Aerocapture can significantly reduce the velocity increment required for a planetary orbital mission and reduce the amount of propellant needed. And it may be one of the key technologies necessary for large-scale space exploration missions in the future. In this paper, the analytical solution of aerocapture based on the piecewise variable ballistic coefficient is studied around the exploration of Mars. An aerocapture analytical predictive guidance algorithm for single ballistic coefficient switching is proposed. The terminal velocity after the ballistic coefficient switching can be obtained by analytical calculation in real time. The adaptive control of the switching time of the ballistic coefficient is realized. The simulation results show that the guidance algorithm is accurate and robust, which can effectively overcome the influence of atmospheric density error, aerodynamic parameter error, and initial state uncertainty.