Note on the analytical integration of circumterrestrial orbits

TL;DR

This paper compares classical and fictitious time-based analytical solutions for circumterrestrial orbits, highlighting their relative accuracy and the impact of higher-order extensions to guide better application choices.

Contribution

It provides a more objective comparison of classical and fictitious time analytical solutions, emphasizing the importance of proper initialization and higher-order extensions.

Findings

Proper initialization improves classical solutions' accuracy.

Higher-order extensions reveal distinct advantages and disadvantages.

Both approaches can be effectively used depending on the application context.

Abstract

The acclaimed merits of analytical solutions based on a fictitious time developed in the 1970's were partially overvalued due to a common misuse of classical analytical solutions based on the physical time that were taken as reference. With the main problem of the artificial satellite theory as a model, we carry out a more objective comparison of both kinds of theories. We find that the proper initialization of classical solutions notably balances the performance of the two distinct approaches in what respects to accuracy. Besides, extension of both kinds of satellite theories to higher orders show additional pros and cons of each different perturbation approach, thus providing complementary information to prospective users on which kind of analytical solution may better support their needs.