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We study two-bodies gravitational problem where the mass of one of the bodiesvaries and suffers a damping-antidamping effect due to star wind during itsmotion. A constant of motion, a Lagrangian and a Hamiltonian are given for theradial motion of the system, and the period of the body is studied using theconstant of motion of the system. An application to the comet motion is given,using the comet Halley as an example.

Two bodies gravitational system with variable mass and damping-antidamping effect due to star wind