About Galilean transformation on a mass variable system and two bodies gravitational system with variable mass and damping-anti damping effect due to star wind

Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics

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20 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:0910.4684

Scientific paper

We make an observation about Galilean transformation on a 1-D mass variable systems which leads us to the right way to deal with these systems. Then using this observation, we study two-bodies gravitational problem where the mass of one of the bodies varies and suffers a damping-anti damping effect due to star wind during its motion. for this system, a constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion, and the period of the body is studied using the constant of motion of the system. An application to the comet motion is given, using the comet Halley as an example.

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