Error Propagation in a Two-Body Problem

Details Error Propagation in a Two-Body Problem Error Propagation in a Two-Body Problem

Sep 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002dda....33.1304l&link_type=abstract

American Astronomical Society, DDA Meeting #33, #13.04; Bulletin of the American Astronomical Society, Vol. 34, p.942

Astronomy and Astrophysics

Astronomy

Scientific paper

A two-body problem is augmented by a single tracking station at the earth's North Pole having an error (δ Zs) in the value of its geocentric Z-coordinate. An analytical expression is presented relating the error to a change (δ e) in the orbital eccentricity that results from propagation of the error during the least squares processing of tracking data. An outline of the analysis leading to the expression is presented. The expression is δ Zs=κ (aδ e), where a is the semi-major axis and κ is a ratio of closed-form power series in a parameter η , defined as the ratio of the earth's radius to the semi-major axis. Assumed are a circular orbit and ω =90 degrees. It is notable that the expression for η is not unique, separate ratios being required for range and range-rate data, respectively. Results of numerical checks using the general-purpose orbit analysis tool TRACE are presented, wherein close agreement between expected and computed results are found. Possible application to problems in satellite geodesy is discussed, as are plans for further study.

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