The zonal satellite problem - I: Near-collision flow

• Published in: Serbian astronomical journal. Vol. 1998; no. 158; pp. 31 - 36
• Main Authors: Mioc, V., Stavinschi, M.
• Format: Journal Article
• Language: English
• Published: Astronomical Observatory, Department of Astronomy, Belgrade 1998
• ISSN: 1450-698X; 1820-9289
• DOI: 10.2298/SAJ9858031M

The force field described by a potential function of the form U = ?n k=1 ak/rk (r = distance between particles, ak = real parameters) models various concrete situations belonging to astronomy, physics, mechanics, astrodynamics, etc. The two-body problem is being tackled in such a field. The motion equations and the first integrals of energy and angular momentum are established. The McGehee-type coordinates are used to blow up the collision singularity and to paste the resulting manifold on the phase space. The flow on the collision manifold is depicted. Then, using the rotational symmetry of the problem and the angular momentum integral, the local flow near collision is described and interpreted in terms of physical motion. nema