Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cemda.109..409l&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 109, Issue 4, pp.409-427
Astronomy and Astrophysics
Astronomy
Two-Point Boundary Value Problem, Quasi-Lambert'S Problem, Flight-Direction Angle, Universal Variable, Iteration Algorithm
Scientific paper
A two-point boundary value problem of the Kepler orbit similar to Lambert's problem is proposed. The problem is to find a Kepler orbit that will travel through the initial and final points in a specified flight time given the radial distances of the two points and the flight-direction angle at the initial point. The Kepler orbits that meet the geometric constraints are parameterized via the universal variable z introduced by Bate. The formula for flight time of the orbits is derived. The admissible interval of the universal variable and the variation pattern of the flight time are explored intensively. A numerical iteration algorithm based on the analytical results is presented to solve the problem. A large number of randomly generated examples are used to test the reliability and efficiency of the algorithm.
Han Chao
Luo Qinqin
Meng Zhanfeng
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