Journal Article

Analytic orbits in any central potential

D. Lynden-Bell

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 402, issue 3, pages 1937-1941
Published in print March 2010 | ISSN: 0035-8711
Published online February 2010 | e-ISSN: 1365-2966 | DOI:
Analytic orbits in any central potential

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Stable central orbits in any central potential are well approximated by a simple analytical expression whose parameters are readily determined from the potential and its gradient. The method yields better than 1 per cent accuracy for the angle between pericentre and apocentre but is somewhat less accurate for the periods of highly eccentric orbits when the logarithmic gradient of the potential changes rapidly over the orbit. A related method is proposed for unbound orbits.

Keywords: celestial mechanics; galaxies: kinematics and dynamics

Journal Article.  2887 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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