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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
Universe 2019, 5(4), 87; https://doi.org/10.3390/universe5040087
Received: 4 March 2019 / Revised: 20 March 2019 / Accepted: 28 March 2019 / Published: 31 March 2019
(This article belongs to the Special Issue Universe: Feature Papers 2019 - Gravitational Physics)
We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum S X of a rotating mass M X orbited at distance r X by a local gravitationally bound restricted two-body system S of size r r X 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 Ω and the pericenter ω . 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 Δ ρ ˙ can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e., σ ρ ˙ = 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). View Full-Text
Keywords: general relativity and gravitation; experimental studies of gravity; experimental tests of gravitational theories; satellite orbits general relativity and gravitation; experimental studies of gravity; experimental tests of gravitational theories; satellite orbits
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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.

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