Time element for a general anomaly (orbits).

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.