Abstract: Green's theorem is employed to find the quantity relationship among the constraints of heating rate,dynamic pressure and lift in reentry flight.The paper deduced the approximate solution of the optimal aeroassisted coplanar trajectories under the three typical constraints.The performance index to be minimized are either heat input,the total dynamic pressure,time during the atmospheric flight,the time integral of the square of the path inclination;or maximize the time of flight during the atmospheric portion of the trajetory.An important conclusion is firstly obtained:under the three constraints above,the optimal aeroassisted coplanar transfers with the first forth kinds payoffs have the same optimal control laws.