Delta-Rho, A perturbation method for general and astrodynamical trajectories

Abstract

The Delta-Rho perturbation technique is developed in a form applicable to both general dynamical and astrodynamical trajectories. It is subsequently verified for a specific astrodynamic example. It can be described as an extension of Encke's perturbation method. Like Encke it uses analytically determined trajectories, but unlike Encke it requires the definition and storage of a reference trajectory. If the reference trajectory includes all of the important perturbing forces to be considered, the integration of the state equations for the dispersed trajectories can yield satisfactory results when implemented using a highly simplified perturbation-force model. The Delta-Rho method is particularly useful when considering trajectories in the neighborhood of a reference (nominal) trajectory and has potential application to Monte Carlo studies of spacecraft missions, development of real-time guidance laws, and real-time generation of satellite ephemerides in small, vehicle-borne computers, to name a few.