Equilibrium points stability analysis for the asteroid 21 Lutetia

Abstract

This work investigates the stability of the equilibrium points that occur around the asteroid (21) Lutetia, assuming that this body has a constant velocity of rotation and is immersed in a gravitational field, whose force of attraction presents a perturbation with respect to the central force due to the irregular mass distribution of the asteroid. For the calculation of the potential, as well as of the effective potential, was used the method of the expansion of the potential in series, associated to the asteroid decomposition in tetrahedral elements. The zero velocity curves for a massless particle orbiting the gravitational environment were analyzed. The linearized dynamic equation in the vicinity of the equilibrium points, the associated characteristic equation, and the Jacobi constant were calculated. The validation of the results was ratified by simulations of trajectories around these equilibrium points, considering the gravitational field modelled. It should be emphasized the general nature of the procedures adopted in this work, that is, they can be applied to any other asteroid.