The Motion of Spacecraft in the Atmosphere

Abstract

This investigation treats the motion of a space vehicle in the atmosphere, and includes an analysis of the possibilites for using a small lifting force to reduce the demands on reentry accuracy, and to diminish the deceleration load on reentry into the atmosphere at the second space velocity.Landing trajectories are considered which have a locally parabolic velocity at height y = 100 km. The reentry angle Ө (the angle between the transversal and the velocity at height y) is uniquely determined by the height h of osculating perigee, that is, by the perigee height of an undisturbed orbit in the absence of atmospheric resistance.The perigee height uniquely characterizes the reentry conditions for a trajectory of given energy. The choice of the perigee height as a basic parameter enables the outer part of the trajectory to be tied in with the descent through the atmosphere in the most natural way. It is convenient to measure the range and time along the descending portion of the trajectory from the point that would have corresponded to perigee passage in undisturbed motion.The interval in perigee height for which a descent of prescribed range can be effected is called the “width of the perigee corridor.” The wider the corridor for reentry, the lower the accuracy required in the approach of the spacecraft to the earth prior to descent.Control of the lift of the spacecraft permits the deceleration load to be reduced. For a prescribed level of maximum permissible decelerations, the lift control may be used to ensure as wide a reentry corridor as possible.We shall regard the lift control as providing for a switching operation from the greatest possible positive value to the greatest possible negative value, and inversely. With this discontinuous mode of varying the lift, the problem reduces to making an optimal choice for the number and timing of the reversal operations.We consider first the case of descent at a constant lift/drag ratio (no lift reversals). We then consider descents with one, two, or more reversals. The manner in which the deceleration varies during the motion and the position of the principal maximum are analyzed. The amounts by which the deceleration and perigee height vary are determined. With some approximation, the standard atmosphere of [1] was used in the calculations.