This presentation will summarize the results of my analysis of Cassini's Earth flyby of 1999 August 18, based upon two sets of CCD astrometric observations. The first set (11 observations) was taken by G. J. Garradd at Loomberah. The second set (four observations) was taken by R. H. McNaught at Siding Spring. Both sets of observations were obtained from the Project Pluto website (http://www.projectpluto.com/cassini.htm) as posted there by Bill J. Gray. My analysis applies Herget's method of preliminary orbit determination with the following two modifications. 1. Gauss's hypergeometric X-function is expressed as a quotient of Stumpff's c-functions, rather than as a truncated series. The velocity at the first observation time is solved for explicitly via Gauss's method. 2. Position and velocity at the first observation time are propagated to the intermediate observation times as f and g functions of c-functions. Further, the analysis uses batch least squares differential correction (DC) to improve the initial estimates of cartesian position and velocity as obtained via Herget's method. The batch DC uses analytical partials based upon W. H. Goodyear's two-body state transition matrix, with Goodyear's s-functions reformulated in terms of Stumpff's c-functions. The preliminary and improved orbit determination algorithms were implemented in both the heliocentric ecliptic (sun as primary) and geocentric equatorial (Earth as primary) reference frames. Each algorithm was then realized as two complementary Mathcad worksheets, one an "initiator" and the other an "iterator". All four pairs of worksheets were applied to the same set of 15 CCD astrometric observations. I will describe the algorithms as so implemented, their limitations and their capabilities, and the results that I obtained with them.
AAS/Division of Dynamical Astronomy Meeting
- Pub Date:
- May 2000