An analytic approach to twofixedimpulse transfers between Keplerian orbits
Abstract
Solutions are obtained for the twoimpulse transfer of a vehicle between arbitrary inclined orbits in an inversesquare force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.
 Publication:

Journal of Guidance Control Dynamics
 Pub Date:
 October 1982
 DOI:
 10.2514/3.19779
 Bibcode:
 1982JGCD....5..458J
 Keywords:

 Celestial Mechanics;
 Kepler Laws;
 Laplace Equation;
 Transfer Orbits;
 Angular Momentum;
 Conservation Equations;
 Energy Conservation;
 Extremum Values;
 Linear Equations;
 Specific Impulse;
 Astrodynamics