https://doi.org/10.1140/epjc/s10052-019-7337-8
Regular Article - Theoretical Physics
On the mean anomaly and the mean longitude in tests of post-Newtonian gravity
Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Viale Unità di Italia 68, 70125, Bari, BA, Italy
* e-mail: lorenzo.iorio@libero.it
Received:
2
July
2019
Accepted:
21
September
2019
Published online:
4
October
2019
The distinction between the mean anomaly 
and the mean anomaly at epoch 
, and the mean longitude l(t) and the mean longitude at epoch 
is clarified in the context of a their possible use in post-Keplerian tests of gravity, both Newtonian and post-Newtonian. In particular, the perturbations induced on 
by the post-Newtonian Schwarzschild and Lense–Thirring fields, and the classical accelerations due to the atmospheric drag and the oblateness 
of the central body are calculated for an arbitrary orbital configuration of the test particle and a generic orientation of the primary’s spin axis 
. They provide us with further observables which could be fruitfully used, e.g., in better characterizing astrophysical binary systems and in more accurate satellite-based tests around major bodies of the Solar System. Some erroneous claims by Ciufolini and Pavlis appeared in the literature are confuted. In particular, it is shown that there are no net perturbations of the Lense–Thirring acceleration on either the semimajor axis a and the mean motion 
. Furthermore, the quadratic signatures on and l(t) due to certain disturbing non-gravitational accelerations like the atmospheric drag can be effectively disentangled from the post-Newtonian linear trends of interest provided that a sufficiently long temporal interval for the data analysis is assumed. A possible use of along with the longitudes of the ascending node 
in tests of general relativity with the existing LAGEOS and LAGEOS II satellites is suggested.
© The Author(s), 2019
