Missions to the Asteroids

In this chapter, the focus is on asteroids. As the shape of most asteroids is quite variable, the gravitational modelling of the asteroids is first discussed in detail, providing several methods of modelling the gravitational field. These include spherical harmonics-based models, MacCullagh’s moment of inertia based modelling of the gravitational potential, geoid models, geometrical modelling, polyhedron model, discrete element models, modelling based on distributed concentrated masses as well as other models. Following a discussion of the equations of motion of an asteroid, particularly in the presence of a finite second body in addition to the central body and the spacecraft, the applications of these equations to the problem of synthesizing a feasible optimal trajectory is considered.