For the gravity with asymmetric terms it is about 120 m/s at the anti-sub-Mars point. The maximum value of ΔV was about 301 m/s at poles in the point-mass approximation. For the gravity with asymmetric terms it ls about 340 m/s at the neighborhood of the Stickney crater. In the horizontal movement in hovering condition, it turns out that the optimum movement velocity is not so affected by the asymmetric terms of the Phobos gravity. A trajectory connecting the L1 and L2 points is obtained even in the gravity model with asymmetric terms. The obtained trajectory is also asymmetric. The minimum altitude of the orbit, the transit time, and the necessary velocity increment are about 1.5 km, 3.4 hours, and 21 m/s, respectively. From the error analysis, it is found that in the case of the symmetric trajectory of the point-mass model, the sensitivity to the initial velocity error ls very high, while not so high in the case of the asymmetric trajectory considering the harmonics of the gravity potential.
