The eleventh motion constant of the two-body problem

Details The eleventh motion constant of the two-body problem The eleventh motion constant of the two-body problem

Jul 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cemda.110..189s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 110, Issue 3, pp.189-198

Astronomy and Astrophysics

Astronomy

Two-Body Problem, Motion Constants, Boundary-Value Problems

Scientific paper

The two-body problem is a twelfth-order time-invariant dynamic system, and therefore has eleven mutually-independent time-independent integrals, here referred to as motion constants. Some of these motion constants are related to the ten mutually-independent algebraic integrals of the n-body problem, whereas some are particular to the two-body problem. The problem can be decomposed into mass-center and relative-motion subsystems, each being sixth-order and each having five mutually-independent motion constants. This paper presents solutions for the eleventh motion constant, which relates the behavior of the two subsystems. The complete set of mutually-independent motion constants describes the shape of the state-space trajectories. The use of the eleventh motion constant is demonstrated in computing a solution to a two-point boundary-value problem.

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