Jay McMahon, University of Colorado Boulder, Daniel J. Scheeres, University of Colorado Boulder
Keywords: orbit determination, solar radiation pressure, tracking, HAMR debris
Abstract:
This paper investigates the weaknesses of using the cannonball model to represent the solar radiation pressure force on an object in an orbit determination process, and presents a number of alternative models that greatly improve the orbit determination performance. These weaknesses are rooted in the fact that the cannonball model is not a good representation of the true solar radiation pressure force acting on an arbitrary object. Using an erroneous force model results in poor estimates, inaccurate trajectory propagation, unrealistic covariances, and the inability to fit long and/or dense arcs of data. The alternative models presented are derived from a Fourier series representation of the solar radiation pressure force. The simplest instantiation of this model requires only two more parameters to be estimated, however this results in orders of magnitude improvements in tracking accuracy.
This improvement is illustrated through numerical examples of a discarded upper stage in a geosynchronous transfer orbit, and more drastically for a piece of high area-to-mass ratio debris in a near-geosynchronous orbit. The upper stage example shows that using the proposed 3-parameter model can improve the orbit fit from 5 days of tracking data by 2-4 orders of magnitude over the cannonball model. Perhaps more importantly, over a 28 day propagation arc with the estimated models, the prediction errors with the 3-parameter model rarely exceed 2-sigma of the propagated covariance, whereas the cannonball prediction errors grow to over 70-sigmaof the propagated covariance.
Most significantly, we show that using the proposed Fourier model greatly improves estimation of HAMR debris orbits, where the cannonball model can struggle to fit the data at any level. In the most extreme case tested, fitting 3 short arcs of data each separated by 100 hours, the Fourier model fits the orbit to the centimeter level, while the cannonball model has errors on the order of 1000 km.
Implementation of the improved solar radiation pressure models can therefore help to alleviate track correlation, object identification, and sensor tasking issues that plague current catalog maintenance due to the standard inaccurate dynamic model.
Date of Conference: September 15-18, 2015
Track: Astrodynamics