Planar dynamics of non-spherical close tidally locked binaries asteroids 

Abstract

Asteroids are originated by the evolution of the disk in the Solar System and, in general, do not have spherical and symmetrical shapes. The reason for those irregular shapes is the small mass of the bodies, such that gravity is not sufficient to make them reach a spherical shape. Those irregular shapes make the study of spacecraft orbits to investigate those objects  complex. Adding this to the fact that their weak gravitational field allows forces that are usually negligible or of second order  for spacecraft near a massive body (e.g.,  solar radiation pressure) to be comparable to the gravitational forces, provides an interesting and important problem to be studied in terms of astrodynamics. The study of asteroids is important because they carry essential scientific information about the origin and evolution of the Solar System. For all these points, it is important to understand their motion and investigate the motion of a spacecraft close to the asteroid. Asteroids may exist alone or in groups of two or three. Recent observations show that binary asteroids could be even more common than we think. In that sense, the present research focused on studying the orbital evolution of a binary asteroid system with almost equal masses composed of two non-spherical asteroids tidally locked that are close to each other, and the dynamical evolution of spacecraft orbiting the system. Since Keplerian orbital elements are not always a good approach for spacecraft in high mass ratio binary systems, to study this problem, we consider the mathematical models of the planar full two-body-problem for the binary asteroid, and the circular restricted three-body problem for the spacecraft, adding ellipsoidal geometry to represent the non-spherical shapes of the binary in order to find natural stable solutions. We also analyzed the structure of the phase space and the importance of the effect of solar radiation pressure on this dynamics. We studied the dynamics and the effect of the gravitational shape of close binary systems in their mutual orbits, as well as the existence of spacecraft circular and resonant orbits. As an application of this research, we studied the binary system Antiope 90. We found stable, close direct and retrograde orbits for the jacobi constants between -1.1 and -0.5; and internal resonant retrograde orbits within the primary and the secondary for the energy -0.7. The majority of the dynamical structure has survived over 90 days assuming the effects of solar pressure radiation.