Time element for a general anomaly

Details Time element for a general anomaly Time element for a general anomaly

Dec 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jansc..31..561z&link_type=abstract

Journal of the Astronautical Sciences (ISSN 0021-9142), vol. 31, Oct.-Dec. 1983, p. 561-567.

Mathematics

Orbit Perturbation, Orbital Mechanics, Time Functions, Transformations (Mathematics), Anomalies, Eccentric Orbits, Elliptical Orbits, Equations Of Motion, Transfer Orbits

Scientific paper

A general anomaly, introduced in connection with the time transformation dt/dS(alpha) = r to the alpha, reduces to the classical mean, eccentric, elliptic, and true anomaly with alpha = 0, 1, 1.5, and 2, respectively. A time element associated with this general anomaly is introduced, and a differential equation in Cartesian coordinates for this element is obtained. The errors in position after one and after ten Keplerian periods with and without the time element are calculated for a geosynchronous transfer orbit with semimajor axis of 24,371 km, eccentricity of 0.73, and inclination of 27 deg. Using the time transformation only, the propagation of error increases with increasing alpha, while the effectiveness of time elements also increases with increasing alpha.

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