Physics
Scientific paper
Jun 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992mgeo...17..155c&link_type=abstract
Manuscr. Geod., Vol. 17, No. 3, p. 155 - 163
Physics
Scientific paper
A new system of differential equations describing the motion of a celestial body is introduced. It is derived directly form Newton's law of motion in terms of Hill variables. In contrast to the use of Kepler elements, the application of Hill variables does not require any assumptions on the force (central gravitation as dominant force) and the shape of the orbit (e ≠ 0) and allows a clear distinction between position and velocity quantities. Furthermore, the Hill variables have the same advantage as the Kepler elements, i.e. they vary more smoothly in time than the rectangular coordinates. This property results in useful effects on the accuracy of a numerical orbit integration for long arcs in general. Numerical experiments have been carried out by integration of the orbits of a high satellite with both rectangluar coordinates and Hill variables using several integration methods. The first results demonstrate the advantages of the use of Hill variables.
Cui Chenzhou
Mareyen M.
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