Universal variable formulation: Difference between revisions

Revision as of 02:34, 30 August 2009

Revision as of 17:03, 28 November 2009

Line 3:

==Introduction==

A common problem in orbital mechanics is the following: given a body in an [[orbit]] and a time ''t₀'', find the position of the body at any other given time ''t''.

For [[elliptical orbit]]s with a reasonably small [[Orbital eccentricity|eccentricity]], solving [[Kepler's Equation]] by methods like [[Newton's method]] gives adequate results. However, as the orbit becomes more and more eccentric, the numerical iteration may start to [[Convergencelimit (mathematics)of a sequence|converge]] slowly or not at all.<ref name=Danby>{{cite |author=Danby, J. M. A.|title=Fundamentals of Celestial Mechanics|publisher=Willman-Bell|date=1988}}</ref>. Furthermore, Kepler's equation cannot be applied to [[Parabolic orbit|parabolic]] and [[hyperbolic orbit]]s, since it specifically is tailored to elliptic orbits.

==Derivation==