Comparison of optimal low thrust ascent and descent trajectories for upper stages and planetary landers

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Parallels may easily be drawn between powered ascent and descent from a planet without atmosphere. The lack of any explicit time dependence and no dissipative forces allows a simple time reversal. Departure from the Earth is complicated by the presence of the atmosphere. However, the upper stage phase of a multi-stage launcher shows similarities to ascent and descent from atmosphere-free planets. The use of relatively low thrust propulsion systems results in a more difficult problem, but when used for upper stages can ultimately yield payload advantages. Low thrust propulsion systems can also be used to advantage for planetary landers. This paper describes an efficient, multi-purpose optimisation technique used in the solution of these problems and compares the characteristics of solutions so obtained. The optimisation tool uses a direct multiple shooting method and variational calculus techniques for gradient calculation. The behaviour of an Earth departing upper stage is compared with landers on planets without atmosphere, such as Mercury. Optimisation of both classes of trajectories, when relatively low thrust engines are considered, shows a significant variation from more traditional, high thrust trajectories. In particular, high arcing phases are observed. This feature can also be seen in solutions of a simplified Pontryagin problem of minimum time ascent with low thrust, providing an insight into the nature of the full ascent and landing problems.