Other
Scientific paper
Sep 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cosre..31..187l&link_type=abstract
Cosmic Res., Vol. 31, No. 2, p. 187 - 207
Other
Scientific paper
A class of orbits about the body of lesser mass and located beyond its sphere of influence is examined in the restricted elliptical three-body problem. The ratio of the two finite masses, the orbital eccentricity of the body of lesser mass, the orbital inclination of the body of zero mass (spacecraft), and the ratio of the distance between the bodies of zero and lesser mass to the distance between the bodies of finite mass are taken as small parameters. The principal difficulty of this problem is the presence of another small parameter whose numerical value is defined by the reciprocal of the minimum distance between the spacecraft and the body of lesser mass and the ratio of the two finite masses. For the class of orbits under considerations, the value of this parameter in the Mars-Phobos system is of the order 0.1, which is insufficiently small to be able to use only the first approximation of perturbation theory as is usually done in evolution problems. A succession of canonical transformations is used to reduce the equations of motion to the form required for application of the Lie method. To terms of second order, a replacement of variables is found to eliminate from the Hamiltonian the fast variables related to the unperturbed motion of the body of zero mass in the elliptical libration orbit and to the orbital motion of the body of lesser mass. Evolution equations describing the change in the slow variables are found to terms of third order, and their approximate solution may be used for analysis of the principal features of the evolution of quasi-satellite orbits. Test calculations are carried out, in particular, for the Mars-Phobos system.
Lidov M. L.
Vashkov'yak M. A.
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