The Schwarzschild Problem in Astrophysics |
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| Authors: | Cristina Stoica Vasile Mioc |
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| Institution: | (1) Gravitational Research Laboratory, Institute for Gravitation and Space Sciences, Str. Mendeleev 21-25, 70168 Bucharest, Romania;(2) Astronomical Observatory Cluj-Napoca, Astronomical Institute of the Romanian Academy, Str. Ciresilor 19, 3400 Cluj-Napoca, Romania |
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| Abstract: | The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold  (a torus)pasted on the phase space. The flow on is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel. |
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