Relativistic satellite orbits: central body with higher zonal harmonics

Schanner, Maximilian Arthus; Söffel, M.

doi:10.1007/s10569-018-9836-6

Cited by 6 publications

(9 citation statements)

References 20 publications

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“…Instead, neglecting such changes gives rise to the usual, time-honored Einstein-like 1PN precession. In principle, also other general relativistic precessions may be calculated, to the order O c −4 , from the mutual interaction of some 1PN accelerations induced by the bodies' mass and spin moments (Soffel et al 1987;Heimberger, Soffel & Ruder 1990;Panhans & Soffel 2014;Meichsner & Soffel 2015;Frutos-Alfaro & Soffel 2018;Schanner & Soffel 2018) entering the equations of motion; they will not be treated here because of their smallness. For some of them, see Iorio (2015).…”

Section: Introductionmentioning

confidence: 99%

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Iorio

2020

Universe

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At the second post-Newtonian (2PN) order, the secular pericentre precessionω 2PN of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computingω 2PN in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration A 2PN , and also an indirect part arising from the self-interaction of the 1PN acceleration A 1PN in the orbital average accounting for the instantaneous shifts induced by A 1PN itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity e. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericentre precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

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Section: Introductionmentioning

confidence: 99%

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Iorio

2020

Universe

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“…The two relativistic terms proportional to J 2 /c 2 appearing in ( 9) and ( 10) have the same structure. However, in the literature (Heimberger et al, 1990;Schanner and Soffel, 2018), they are usually kept separate and are respectively referred to as the indirect and direct term related to the non-trivial relativistic contribution of the quadrupole of the gravity field of the central body. The ordering of the perturbing terms is performed by assuming (with a certain degree of arbitrariness) the J 2 and c −2 terms to be of order and the J 4 term of order 2 , like the J 2 2 and J 2 × c −2 terms.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of frozen orbits in a gravity field with zonal harmonics

Cavallari

Pucacco

2022

Celest Mech Dyn Astron

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We propose a methodology to study the bifurcation sequences of frozen orbits when the second-order fundamental model of the satellite problem is augmented with the contribution of octupolar terms and relativistic corrections. The method is based on the analysis of twice-reduced closed normal forms expressed in terms of suitable combinations of the invariants of the Kepler problem, able to provide a clear geometric view of the problem.

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“…Let us consider a local gravitationally bound restricted two-body system S composed by a test particle completing a full orbital revolution around a planet of mass M at distance r in a time interval P b , and a distant 3rd body X with mass M X ≫ M and proper spin S X around which S revolves at distance r X ≫ r with orbital period P X b . In general, M may be endowed with its own Newtonian and post-Newtonian mass and spin multipole moments (Soffel & Frutos 2016;Frutos-Alfaro & Soffel 2018) affecting the satellite's motion with known (Capderou 2005;Poisson & Will 2014) and less known (Angélil et al 2014;Schärer et al 2017;Schanner & Soffel 2018) Newtonian and post-Newtonian orbital effects like the classical oblateness-driven orbital precessions, the gravitoelectric Einstein pericentre shift, the gravitomagnetic Lense-Thirring effect, etc. Let us consider a kinematically rotating and dynamically non-rotating coordinate system K (Brumberg & Kopeikin 1989;Damour, Soffel & Xu 1994;Kopeikin, Efroimsky & Kaplan 2011) attached to M in geodesic motion through the external spacetime deformed by the mass-energy currents of X, assumed stationary in a kinematically and dynamically non-rotating coordinate system K X whose axes point towards the distant quasars (Brumberg & Kopeikin 1989;Damour, Soffel & Xu 1994;Kopeikin, Efroimsky & Kaplan 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Less known features of motion are the pN gravitoelectric and gravitomagnetic effects associated with the asphericity of a central body induced by its mass quadrupole and spin octupole moments, respectively (Soffel et al 1988;Soffel 1989;Heimberger et al 1989;Brumberg 1991;Huang and Liu 1992;Panhans and Soffel 2014;Iorio 2015;Meichsner and Soffel 2015;Frutos-Alfaro and Soffel 2018;Schanner and Soffel 2018). To date, they have never been measured; a detailed study for a proposed satellite-based mission in the field of the Earth, dubbed HERO (Highly Elliptical Relativity Orbiter), can be found in Iorio (2019c).…”

Section: Introductionmentioning

confidence: 99%

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

Iorio

2019

Universe

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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 yr −1 . A preliminary numerical simulation shows that, for certain orbital configurations of a hypothetical Europa orbiter, its range-rate signal ∆ρ can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e. σρ = 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 yr −1 .

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Relativistic satellite orbits: central body with higher zonal harmonics

Cited by 6 publications

References 20 publications

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Bifurcation of frozen orbits in a gravity field with zonal harmonics

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

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