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.
Inverse solution of Kepler's equation for hyperbolic orbits
01.09.1987
Sonstige
Keine Angabe
Englisch
Efficient inverse solution of Kepler's equation
NTRS | 1986
|Solution of Kepler's equation as a differential equation
AIAA | 1984
|Bounds on the solution to a universal Kepler's equation
AIAA | 1978
|A Non-Iterative Solution for Kepler's Equation (AAS 07-282)
British Library Conference Proceedings | 2008
|Autonomous orbital navigation using Kepler's equation
AIAA | 1974
|