Artificial satellites preliminary orbit determination by the modified high-order Gauss method

Abstract

In recent years, high-order methods have shown to be very useful in many practical applications, in which nonlinear systems arise. In this case, a classical method of positional astronomy have been modified in order to hold a nonlinear system in its establishments (that in the classical method is reduced to a single equation). At this point, high-order methods have been introduced in order to estimate the solutions of this system and, then, determine the orbit of the celestial body. We also have implemented a user friendly application, which will allow us to make a numerical and graphical comparison of the different methods with reference orbits, or user defined orbits.

Keywords:

• orbit determination
• Gauss method
• nonlinear systems
• Newton's method
• order of convergence
• efficiency index

2010 AMS Subject Classifications :

• 65H05
• 65L20

Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions that have improved the content of the paper. This research was supported by Ministerio de Ciencia y Tecnología MTM2010-18539.