Preliminary orbit-determination method having no co-planar singularity

Details Preliminary orbit-determination method having no co-planar singularity Preliminary orbit-determination method having no co-planar singularity

Mar 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..15..137b&link_type=abstract

Celestial Mechanics, vol. 15, Mar. 1977, p. 137-160.

Mathematics

2

Astrodynamics, Orbit Calculation, Orbital Position Estimation, Celestial Mechanics, Singularity (Mathematics), Vector Analysis

Scientific paper

In order to avoid the singularity that arises when determining the orbit of an object from three angular position observations when the plane of the observer is nearly coincident with the plane of the object, an efficient method is developed for determining an orbit based on four observations. Three observations yield the unit vector L in the direction of the object at epoch and the first two time derivatives of L at epoch, while a fourth observation allows one to compute the third time derivative of L at epoch. L and the first derivative of L at epoch define the orbit except for the range and the range-rate. A simple expression relates range and range rate with the dot product of the second and first time derivative of L. Range is determined by a differential correction scheme given observed-minus-computed residuals.

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