Analysis of position and velocity variations for hyperbolic orbits and application to flyby anomaly

Flyby anomaly indicates the existence of an unknown perturbation (i.e., anomalous acceleration) that affects hyperbolic trajectories. Based on the analytical position and velocity variations, this paper investigates the general kinematics of perturbed hyperbolic orbits. As a result, post-interaction approximation formulas are derived. Based on these results, the observation data of the Galileo and NEAR Earth flybys are analyzed. The analysis results derive new constraints for flyby kinematics. The authors of this paper selected a few of the hypothetical acceleration models and analyzed their kinematical properties as representative examples. The simulation results show that the acceleration models fail to reproduce the characteristics of the range and Doppler observation data. This means that, in modeling the flyby anomaly, not only energy variation, but also kinematical constraints must be considered to reproduce the observation data.