Mitigation of satellite orbit errors resulting from the numerical integration across shadow boundaries

Abstract

The tracking of geodetic satellites through the use of very precise laser ranging has led to the development and application of techniques to mitigate the effect of various numerical errors that can affect the convergence of orbit solutions or that introduce aliases into the estimated parameters. The dominant numerical integration error is in the along-track direction and has been controlled for long arc solutions through the introduction of empirical along-track acceleration parameters (CTs) and the application of Encke's method (J.B. Lundberg, B.E. Schutz, R.K. Fields, M.M. Watkins, AIAA Journal of Guidance, Control and Dynamics 14 (3) (1991) 683–686; J.B. Lundberg, S. Bettadpur, R.J. Eanes, AAS/AIAA Astrodynamcis Specialist Conference, Durango, Colorado, 19–22 August 1992, pp. AAS 91–351). In the case of orbit solutions for the LAser GEOdynamics Statellites (LAGEOS), the CT parameters are also used to represent the Yarkovsky drag effect. It has been found that the numerical integration across the shadow boundaries can introduce additional integration errors that introduce significant aliases in the CT parameters and compromise their representation of the Yarkovsky effect. With the appropriate choice of stepsize, the additional errors that result from the crossing of shadow boundaries can be mitigated significantly while maintaining a computationally efficient stepsize.