  The usual equation for both motions of a single planet around the sun and
electrons in the deterministic Rutherford-Bohr atomic model is conservative
with a singular potential at the origin. When a dissipation is added, new
phenomena appear. It is shown that whenever the momentum is not zero, the
moving particle does not reach the center in finite time and its displacement
does not blow-up either, even in the classical context where arbitrarily large
velocities are allowed. Moreover we prove that all bounded solutions tend to
$0$ for $t$ large, and some formal calculations suggest the existence of
special orbits with an asymptotically spiraling exponentially fast convergence
to the center.
