Celestial Mechanics and Dynamical Astronomy

, Volume 110, Issue 3, pp 189–198 | Cite as

The eleventh motion constant of the two-body problem

  • Andrew J. Sinclair
  • John E. Hurtado
Original Article


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.


Two-body problem Motion constants Boundary-value problems 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Aerospace Engineering DepartmentAuburn UniversityAuburnUSA
  2. 2.Aerospace Engineering DepartmentTexas A&M UniversityCollege StationUSA

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