Ballistic reentry motion, including gravity - Constant drag coefficient case

Existing theories describe ballistic reentry motion from pierce point to impact using a single analytic solution. Large reductions in air speed and changes in flight path angle cannot be predicted accurately using this approach. A new solution of the equations of motion, assuming flat earth gravity, will be presented. A trajectory profile will be constructed using two asymptotic expansions. In the expansions appear quadratures involving the drag coefficient, which is assumed constant, and atmospheric density profile. It will be shown that the entry expansion, accurate near the pierce point, can diverge typically after peak deceleration. Asymptotic matching concepts are then used to transfer from the entry to the more accurate terminal expansion.