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Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into a sequence of convex subproblems instead of a single convex problem when aerodynamic forces are ignored. Besides, each subproblem is significantly more complicated, which increases computation. A fast real-time interior point method was presented to solve the correlated convex subproblems onboard in the work. The main contributions are as follows: Firstly, an algorithm was proposed to accelerate the solution of linear systems that cost most of the computation in each iterative step by exploiting the specific problem structure. Secondly, a warm-starting scheme was introduced to refine the initial value of a subproblem with a rough approximate solution of the former subproblem, which lessened the iterative steps required for each subproblem. The method proposed reduced the run time by a factor of 9 compared with the fastest publicly available solver tested in Monte Carlo simulations to evaluate the efficiency of solvers. Runtimes on the order of 0.6 s are achieved on a radiation-hardened flight processor, which demonstrated the potential of the real-time onboard application.