The Conditional Equivalence of ΔV Minimization and Apoapsis Targeting in Numerical Predictor-Corrector Aerocapture Guidance
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Lafleur, Jarret M.
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Abstract
Interest in aerocapture, a maneuver in which a spacecraft dives into the atmosphere of a planet
for nearly propellantless capture into planetary orbit, has grown steadily in recent years. One key
element required to execute this maneuver is an appropriate guidance algorithm for the
atmospheric phase of flight. A popular algorithm choice has been the numerical-predictor
corrector (NPC), which typically iterates on a time-invariant bank angle to target apoapsis of the
desired final orbit. This paper introduces the idea of using the NPC to select the bank angle that
instead minimizes the sum of periapsis-raise ΔV and apoapsis-cleanup ΔV, and demonstrates the
surprising finding that the two approaches are equivalent under a certain analytic condition. This
condition is derived and then applied to correctly predict a scenario in which apoapsis targeting
produces a suboptimal ΔV. This scenario is simulated, and the ΔV minimization algorithm is
shown to reduce the required ΔV by 23%. Monte Carlo simulations confirm both the scenarios of
equivalence and non-equivalence, and an automatable procedure is outlined that a user can
execute prior to simulating or flying a trajectory to determine whether apoapsis targeting is ΔV
optimal or whether a ΔV minimization algorithm is required.
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Date
2011-08
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