Formulas of Position and Velocity Perturbation for Hyperbolic Orbit and Its Application to Flyby Anomaly

  • Published : 2011.04.15

Abstract

Flyby anomaly (unexpected energy increase during Earth Gravity Assists) indicates existence of an unknown non-conservative perturbation which affects hyperbolic trajectories. This presentation focuses on first order position and velocity perturbation formulas derived in terms of classical orbital element variations for hyperbolic orbit. By using both the perturbation formulas and numerical approach, we analyze effects of hypothetical acceleration models proposed by Hasse (2009), Lewis (2009), Gerrad and Sumner (2008), and Busack (2007). Based on analysis of perturbation effect on low earth orbit, we find that typical position perturbation is about 10m which is much larger than current orbit determination accuracy. From this, we deduce that anomalous acceleration only affects hyperbolic orbit or behaves differently in bound orbit. On the other hand, based on analysis of perturbation effects on hyperbolic trajectories, we find that position and velocity perturbations are highly different from acceleration models, and all of proposed models fail to explain observed range and Doppler data. Thus, it can be concluded that not only energy variations but also kinematics gives us crucial clues on the flyby anomaly, and kinematical characteristic should be considered in modeling flyby anomaly.

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