Vishal Ray, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder; Siamak Hesar, SpaceNAV; Matt Duncan, SpaceNAV
Keywords: Drag coefficient, Fourier series, attitude, estimation
Abstract:
The estimation and modeling of drag on low altitude satellites and debris is a limiting problem in the prediction of their orbits over time. Independent of the stochastic variations in atmospheric density, which drive the magnitude of the drag force, there are systematic variations in the force acting on a body due to satellite specific factors and atmospheric conditions. These include satellite attitude shifts which cause variations in projected area, variations in ambient atmospheric parameters such as temperature, molecular composition, and the satellite wall temperature. All of these factors affect the gas-surface interactions which lead to different drag levels. Conventionally, these variations are mapped into the force by the drag coefficient. Thus, even with accurate empirical models for the atmospheric density, there remain systematic model uncertainties and time variations in the effective coefficient of drag of a body that affect its motion, which are not captured using the standard constant drag coefficient model. We report on our recent research on developing improved models of an arbitrary objects coefficient of drag with the overall purpose to develop corrections to the standard model. The new approach would allow these variations to be accurately estimated based on tracking data, enabling higher accuracy predictions.
Our approach leverages previous research on improving solar radiation pressure models (McMahon & Scheeres; JGCD 33(5) 2010, JGCD 37(1) 2014, JGCD 38(8) 2015). If the attitude profile of a satellite or object is known, a Fourier Series expansion of the overall coefficient of drag as a function of wind vector direction in the body-frame can be introduced. This formulation allows for the application of averaging theories that identify the components of the body that contribute to secular effects on the orbit, enabling these terms to be directly estimated in a filter. For bodies with unknown or more complex attitude profiles, we introduce a periodically varying drag coefficient tied to a satellites position in its orbit. This model enables the estimation of higher-order temporal variations in drag that would be correlated with variations in attitude, temperature and density. The abstract representation of the coefficient as a Fourier series expansion allows for these effects to be captured through estimation, without the need for sophisticated forward models.
At AMOS we plan to present the theoretical foundations of our approach and its application to both simulated and actual tracking data. We will show an improved prediction capability with the model and indicate how it can be incorporated into standard Kalman filter techniques.
Date of Conference: September 11-14, 2018
Track: Astrodynamics