Transfer Between Circular and Hyperbolic Orbits Using Analytical Maximum Thrust Arcs

It is known that in the case of motion in a central Newtonian field there may exist two different types of optimal trajectory structure. The first trajectory structure contains null thrust (NT), intermediate thrust, and maximum thrust (MT) arcs and consists of null and maximum power arcs. It has been shown that, in the case of constraints on unit thrust direction cosines, specific impulse, and power; one can obtain analytical trajectories associated with constant or variable exhaust speed. In this Note, the same problem statement used to describe the low thrust (LT) arcs are used to obtain analytic MT arcs and to investigate the transfer between circular and hyperbolic orbits in a Newtonian gravity field. This represents a step toward a generalized problem statement from which many optimal space trajectory analytic solutions flow and from which existing thrust arcs can be classified. The equations of optimal motion can be represented as a 14th-order canonical system of equations, and the principal difficulty of solving the problem in quadratures for the MT arcs consists of finding two first integrals of this canonical system. However, an analytical approximation of the Newtonian gravity field by a linear central field during the motion on an MT arc leads to closed-form analytical solutions. Investigations of MT arcs obtained by various numerical and approximate analytical methods may be found in Refs. 6-12. In the present Note, it will be shown that the linear field approximation can be used to analyze the maximum thrust transfer maneuver mentioned earlier.