Lower bounds for the spacings of bodies in the restricted three body problem

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Hill Method, Orbital Mechanics, Three Body Problem, Astrodynamics, Center Of Gravity, Orbit Perturbation

Scientific paper

In the present paper, the Newtonian restricted problem of three different mass points is analyzed, placing the origin of the coordinates at the barycenter (the center of mass of the three points). It is assumed that the constant vector, C, of the moment of momentum of the system with respect to the barycenter is other than zero. The case where the constant, h, of the energy integral T = U + h (where T is the momentum, and U a force function) is smaller than zero is examined, assuming that the sufficient conditions of absolute stability in Hill's sense of the motion of a fixed pair of bodies are satisfied in this case. A method for obtaining lower bounds of the distances of such bodies to the third body is proposed.

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