A CLOSED-FORM SOLUTION TO THE MINIMUM Delta V-TOT(2) LAMBERT'S PROBLEM

A closed form solution to the minimum v tot2 Lambert problem between two assigned positions in two general orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices for solving the re-configuration problem of satellite constellations and the complexity associated in facing this problem with the minimization of v tot . The difference between a two-impulse v tot2 and v tot orbit transfer is investigated and shown to be bounded. Two unique approaches derive the solving equation of minimum v tot2 Lambert problem as a quartic polynomial. Root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. One numerical example is given for the general case (transfer between no-coplanar elliptical orbits), and an example is provided for the singular case (Hohmann transfer).

A CLOSED-FORM SOLUTION TO THE MINIMUM Delta V-TOT(2) LAMBERT'S PROBLEM Conference Paper