THE SCHWARZSCHILD PROBLEM IN ASTROPHYSICS

The Schwarzschild problem (the two-body problem associated to a potent ial of the form A/r + B/r(3)) has been qualitatively investigated in a n astrophysical framework, exemplified by two likely situations: motio n of a particle in the photogravitational field of an oblate, rotating star, or in that of a star which generates a Schwarzschild field. Usi ng McGehee-type transformations, regularized equations of motion are o btained, and the collision singularity is blown up and replaced by the collision manifold Lambda (a torus) pasted on the phase space. The fl ow on Lambda is fully characterized. Then, reducing the 4D phase space to dimension 2, the global how in the phase plane is depicted for all possible values of the energy and for all combinations of nonzero A a nd B. Each phase trajectory is interpreted in terms of physical motion , obtaining in this way a telling geometric and physical picture of th e model.