The reasons why the post-Newtonian approximation is so “unreasonably effective” (quoting C. M. Will) in the quasistrong regime of binary pulsar systems—like the one mentioned—but also in the strong regime of inspiraling compact systems (e.g. black holes before final fusion [19]) are unknown [20].

This is the Laplace-Runge-Lenz vector that identifies the satellite pericenter direction: A constant of motion in the ideal case of the 2-body Newtonian problem.

The mean argument of latitude is not a true longitude along the orbit of the satellite, as is the argument of latitude $u=\omega +f$, with $f$ the true anomaly.

These mean elements were calculated from the Keplerian osculating elements estimated during a previous analysis of the satellite orbit.

This is not the case for LAGEOS II, whose radiation coefficient ($C_R\simeq 1.12$) has a relative error of 0.5%, and is therefore sufficiently known. However, we must take into account that this coefficient, if estimated in the POD, acts as a sort of scaling factor for the entire surface of the satellite and is therefore capable of absorbing the imperfections of the dynamical model.

Specifically, we mean the differences in the models used by the two software in our analyses.

Indeed, thanks to the relation ${\sin }^2(x)=\frac{1-\cos 2x}{2}$, the signal at $f_0$ splits into a d.c. component and one oscillating at twice the target frequency.

With $J_{\ell }=-\sqrt{2\ell +1}{\overline{C}}_{\ell ,0}$ and ${\overline{C}}_{\ell ,0}$ the normalized zonal harmonics.

Where $\cos \theta =\sin i\sin (\omega +f)$ and $f$ represents the true anomaly. By expressing the true anomaly as a function of the mean anomaly and averaging over this variable, the long-term effects are obtained.

See ICGEM Temporal Models at https://icgem.gfz-potsdam.de/sl/temporal.

The values reported for the quadrupole were obtained from two different analyses performed by the CSR, the first and of greater temporal extension is plotted in black while the second is plotted in gray. In the time interval common to the two analyses, the values for the coefficient are in good agreement.

UTOPIA is based on a zero-tide potential, i.e., based on the removal of the permanent part of the external potential from the mean-tide potential.

The GRACE and GRACE-FO data were considered to compare whether the trends measured for these coefficients using the SLR technique were still consistent, including their periodic behavior, with those obtained with a different technique and with non-geodetic satellites.

In SATAN, the secular trends of the gravity field coefficients were modeled following [54].

This estimate is comparable with the error provided by Lemoine2019.

In [33], we conservatively assumed a 1% error in knowledge of the radiation coefficient based on the $C_R$ estimate performed in 2004 by [122] in a dedicated POD. A 1% error was independently confirmed by [123] and by [124].