The Accelerated Kepler Problem

Details The Accelerated Kepler Problem The Accelerated Kepler Problem

2007-05-22

arxiv.org/abs/0705.3219v1

Astronomy and Astrophysics

Astrophysics

16 pages, 9 figures, in press at Celestial Mechanics and Dynamical Astronomy

Scientific paper

10.1007/s10569-007-9087-4

The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem's Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the accelerated Kepler problem and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.

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