  We make an observation about Galilean transformation on a 1-D mass variable
systems which leads us to the right way to deal with mass variable systems.
Then using this observation, we study two-bodies gravitational problem where
the mass of one of the bodies varies and suffers a damping-antidamping 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. Our theoretical
results are applied to Halley's comet.
