“…The simplified expressions in Eqs. (20)(21)(22)(23)(24)(25)(26)(27)(28) are typically presented in texts on atmospheric entry [12][13][14]26,27], as they readily provide insight into several ballistic entry phenomena. First, the altitudes at which maximum acceleration and heat rate occur are not functions of velocity to first order: they are determined by vehicle parameters, planetary parameters, and the flight-path angle.…”