Design of multi-body Lambert type orbits with specified departure and arrival positions

Astronomy and Astrophysics – Astronomy

Scientific paper

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Lunar Orbits, Orbit Calculation, Satellite Orbits, Spacecraft Trajectories, Swingby Technique, Algorithms, Eigenvectors, Linearization, Lunar Gravitation, Recursive Functions

Scientific paper

A new procedure for designing a multi-body Lambert type orbit comprising a multiple swingby process is developed, aiming at relieving a numerical difficulty inherent to a highly nonlinear swingby mechanism. The proposed algorithm, Recursive Multi-Step Linearization, first divides a whole orbit into several trajectory segments. Then, with a maximum use of piecewised transition matrices, a segmentized orbit is repeatedly upgraded until an approximated orbit initially based on a patched conics method eventually converges. In application to the four body earth-moon system with sun's gravitation, one of the double lunar swingby orbits including 12 lunar swingbys is successfully designed without any velocity mismatch.

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