New general relativistic contributions to Mercury’s orbital elements and their measurability. (arXiv:1908.09670v3 [gr-qc] UPDATED)

New general relativistic contributions to Mercury’s orbital elements and their measurability. (arXiv:1908.09670v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Iorio_L/0/1/0/all/0/1">Lorenzo Iorio</a>

We numerically and analytically work out the first-order post-Newtonian (1pN)
orbital effects induced on the semimajor axis $a$, the eccentricity $e$, the
inclination $I$, the longitude of the ascending node $Omega$, the longitude of
perihelion $varpi$, and the mean longitude at epoch $epsilon$ of a test
particle orbiting its primary, assumed static and spherically symmetric, by a
distant massive third body X. For Mercury, the rates of change of the linear
trends found are $dot I_mathrm{1pN}^mathrm{X} =
-4.3,mathrm{microarcseconds,per,century},left(mumathrm{as,cty}^{-1}right)$,
$dotOmega_mathrm{1pN}^mathrm{X} = 18.2,mumathrm{as,cty}^{-1}$,
$dotvarpi_mathrm{1pN}^mathrm{X} = 30.4,mumathrm{as,cty}^{-1}$,
$dotepsilon_mathrm{1pN}^mathrm{X} = 271.4,mumathrm{as,cty}^{-1}$,
respectively. Such values, which are due to the added actions of the other
planets from Venus to Saturn, are essentially at the same level of, or larger
by one order of magnitude than, the latest formal errors in the Hermean orbital
precessions calculated with the EPM2017 ephemerides. The perihelion precession
$dotvarpi_mathrm{1pN}^mathrm{X}$ turns out to be smaller than some values
recently appeared in the literature in view of a possible measurement with the
ongoing BepiColombo mission. Linear combinations of the supplementary advances
of the Keplerian orbital elements for several planets, if determined
experimentally by the astronomers, could be set up in order to disentangle the
1pN $N$-body effects of interest from the competing larger precessions like
those due to the Sun’s quadrupole moment $J_2$ and angular momentum
$boldsymbol{S}$.

We numerically and analytically work out the first-order post-Newtonian (1pN)
orbital effects induced on the semimajor axis $a$, the eccentricity $e$, the
inclination $I$, the longitude of the ascending node $Omega$, the longitude of
perihelion $varpi$, and the mean longitude at epoch $epsilon$ of a test
particle orbiting its primary, assumed static and spherically symmetric, by a
distant massive third body X. For Mercury, the rates of change of the linear
trends found are $dot I_mathrm{1pN}^mathrm{X} =
-4.3,mathrm{microarcseconds,per,century},left(mumathrm{as,cty}^{-1}right)$,
$dotOmega_mathrm{1pN}^mathrm{X} = 18.2,mumathrm{as,cty}^{-1}$,
$dotvarpi_mathrm{1pN}^mathrm{X} = 30.4,mumathrm{as,cty}^{-1}$,
$dotepsilon_mathrm{1pN}^mathrm{X} = 271.4,mumathrm{as,cty}^{-1}$,
respectively. Such values, which are due to the added actions of the other
planets from Venus to Saturn, are essentially at the same level of, or larger
by one order of magnitude than, the latest formal errors in the Hermean orbital
precessions calculated with the EPM2017 ephemerides. The perihelion precession
$dotvarpi_mathrm{1pN}^mathrm{X}$ turns out to be smaller than some values
recently appeared in the literature in view of a possible measurement with the
ongoing BepiColombo mission. Linear combinations of the supplementary advances
of the Keplerian orbital elements for several planets, if determined
experimentally by the astronomers, could be set up in order to disentangle the
1pN $N$-body effects of interest from the competing larger precessions like
those due to the Sun’s quadrupole moment $J_2$ and angular momentum
$boldsymbol{S}$.

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