An Approximate Analytical Method for Studying Entry Into Planetary Atmospheres
The pair of motion equations for entry into an exponential 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. The reduced equation includes various terms, certain of which represent the gravity force, the centrifugal acceleration, and the lift force. If these particular terms are disregarded, the differential equation is linear and yields precisely the solution of Allen and Eggers applicable to ballistic entry at relatively steep angles of descent. If all the other terms in the basic equation are disregarded (corresponding to negligible vertical acceleration and negligible vertical component of drag force), the resulting truncated differential equation yields the solution of Sanger for equilibrium flight of glide vehicles with relatively large lift-drag ratios.
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aerodynamic heating Allen and Eggers altitude angle of descent appendix applied approximate solution coefficient component of drag corresponding curves in figure decaying orbits deflected orbit density differential equation 21 Dimensionless velocity disregarded dr/r drag coefficient drag device drag force du/u earth's atmosphere entry from decaying escape velocity exit flight path gravity minus centrifugal hence human tolerance increase in L/D initial descent angle Jupiter Keplerian ellipse L/D ratios laminar flow laminar heating rate lift force lifting vehicle maximum deceleration maximum heating rate maximum laminar heating minus centrifugal force motion equations nonlifting entry nonlifting vehicles obtained occurs orbital decay pair of motion parameter peak heating planetary atmosphere present analysis present solution presented in figure qmax relatively representing Reynolds number single pass skip vehicles small initial angles sorbed stagnation point surface temperature tion total heat absorbed trajectory types of entry values various planets vehicles entering Venus W/CDA