Necessary conditions are derived for the optimal orbit transfer problem for a spacecraft equipped with two distinct thrust limited, constant specific impulse propulsion systems. These conditions are required to optimize the transfer of a spacecraft launched on to the transfer orbit with a high thrust booster and the spacecraft (which is the booster's payload) itself has a dedicated propulsion system that is used for the final orbit insertion maneuvers). The propulsion system that makes the final maneuvers) may be low thrust and be more efficient than the one making the first injection maneuver. The transfer of a low thrust satellite to an orbit distant from the Earth is one example of a problem that can be modelled this way since the near Earth departure maneuver may be provided by a high thrust booster. For such a transfer, considerable time is saved since the low thrust spiral escape from the Earth is avoided entirely. The analysis includes the possibility of mass discontinuities arising from stage mass drop off. An example is given for the transfer of a spacecraft in low Earth orbit (LEO) to a Distant Earth Orbit (DEO) which is defined to be an orbit with hyperbolic energy with respect to the Earth but remains bounded to it due to the third body Solar attraction. This example uses the restricted three body problem (RTBP) force model since the target orbit is a periodic orbit in an approximate representation of spacecraft motion in the Sun-Earth/Moon system.
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