ROSETTA Mission: satellite orbits around a cometary nucleus

This paper discusses the problem of orbiting a comet nucleus from a perspective of orbital stability. The main forces perturbing the motion of the spacecraft around the comet : shape and rotation rate of the nucleus, comet outgassing, solar radiation pressure; are derived and quantified for the nominal case of the ROSETTA spacecraft at the comet Wirtanen. Their effects on the stability of the spacecraft orbit are analyzed in detail and orbital stability criteria are developed analytically. These criteria have been tested numerically, for select cases of interest, integrating the spacecraft orbit about a Wirtanen model constructed from mascons (mass concentrations at a point). This numerical model allows very irregular nucleus shapes to be modelled accurately if a large number of point masses is used. The stability criteria derived in this paper denote stability of the spacecraft against crashing onto the comet surface or escaping from the comet on a hyperbolic orbit. They are developed and applied only over the relatively short time scales that are of interest to a spacecraft mission. The stability criteria are expressed in terms of minimum periapsis radii for stability against the non-spherical gravitational field, in terms of maximum semi-major axis for stability against escape due to the solar radiation pressure, and in terms of preferred planes and orbit elements of a spacecraft orbit for stability against the combined non-gravitational forces of comet outgassing and solar radiation pressure. For orbits close to an irregular body the gravity perturbations are minimized, and orbital stability achieved, if the periapsis radius is above five mean comet radii if the inclination is close to 0° and above three mean comet radii if inclinations are between 90 and 180° with respect to the comet rotation pole. When considering the combined solar radiation pressure and comet outgassing forces, stable orbits can be found which ``freeze'' the orbit geometry with respect to the rotating reference frame defined along the comet-sun line. The dependence of these stability criteria on the comet model parameters is discussed. The analysis in this paper is general enough to be applicable to a wide range of orbital cases, including spacecraft orbits about asteroids and natural satellites about comets and asteroids.