A generalized problem of two fixed centres with variable masses. I - The equations for the variations of orbital elements

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Celestial Mechanics, Two Body Problem, Variable Mass Systems, Angular Momentum, Equations Of Motion

Scientific paper

A generalized two-body problem of fixed centers is studied, under the assumption that the mass is an arbitrarily slowly varying function of time and, therefore, that changes in the motion of the test particle are relatively small. A problem is also formulated for the motion of a planet around an oblate rapidly rotating star which is losing mass. Equations for the variations of three orbit elements are derived and it is shown that the component z of the angular momentum vector remains constant. Equations for changes in two other orbital elements can be applied.

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