Orbital Planar Maneuvers Using Two and Three-Four (Through Infinity) Impulses

We consider the problem of minimum AV time-free impulsive transfers between coplanar Keplerian orbits. We studied two types of maneuvers: the ones performed with two impulses and the ones performed with three or four impulses that go to infinity in the middle of the transfer. For the two-impulse maneuver, we develop optimality conditions that lead to a nonlinear system of three equations and three unknowns. For the three-impulse maneuver, we develop a new maneuver that uses two elliptic transfer orbits that are connected by a negligible impulse applied at an infinite distance from the attracting body. It is an extension of the bi-elliptic transfer, where the two orbits involved in the transfer are not coaxial. We study in detail and show regions of optimality for the most trivial cases of transfers: between two circular orbits, one circular and one elliptic orbit, and two elliptic coaxial orbits. We complete the research by studying a scheme to reduce the total AF for some of those maneuvers, by adding a second impulse at infinity, and making it a four-impulse maneuver.

[1]  M. Handelsman,et al.  Primer Vector on Fixed-Time Impulsive Trajectories , 1967 .

[2]  D. F. Lawden.  Minimal Rocket Trajectories , 1953 .

[3]  Derek F. Lawden.  Impulsive Transfer between Elliptical Orbits , 1962 .

[4]  F. W. Gobetz,et al.  A survey of impulsive trajectories. , 1969 .

[5]  D. J. Jezewski,et al.  An efficient method for calculating optimal free-space n-impulse trajectories. , 1968 .

[6]  T. N. Edelbaum,et al.  How many impulses , 1967 .

[7]  H. Mendlowitz,et al.  Soviet Space Science , 1959 .

[8]  Yasunori Matogawa.  Optimum low thrust transfer to geosynchronous orbit , 1983 .

[9]  Derek F. Lawden,et al.  Optimal transfers between coplanar elliptical orbits , 1992 .

[10]  Optimum burn scheduling for low-thrust orbital transfers , 1989 .

[11]  Low-Thrust Orbit Raising for Shuttle Payloads , 1982 .

[12]  John E. Prussing,et al.  Optimal two- and three-impulse fixed-time rendezvous in the vicinityof a circular orbit , 1970 .

[13]  John E. Prussing,et al.  Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit. , 1969 .

[14]  Jean Pierre Marec,et al.  Optimal Space Trajectories , 1979 .

[15]  David C. Redding.  Highly efficient, very low-thrust transfer to geosynchronous orbit -Exact and approximate solutions , 1982 .

[16]  R. Barrar.  AN ANALYTIC PROOF THAT THE HOHMANN-TYPE TRANSFER IS THE TRUE MINIMUM TWO-IMPULSE TRANSFER , 1962 .

[17]  R. Goddard.  A Method of Reaching Extreme Altitudes. , 1920, Nature.