 approxim analyt method studi entri planetari atmospher approxim analyt method studi entri planetari atmospher pair motion equat entri planetari atmospher reduc singl ordinari nonlinear differenti equat second order disregard small term introdur mathemat transform reduc equat includ term repres graviti forc centrifug acceler lift forc term disregard differenti equat linear yield precis solut allen egger applic ballist entri steep angl descent term basic equat disregard correspond neglig vertic acceler neglig vertic compon drag forc truncat differenti equat yield solut sanger equilibrium flight glide vehicl larg lift-drag ratio number solut lift nonlift vehicl enter initi angl complet nonlinear equat solut univers sens singl solut determin motion heat vehicl arbitrari weight dimens shape enter arbitrari planetari atmospher solut requir lift-drag ratio solut studi deceler heat rate total heat absorb entri venu earth mar jupit equat develop heat rate human toler limit acceler stress approxim condit minim aerodynam heat trim vehicl constant lift-drag ratio establish type man entri studi includ process atmospher brake slow vehicl escap veloc satellit veloc 