A general time element for orbit integration in cartesian coordinates
Abstract
For increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates, two techniques are discussed:
the use of an independent variable different from the time, which increases the efficiency of the numerical integration, the use of a time element, which reduces the in-track error. A general expression of a time element valid for an arbitrary independent variable is presented. This time element allows to switch independent variable just by applying a scaling factor without having to change the differential equations of the motion. Taking the example of a transfer orbit for a geosynchronous mission, a comparison between the use of the eccentric, true and elliptic anomaly as independent variable is shown. The elliptic anomaly (a newly defined anomaly intermediate between the eccentric and the true anomaly) is shown to perform significantly better than the other classical anomalies.- Publication:
-
Advances in Space Research
- Pub Date:
- 1981
- DOI:
- 10.1016/0273-1177(81)90008-9
- Bibcode:
- 1981AdSpR...1f..69J
- Keywords:
-
- Cartesian Coordinates;
- Eccentric Orbits;
- Numerical Integration;
- Orbit Calculation;
- Satellite Orbits;
- Accuracy;
- Astrodynamics;
- Equations Of Motion;
- Orbital Elements;
- Orbital Mechanics;
- Transfer Orbits;
- Astrodynamics