Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.106...25a&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Vol. 106, Issue 1, p. 25-37
Astronomy and Astrophysics
Astronomy
2
Orbit Transfer, Two-Impulse, Rendezvous, Lambert'S Problem
Scientific paper
A closed form solution to the minimum {Δ V_tot^2} Lambert problem between two assigned positions in two distinct orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices to solve re-configuration problems of satellite constellations and the complexity associated in facing these problems with the minimization of {Δ V_tot}. Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing {Δ V_tot^2} and {Δ V_tot} does not exceed 17%. The {Δ V_tot^2} solution can be adopted as starting point to find the minimum {Δ V_tot}. The solving equation for minimum {Δ V_tot^2} Lambert problem is a quartic polynomial in term of the angular momentum modulus of the optimal transfer orbit. The root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. A numerical example for the general case (orbit transfer “pork-chop” between two non-coplanar elliptical orbits) and two examples for the singular case (Hohmann and GTO transfers) are provided.
Avendano Martin
Mortari Daniele
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