Binary collisions in popovici’s photogravitational model

Abstract

The dynamics of bodies under the combined action of the gravitational attraction and the radiative repelling force has large and deep implications in astronomy. In the 1920s, the Romanian astronomer Constantin Popovici proposed a modified photogravitational law (considered by other scientists too). This paper deals with the collisions of the two-body problem associated with Popovici’s model. Resorting to McGehee-type transformations of the second kind, we obtain regular equations of motion and define the collision manifold. The flow on this boundary manifold is wholly described. This allows to point out some important qualitative features of the collisional motion: existence of the black-hole effect, gradientlikeness of the flow on the collision manifold, regularizability of collisions under certain conditions. Some questions, coming from the comparison of Levi-Civita’s regularizing transformations and McGehee’s ones, are formulated.