Inverse solution of Kepler's equation for hyperbolic orbits

Details Inverse solution of Kepler's equation for hyperbolic orbits Inverse solution of Kepler's equation for hyperbolic orbits

Sep 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987jansc..35..347b&link_type=abstract

Journal of the Astronautical Sciences (ISSN 0021-9142), vol. 35, July-Sept. 1987, p. 347-358.

Other

Elliptical Orbits, Hyperbolic Trajectories, Orbital Mechanics, Spacecraft Orbits, Algorithms, Roots Of Equations

Scientific paper

An algorithm is presented for efficient inverse solution of Kepler's equation for hyperbolic orbits. It is shown that an expansion of Barker's equation into a bicubic polynomial provides a good approximation to obtain accurate starting values for rapid numerical solution of Kepler's equation. In the approximate equation a cubic in normalized elapsed flight time from pericenter is set equal to a cubic in a function S of eccentricity and true anomaly. The initial estimate of S to use in an iteration formula is obtained by evaluating the cubic in normalized flight time and finding in most cases the single real root of the other cubic. This initial estimate has an accuracy corresponding to values of true anomaly in error by less than 0.5 degrees generally.

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