Bounds on the solution to Kepler's problem

Details Bounds on the solution to Kepler's problem Bounds on the solution to Kepler's problem

Jun 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977jansc..25..123p&link_type=abstract

Journal of the Astronautical Sciences, vol. 25, Apr.-June 1977, p. 123-128.

Astronomy and Astrophysics

Astronomy

6

Elliptical Orbits, Hyperbolic Trajectories, Kepler Laws, Orbit Calculation, Boundary Value Problems, Conics, Convergence, Orbital Mechanics, Two Body Problem

Scientific paper

Upper and lower bounds are derived for the solutions to three forms of Kepler's problem: (1) Kepler's equation for an elliptical orbit, (2) the analog of Kepler's equation for a hyperbolic orbit, and (3) the universal form of Kepler's equation, applicable to all types of conic orbits. The bounds are expressed in classical variables and in a universal formulation. The upper bounds, which are assumed to be new, are functions of the orbital elements and the specified time. In addition to their theoretical importance, the bounds provide faster convergence for iterative numerical schemes.

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