Zero velocity curves and orbits in the restricted problem of three bodies

Abstract

view Abstract Citations (9) References (2) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Zero velocity curves and orbits in the restricted problem of three bodies Szebehely, V. G. Abstract Relations between zero velocity curves and orbits are investigated for the restricted problem of three bodies. A condition which the force function must satisfy is derived, giving a criterion for identifying certain periodic orbits with zero velocity curves. This general result is applied to the limiting case of the problem ( = 0), and to the case of "small" , i.e., when terms of the order of ,o2 are neglected. It is shown that, in the latter case, perturbations of the order of r2 for the satellite motion (r 1) and of the order of for the planetary case (r 1) limit the applicability of the general results. Publication: The Astronomical Journal Pub Date: April 1963 DOI: 10.1086/108931 Bibcode: 1963AJ.....68..147S full text sources ADS |