Statistics – Computation
Scientific paper
Sep 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989ap%26ss.159..239d&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 159, no. 2, Sept. 1989, p. 239-270.
Statistics
Computation
3
Computational Astrophysics, Orbital Mechanics, Solar System, Hamiltonian Functions, Lie Groups, Perturbation Theory, Relativity, Solar Wind
Scientific paper
A canonical transformation in phase space and a rescaling of time are proposed to reduce a Keplerian system with a time-dependent Gaussian parameter (Gylden, 1884) to a perturbed Keplerian system with a constant Gaussian parameter. When the time variation is slow, the perturbation through second order in the reduced problem is conservative, and, as a result, the orbital space of the averaged system is a sphere on which the phase flow causes a differential rotation representing a circulation of the line of apsides. The flow presents two isolated singularities corresponding to circular orbits travelled, respectively, in the direct and retrograde sense, and a degenerate manifold of fixed points corresponding to the collision orbits. As an application, an estimate is offered for the apsidal rotation that a second-order time derivative in the mass of the sun would induce on planetary orbits.
Deprit Andre
Miller Bruce
Williams Carol A.
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