Second-order p-iterative solution of the Lambert/Gauss problem

Details Second-order p-iterative solution of the Lambert/Gauss problem Second-order p-iterative solution of the Lambert/Gauss problem

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984jansc..32..475b&link_type=abstract

Journal of the Astronautical Sciences (ISSN 0021-9142), vol. 32, Oct.-Dec. 1984, p. 475-485.

Statistics

Computation

Iterative Solution, Kepler Laws, Orbit Calculation, Orbital Mechanics, Trajectory Analysis, Algorithms, Eccentric Orbits, Error Analysis, Flight Paths, Flight Time, Gauss Equation, Newton Theory

Scientific paper

An algorithm is presented for efficient p-iterative solution of the Lambert/Gauss orbit-determination problem using second-order Newton iteration. The algorithm is based on a universal transformation of Kepler's time-of-flight equation and approximate inverse solutions of this equation for short-way and long-way flight paths. The approximate solutions provide both good starting values for iteration and simplified computation of the second-order term in the iteration formula. Numerical results are presented which indicate that in many cases of practical significance (except those having collinear position vectors) the algorithm produces at least eight significant digits of accuracy with just two or three steps of iteration.

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