A general time element for orbit integration in Cartesian coordinates
Abstract
Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the intrack error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.
 Publication:

Advances in Space Research
 Pub Date:
 1981
 DOI:
 10.1016/02731177(81)900089
 Bibcode:
 1981AdSpR...1...69J
 Keywords:

 Cartesian Coordinates;
 Eccentric Orbits;
 Numerical Integration;
 Orbit Calculation;
 Satellite Orbits;
 Accuracy;
 Astrodynamics;
 Equations Of Motion;
 Orbital Elements;
 Orbital Mechanics;
 Transfer Orbits;
 Astrodynamics