Physics
Scientific paper
Mar 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..13..203b&link_type=abstract
Celestial Mechanics, vol. 13, Mar. 1976, p. 203-215.
Physics
6
Circular Orbits, Hill Method, Librational Motion, Orbital Mechanics, Satellite Orbits, Three Body Problem, Calculus Of Variations, Jacobi Integral, Orbital Elements, Two Body Problem
Scientific paper
The libration associated with stable large nonperiodic retrograde satellite orbits in the restricted three-body problem is studied in the case of the circular plane Hill's problem, where the 'reference motion' is elliptic. Equations of motion are formulated for the coordinates of the ellipse's center. Two integrals of motion are found: the semimajor axis of the ellipse and Jacobi's integral translated to the new coordinates. An equation for the libration period is obtained, and its limiting value for small libration amplitudes is determined. Numerical verification of the theoretical results is presented.
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