Constant-speed ramps for a central force field

We investigate the problem of determining planar curves that describe ramps where a particle mass \begin{document}$ m $\end{document} moves with constant-speed when is subject to action friction force and whose magnitude id="M2">\begin{document}$ F(r) depends only on distance id="M3">\begin{document}$ r from origin. In this paper we all for case id="M4">\begin{document}$ = -m/r $\end{document}. We show circles logarithmic spirals play an important role. Not they are solutions but every other solution approaches either circle or spiral.