Two-body problems with drag or thrust: Qualitative results

We consider two-body problems in which the drag is proportional to the velo city divided by the square of the distance and whose radial and tangential components have distinct coefficients. For all parameters, we study the flo w of the system obtained by suitable coordinate and time transformations an d draw conclusions about the qualitative behavior of solutions. In each cas e, we examine the existence of collision-ejection, collision-escape, captur e-collision, capture-escape, and oscillatory rectilinear orbits, study the motion near collision, and show that if periodic orbits exist they must be limit cycles.