Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

Abstract

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

Systematic performance-oriented guidance tuning for descent & landing on small planetary bodies

“…In this work, each coefficient is assumed to follow a Gaussian distribution with standard deviation equal to its nominal value. Further details on this assumption and on the nominal GH coefficients are provided in (Zamaro & Biggs, 2015;Joffre et al, 2017).…”

“…where the state vector r (3) and become particularly complex due to the frame transformations involved, see (Zamaro & Biggs, 2015). The remaining terms account for the non-inertial acceleration caused by the fact that the BCBF frame is rotating with Phobos at a rate ω Pho .…”

Synthesis and analysis of robust control compensators for Space descent & landing

“…In this equation, the first 3 terms represent respectively the gravity of Phobos on the spacecraft (SC), Mars on the spacecraft, and Mars on Phobos, computed as a function of the position r of the spacecraft relative to Phobos and of the latter's location around Mars (via its true anomaly ν ). These calculations rely on the potential description of Equation and become particularly complex due to the frame transformations involved, as detailed in the work of Zamaro and Biggs . The remaining terms account for the noninertial acceleration caused by the fact that the BCBF frame is rotating with Phobos at rate ω Pho .…”

Robust Control Compensation for Space Descent & Landing *

“…Furthermore, due to the irregular shape and mass distribution of Phobos, the gravity of the moon cannot be accurately accounted for by a spherical field, thus it has to be described using a gravity harmonics (GH) model. In this case, using spherical coordinates (r, θ, φ) for distance to barycentre, co-latitude and longitude, as well as R for a reference radius and µ g for the gravitational constant, the gravity potential is given by [8]:…”