The pair of motion equations for entry into a planetary atmosphere is reduced to a single, ordinary, nonlinear differential equation of second order by disregarding two relatively small terms and by introducing a certain mathematical transformation. A number of solutions for lifting and nonlifting vehicles entering at various initial angles have been obtained from the complete nonlinear equation. These solutions are used to study the deceleration, heating rate, and total heat absorbed for entry into Venus, Earth, Mars, and Jupiter. From the equations developed for heating rates, and from available information on human tolerance limits to acceleration stress, approximate conditions for minimizing the aerodynamic heating of a trimmed vehicle with constant lift-drag ratio are established for several types of manned entry. A brief study is included of the process of atmosphere braking for slowing a vehicle from near escape velocity to near satellite velocity.
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