Orbits in a central force field: Bounded orbits

Details Orbits in a central force field: Bounded orbits Orbits in a central force field: Bounded orbits

2004-10-19

arxiv.org/abs/physics/0410149v1

Physics

Physics Education

11 pages, 15 figures, submitted to Am. J. Phys. Nov 14 2003 (ms # 17211)

Scientific paper

The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or anticlockwise, depending on its angular momentum, and at the same time oscillates between a minimum and a maximum radial distance, defining an inner and an outer annulus. There are generic orbits suggested in popular texts displaying the general features of a central orbit. In this work it is demonstrated that some of these orbits, seemingly possible at the first glance, are not compatible with a central force field. For power law forces, the general nature of boundedness and geometric shape of orbits are investigated.

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