Investigation of the Validity of the Non-Rotating Planet Assumption for Three-Dimensional Earth Atmospheric Entry

摘要

The assumption of a non-rotating planet, common in most analytical entry trajectory analyses, has been shown to produce significant errors in some solutions for the lifting atmospheric entry to the earth. This thesis investigates the validity of the non-rotating planet assumption for general three-dimensional Earth atmospheric entry. First, the three-dimensional equations of motion for lifting atmospheric entry are expanded to include a rotating planet model. A strictly exponential atmosphere, rotating at the same rate as the planet, is assumed with density as a function of radial distance from the planet's surface. Solutions are developed for the non-rotating Earth equations of motion and for one of the rotating Earth equations of motion using the method of matched asymptotic expansions. It is shown that the non-rotating Earth assumption produces incorrect entry trajectory results for entry orbital inclination angles between 0.5 and 75.0 deg and vehicle speeds ranging from circular orbital velocities to low supersonic speeds. However, a variety of realistic trajectory states exist where some of the non-rotating Earth equations of motion are found to be valid for the same entry trajectory states. Other, independent trajectory states exist where a fourth non-rotating Earth equation of motion is valid. A fifth equation of motion is never valid for the ranges of orbital inclination angle and speeds investigated.