  I calculate the classical effects induced by an isotropic mass loss of a body
on the orbital motion of a test particle around it; the present analysis is
also valid for a variation of the Newtonian constant of gravitation. I
perturbatively obtain negative secular rates for the osculating semimajor axis,
the eccentricity and the mean anomaly, while the argument of pericenter does
not undergo secular precession; the node and the inclination i remain
unchanged. The anomalistic period is different from the Keplerian one, being
larger than it. The true orbit, instead, expands, as shown by a numerical
integration of the equations of motion in Cartesian coordinates; in fact, this
is in agreement with the seemingly counter-intuitive decreasing of the
semimajor axis and the eccentricity because they refer to the osculating
Keplerian ellipses which approximate the trajectory at each instant. A
comparison with the results obtained with different approaches by other
researchers is made. General relativity induces positive secular rates of the
semimajor axis and the eccentricity completely negligible in the present and
future evolution of the solar system.
