Dynamics and Mission Design Near Libration Points - Vol II: Fundamentals: The Case of Triangular Libration Points

ISBN-13: 9789810242749 / Angielski / Twarda / 2001 / 160 str.

Gerard Gomez;Etc.;C. Simo

Opis

It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, μ, below Routh's critical value, μ₁. It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L₄, L₅ but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains “practical stability” in the sense that the massless particle remains close to the equilibrium point for a big time interval (some millions of years, for example).According to the literature, what has been done in the problem follows two approaches: (a) numerical simulations of more or less accurate models of the real solar system; (b) study of periodic or quasi-periodic orbits of some much simpler problem.The concrete questions that are studied in this volume are: (a) Is there some orbit of the real solar system which looks like the periodic orbits of the second approach? (That is, are there orbits performing revolutions around L₄ covering eventually a thick strip? Furthermore, it would be good if those orbits turn out to be quasi-periodic. However, there is no guarantee that such orbits exist or will be quasi-periodic). (b) If the orbit of (a) exists and two particles (spacecraft) are put close to it, how do the mutual distance and orientation change with time?As a final conclusion of the work, there is evidence that orbits moving in a somewhat big annulus around L₄ and L₅ exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable.