http://arxiv.org/abs/1810.00397
We study a general relativistic gravitomagnetic 3rd-body effect induced by the spin angular momentum ${\boldsymbol{S}}\textrm{X}$ of a rotating mass $M\textrm{X}$ orbited at distance $r_\textrm{X}$ by a local gravitationally bound restricted two-body system $\mathcal{S}$ of size $r\ll r_\textrm{X}$ consisting of a test particle revolving around a massive body $M$. We analytically work out the doubly averaged rates of change of the Keplerian orbital elements of the test particle by finding non-vanishing long-term effects for the inclination $I$, the node $\Omega$ and the pericenter $\omega$. We numerically calculate their magnitudes for some astronomical scenarios in our solar system. For putative man-made orbiters of the natural moons Enceladus and Europa in the external fields of Saturn and Jupiter, the relativistic precessions due to the angular momenta of the gaseous giant planets can be as large as $\simeq 10-50~\textrm{milliarcseconds~per~year}~\left(\textrm{mas~yr}^{-1}\right)$. The effects induced by the Sun’s angular momentum on artificial probes of Mercury and the Earth are at the level of $\simeq 1-0.1~\textrm{microarcseconds~per~year}~\left(\mu\textrm{as~yr}^{-1}\right)$.
L. Iorio
Tue, 2 Oct 18
72/84
Comments: LaTex2e, 15 pages, 3 tables, no figures
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