The Dynamical Environment of an Elongated Body. Application to the Restricted Full Two Body Problem

Computer Science

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Scientific paper

The problem of a massless particle orbiting a nonspherical body is described by computing an approximation of the gravitational potential and using the equations of motion of the Restricted Full Two Body Problem, RF2BP. The gravitational potential is computed by expanding it in terms of spherical Bessel functions and spherical harmonics and by matching this expression with the well known MacCullagh's formula. Therefore, we have developed an expression for the approximate potential of a body, of whom only the mass and moments of inertia are known, which is valid near the surface of the body, as well as, far away from it. This potential is then used to study the dynamical environment of a non-spherical body and how the stable and unstable manifolds of periodic orbits about Lagrange points, or about the entire body, affect the environment.

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