2018/12/27 by Jaime Burgos–García, Burgos-Garcia, Jaime, Alessandra Celletti +7
Engineering · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.1812.10852
openalex publication_date 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a restricted four-body problem with a precise hierarchy between\nthe bodies: two point-mass bigger bodies, a smaller one with oblate shape, and\nan infinitesimal body in the neighborhood of the oblate body. The three heavy\nbodies are assumed to move in a plane under their mutual gravity, and the\nfourth body moves under the gravitational influence of the three heavy bodies,\nbut without affecting them.\n We start by finding the triangular central configurations of the three heavy\nbodies; since one body is oblate, the triangle is isosceles, rather than\nequilateral as in the point mass case. We assume that the three heavy bodies\nare in such a central configuration and we perform a Hill's approximation of\nthe equations of motion describing the dynamics of the infinitesimal body in a\nneighborhood of the oblate body. Through the use of Hill's variables and a\nlimiting procedure, this approximation amounts to sending the two other bodies\nto infinity. Finally, for the Hill approximation, we find the equilibrium\npoints of the infinitesimal body and determine their stability. As a motivating\nexample, we consider the dynamics of the moonlet Skamandrios of Jupiter's\nTrojan asteroid Hektor.\n