Astronomy and Astrophysics – Astronomy
Scientific paper
May 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..24...27p&link_type=abstract
Celestial Mechanics, vol. 24, May 1981, p. 27-52.
Astronomy and Astrophysics
Astronomy
Astronomical Models, Asymptotic Methods, Orbital Mechanics, Three Body Problem, Boundary Value Problems, Coordinate Transformations, Equations Of Motion, Orbital Elements, Solar System
Scientific paper
A simplified model of the planar three-body problem is considered in which two particles, forming a close binary, orbit a distant point. A small parameter related to the distance separating the binary and the remaining mass is defined. The time is eliminated from the equations of motion and an angular variable is used instead. A two-variable expansion procedure is used to find an asymptotic solution. The solution obtained is known completely up to order ten in the small parameter, and it is valid for almost arbitrary initial conditions. Specification of the initial conditions leads to a solution which is periodic with respect to a modified time variable.
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