A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body
Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Viale Unità di Italia 68, 70125 Bari (BA), Italy
Received: 4 March 2019 / Revised: 20 March 2019 / Accepted: 28 March 2019 / Published: 31 March 2019
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We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum
of a rotating mass
orbited at distance
by a local gravitationally bound restricted two-body system
consisting of a test particle revolving around a massive body M
. At the lowest post-Newtonian order, 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
and the pericenter
. Such theoretical results are confirmed by a numerical integration of the equations of motion for a fictitious 3-body system. We numerically calculate the magnitudes of the post-Newtonian gravitomagnetic 3-body precessions 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 ≃10 − 50 milliarcseconds per year (mas year−1
). A preliminary numerical simulation shows that, for certain orbital configurations of a hypothetical Europa orbiter, its range-rate signal
can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e.,
= 0.015 mm s−1
, after 1 d. The effects induced by the Sun’s angular momentum on artificial probes of Mercury and the Earth are at the level of ≃1 − 0.1 microarcseconds per year (μas year−1
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Iorio, L. A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body. Universe 2019, 5, 87.
Iorio L. A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body. Universe. 2019; 5(4):87.
Iorio, Lorenzo. 2019. "A Post-Newtonian Gravitomagnetic Effect on the Orbital Motion of a Test Particle around Its Primary Induced by the Spin of a Distant Third Body." Universe 5, no. 4: 87.
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