The Dynamical Environment of the Cometary Nucleus 67P/Churyumov-Gerasimenko

The Rosetta mission has revealed the comet 67P/Churyumov-Gerasimenko has an asymmetric dumbbell shape with two rather large heads separated on one side by a deep valley, or neck. The focus of this research is to provide an efficient method to represent the gravitational field of such an irregularly shaped body, especially close to the surface, where the usually adopted expansion of the potential in spherical harmonics does not converge. Methods are developed to expand the gravitational potential in Cartesian coordinates using inertial functions as an extension of inertial integrals introduced by MacMillan in 1930. A mapping is then developed that allows to express the harmonic expansion coefficients of the internal potential within the Hotine sphere in terms of inertial functions. This allows the numerical evaluation of the gravitational potential to integrate orbital motion of natural and artificial bodies in close proximity to the cometary nucleus. A successful search is conducted for periodic orbits around the nucleus. Finally, a method is introduced to desing artificial, displaced, Keplerian orbits periodic in the comet-fixed reference system as a tool to explore the comet's valley.