On a Linearly Damped 2 Body Problem

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 nite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover some formal calculations suggest the existence of special orbits with an asymptotically spiraling convergence to the center.