Trajectory optimization for distant earth satellites and satellite constellations

The optimization of transfer trajectories to a class of distant Earth orbits is investigated. This class of orbits, known as Distant Retrograde Orbits (DRO's), provides an ideal observing geometry for astronomical and astrophysical spacecraft. These orbits can also serve as operational orbits for multiple spacecraft interferometer constellations currently being considered by future space physics missions.; Primer vector theory has been used to derive first order necessary conditions for optimal finite burn and impulsive transfer solutions in the Restricted Three Body Problem (RTBP) force field model. The optimal transfer of an astronomical satellite or a multiple spacecraft constellation to these orbits required the solution of two specific problems in optimal spacecraft trajectories. These are the Combined Impulsive/Continuous Low Thrust Orbit Transfer Problem and the Single Booster Multiple Spacecraft Orbit Transfer Problem.; The dynamical systems aspects associated with the identification, computation, and stability properties for several classes of Distant Earth Orbits are presented. Following this, the necessary conditions are derived to compute finite burn and impulsive thrust transfers between arbitrary RTBP trajectories. The theory is extended to obtain the necessary conditions for the impulsive/continuous low thrust orbit transfer problem. The impulsive maneuver is made by a high thrust/low exhaust velocity upper stage booster and the continuous low thrust burns are made by a low thrust/high exhaust velocity engine attached to the spacecraft. The booster stage is dropped after the high thrust boost maneuver is made. The problem is transformed into a multi-point boundary value problem and is solved as a nonlinear root finding problem. An adjoint control transformation is implemented to provide an initial estimate for the Lagrange multipliers and other optimization variables.; The Single Booster Multiple Spacecraft Orbit Transfer Problem considers the optimization of the impulsive transfer for n spacecraft from an initial parking orbit to a final operational orbit where they are required to be positioned according to a specified spacing constraint. An analytical cost gradient is developed for three cases defined as the No Booster, Weak Booster, and Strong Booster cases. This information is then used as the gradient vector for a parameter optimization algorithm.