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universal variable formulation
In orbital mechanics, the universal variable formulation is a method used to solve the two-body Kepler problem. It is a generalized form of Kepler's Equations, extending them to apply not only to elliptic orbits, but also parabolic and hyperbolic orbits. It thus is applicable to many situations in the solar system, where orbits of widely varying eccentricities are present.
==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 orbits with a reasonably small 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 converge slowly or not at all. Furthermore, Kepler's equation cannot be applied to parabolic and hyperbolic orbits, since it specifically is tailored to elliptic orbits.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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