An improved Chapman theory for studying entry into planetary atmospheres

Details An improved Chapman theory for studying entry into planetary atmospheres An improved Chapman theory for studying entry into planetary atmospheres

Sep 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974phdt........64b&link_type=abstract

Ph.D. Thesis Michigan Univ., Ann Arbor.

Other

Atmospheric Entry, Planetary Atmospheres, Equations Of Motion, Gravitational Fields, Three Dimensional Motion, Trajectory Analysis

Scientific paper

The motion of a space vehicle which is entering a planetary atmosphere is analyzed. The three-dimensional motion of a space vehicle over a spherical planet is considered. It is assumed that the vehicle is moving through an isothermal atmosphere under the action of an inverse-square gravitational force. Exact equations of motion are derived in terms of the flight path angle and Chapman's Z bar and u bar variables. No restrictive assumptions regarding the nature of the trajectory are necessary in the derivation. The equations are valid for three-dimensional motion. Even though no restrictive assumptions are necessary in the derivation, the equations possess all the desirable aspects of Chapman's original equation. Because Z bar is approximately zero at high altitudes, an entry trajectory is specified in terms of only three parameters: the initial flight path angle, the initial speed of the vehicle, and lambda where lambda is the lift-drag ratio times the cosine of the bank angle. Thus, three-dimensional motion is analyzed in terms of the exact equations in the same manner that two-dimensional motion is analyzed in terms of Chapman's approximate equation.

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