Bounds on the solution to a universal Kepler's equation

Computer Science – Numerical Analysis

Scientific paper

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Iteration, Kepler Laws, Orbital Mechanics, Algorithms, Convergence, Equations Of Motion, Numerical Analysis, Transfer Orbits, Transformations

Scientific paper

Upper and lower bounds are derived for the solution to Kepler's problem for the position in a known orbit given the elapsed time from an arbitrary epoch. The bounds, expressed in both classical variables and in a universal formulation, bracket the desired solution and provide starting values for iterative numerical solutions to Kepler's problem. Geometrical interpretations of the bounds are given and their use in several iteration algorithms is discussed and illustrated by applying them to examples from the literature.

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