Ejection-collision orbits in the modified Hill's problem
Tutor / directorCors Iglesias, Josep Maria
Document typeMaster thesis
Rights accessOpen Access
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Restricted three-body problem is a special version of n-body problem where an infinitesimal mass is attracted by the gravitation of two positive masses, called primaries, that follow a solution of the Kepler problem. When not specified, restricted three-body problem means the primaries follow a circular orbit with respect to their shared center of mass, that in a rotating reference frame can be seen as two fixed points. Numerical methods are used in these problems since analytical solutions do not exist. Hill’s problem is a modification of the restricted three-body problem where the third body is close to the secondary primary. Within this project, we started reviewing the Hill’s problem (equilibrium points, zero velocity curves, etc.) when the zero velocity curve is a closed region around the origin, since we are interested in ejection-collision orbits. After that we introduced a perturbation due to the solar radiation pressure. This gives us a more realistic model if we can apply to an asteroid. After that, we studied the collision manifold. To do that, first the equations of motion were regularized. We described the flow on the collision manifold. The equilibrium points play an important role together with their stable and unstable invariant manifolds. Finally, we studied the intersection of the previous invariant manifolds. This theoretical work aims to describe the orbits that have a close approach to secondary primary. The study of the ejection-collision orbits were the backbone of the close approaches. The characteristic changes of the desired orbits depending on various parameters are also examined.