An Approximate Analytical Method for Studying Entry Into Planetary Atmospheres

Book excerpt: 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.