Perturbative Analysis on Orbital Kinematics of Flybys and Applications to Doppler Observation

Abstract

This paper presents a new analytical framework for Doppler covariance analysis of planetary flybys. Regardless of the strength of gravitational interaction, this analytical framework is applicable to both conservative and nonconservative perturbations. In this framework, first-order analytical formulas for position and velocity variation are derived for hyperbolic orbits, and a linear model of the Doppler observable is adopted for planetary flybys. Through this method, the analytical variance of the standard gravitational parameter is derived and analyzed for Doppler observations of planetary flybys. This analytical variance can predict the expected precision of the mass determination via analysis of Doppler observation data without regard for the strength of gravitational interactions. The analytical variance is also applicable to preliminary parametric analyses of flyby geometries for mass determinations. Two numerical simulations and one Monte Carlo simulation demonstrate the validity of the analytical framework and the analytical mass variance.