Planar Dynamics of Non-Spherical Close Tidally Locked Binaries and the Restricted Three Body Problem

Kurzfassung

Asteroids have formed during the evolution of the disk in the early 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 insufficient to generate a spherical shape. Those irregular shapes make the study of spacecraft orbits investigating 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 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 thought before. In that sense, the present research focusses on studying the orbital evolution of a binary asteroid system with almost equal masses composed of two non-spherical asteroids tidally locked close to each other, and the dynamical evolution of spacecraft orbiting the system. Since Keplerian orbital elements are not always an accurate approach for spacecraft in high mass ratio binary systems, 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 to find natural stable solutions. We also analyze the structure of the phase space and the importance of the effect of solar radiation pressure on these dynamics. We study 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. 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. As an application of this research, we studied the binary system Antiope 90. The majority of the dynamical structure has survived over 90 days under the effects of solar pressure radiation, which would be well suitable for a detailed investigation of the system by a space mission.