# Astrodynamics/The Kepler Problem

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## The Kepler Problem[edit | edit source]

While Kepler's equation is easy to solve for time, there is no general solution for the reverse problem. To determine eccentric anomaly (and thus spacecraft position) at a given time, generally an iterative numerical method is used, such as Newton's method:

Where

The iteration takes the form

For most elliptical orbits an initial guess of *E _{0}* =

*M*is sufficient; for orbits with eccentricities greater than 0.8,

*E*= π may be used. Better initial guesses are possible, but are not generally required. The iterative process is repeated until required accuracy conditions are achieved, for example:

_{0}Where δ is the desired accuracy.