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To maximize the payload mass, an aerocapture trajectory should be flown in such a way that both the final {\Delta}V and the total heat load are minimized. For some aerocapture missions, the heating due to radiation of high temperature gases in the shock-layer is so much larger than the heat due to convection, that the latter is negligible. This paper provides analytical proof and numerical validation that radiative heat is minimized by the same trajectory that minimizes the final {\Delta}V: a single switch bang-bang trajectory, starting with full lift-up, full lift-down commands. Further, a novel guidance that plans a bang-bang trajectory with constraints in the attitude kinematics is introduced. While achieving similar performance as the current state-of-the-art, the inclusion of constraints in attitude kinematics allows for much less tuning. Finally, a lateral guidance that makes use of information on the final inclination of the predicted trajectory is introduced. Such guidance allows for very high accuracy in the inclination requirements with only two reversals, by requiring a single parameter to be tuned., Comment: Submitted to the Journal of Guidance, Control, and Dynamics