Note on the analytical integration of circumterrestrial orbits

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