The generalized doubly restricted problem of three bodies

Astronomy and Astrophysics – Astronomy

Scientific paper

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Celestial Mechanics, Orbital Mechanics, Three Body Problem, Astronomical Models, Oort Cloud

Scientific paper

An analysis is given of the doubly restricted three-body problem, in which the central force is described by a power law with an arbitrary exponent n. The generalized energy integral is obtained. The restricted problem is shown to have a general solution if n = -1. In the case of the galactic field, n is expressed in terms of the Oort constants A and B as n = 4A/(A - B) - 1 = 1.4.

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