Inkwan Park (University of Colorado at Boulder), Daniel J. Scheeres (University of Colorado at Boulder)
Keywords: Lie transformation, Analytic approach, Simplified dynamical system, Uncertainty propagation
Abstract:
A major topic in the field of space situational awareness is the accurate mapping of the uncertainty of an observed object; this has led to high precision modeling of orbital motion and their associated uncertainty propagation. A main purpose of our research is to explore how much precision is needed in describing the dynamical motion of a spacecraft to accurately map uncertainty. To do this, we define an analytical simplified dynamical system (SDS) and probe the relation between accuracy and precision in uncertainty propagation. The use of an analytical theory that is precise enough can have significant savings in computation time. In this research, our SDS is developed based on analytic solutions found by applying the Deprit-Hori Lie transformation theory. An analytic approach has an advantage in that it can give more insight into how the short-period variations influence the uncertainty propagation as well as provide more efficient computation. The SDS includes multiple perturbations caused by the oblate Earth, gravitational attraction of a third-body, and solar radiation pressure (SRP). An artificial satellite in a Medium-Earth-Orbit (MEO) is chosen to magnify perturbing effects due to the third-body and SRP relative to the Earth oblateness. A reference uncertainty is generated through Monte-Carlo simulations based on the full dynamical system. The accuracy of the SDS is verified through two statistical methods: 1) comparison of the central moments of the probability density function, 2) statistical energy test. Improvements in computational efficiency are investigated by comparing two factors: 1) number of function calls, 2) computation time. In summary, we derive approximate analytic solutions including multiple perturbations, and then define the SDS from them for a satellite in the MEO region. We verify the accuracy of the uncertainty propagation with the SDS by applying two statistical methods as well as show improvements in the computational efficiency of this approach.
Date of Conference: September 9-12, 2014
Track: Astrodynamics