Abstract
In this paper, the thrust programs for minimum propellant consumption during vertical take-off and landing maneuvers of a rocket in a vacuum are derived for an arbitrary central gravitational field. It is shown that, regardless of the mathematical form of the attracting force, the extremal arc for take-off is composed of a maximum thrust subarc followed by a coasting subarc, and the extremal arc for landing is composed of a coasting subarc followed by a maximum thrust subarc.
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