Two Mechanisms of Temporary Capture in Celestial Mechanics

Prof. V.V. Sidorenko & Prof. A.B. Batkhin
Keldysh Institute of Applied Mathematics
Moscow, Russia

Temporary capture in celestial mechanics is interpreted as a close encounter of asteroid or comet with a planet, comprising several revolutions around it. In our talk we discuss two ways in which the temporary capture can be provided: the quasi-satellite (QS) regime of orbital motion and the sticking out to border of regular dynamics area in the system’s phase space.

The motion of a small body in a QS-orbit corresponds to a 1:1 mean motion resonance with a planet. The term “quasi-satellite” reflects the fact that this body, typically, never enters the planet’s Hill sphere and so it cannot be considered as a satellite in the usual sense of the word. To study the secular effects, we have constructed the evolutionary equations by means of numerical averaging. It turns out that in some cases the right-hand sides of these equations are not uniquely defined. Consideration of this ambiguity provides us an opportunity to predict whether the motion in a QS-orbit is permanent or not. For non-permanent motions in QS-orbits, the conditions of capture into this regime and escape from it can be established.

The stickiness phenomenon is an intrinsic property of non-integrable Hamiltonian systems. It occurs when an orbit originating in an immediate vicinity of the last invariant torus remains rather close to this torus for a long time before leaving it for the chaotic sea. Theoretical explanation of stickiness phenomenon is based on the concept of the so-called cantori providing a partial barrier to chaotic orbits. With the help of numerical simulation, we study the stickiness in the Hill problem which is known as effective model for investigation of satellite dynamics. Owing to the time-reversal symmetry of the equations of motion, the existence of sticky trajectories means the existence of the orbits penetrating more or less quickly into the stickiness region and staying there for a long time. Some application to natural satellites in Solar System is provided.

The talk will be given in English

Wed, 19-11-2014, 13:30 (Gathering at 13:00)

ASRI Seminar room (room no. 201)

Light refreshments will be served before the lecture


Two Mechanisms of Temporary Capture in Celestial Mechanics