Tests of General Relativity with Orbiting Bodies  

In General > s.a tests of general relativity / anomalous acceleration; orbits of gravitating bodies.
* Lunar ranging: Lunar laser ranging measurements are crucial for sensitive tests of the laws of gravitational physics (they provide stringent limits on violations of the equivalence principle, and enables very accurate tests of alternative theories) and geophysics, as well as for future human and robotic missions to the Moon; 2015, They currently rely on the corner-cube reflectors (CCR) currently on the Moon, which require no power and still work perfectly since their installation during the Apollo era; Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 mm.
@ Frameworks: Jaekel & Reynaud MPLA(05)gq/04 [for slightly generalized general relativity, and Pioneer]; Carloni et al PRD(11)-a1103 [in the presence of Rindler acceleration].
@ Lunar ranging: Nordtvedt PR(68); Nordtvedt CQG(96) [isotropy of gravity]; Cowsik ap/99 [radio]; Mashhoon & Theiss in(01)gq/00; Nordtvedt CQG(01), GRG(03)gq/02, gq/03-proc, Williams et al IJMPD(04)gq/03-conf, gq/04-conf, PRL(04)gq, ASR(06)gq/04-conf [laser]; Müller et al in(06)gq/05; Turyshev & Williams IJMPD(07)gq/06-proc [and Mars]; Kopeikin PRL(07)gq, a0809-ch [and satellites], a0902-conf [mm-precision]; Merkowitz LRR(10); > s.a. earth and its moon; tests of lorentz symmetry.
@ Solar system ranging: Anderson et al ApJ(96)gq/95 [Mars, Jupiter]; Iorio JGSP(02)gq/01 [satellites]; Turyshev et al gq/04-conf [Moon, Mars & beyond]; Bertolami IJMPD(08)ap/06-conf [high-accuracy solar system tests]; Ashby et al PRD(07) [BepiColombo future mission]; Anderson & Nieto IAU-a0907 [anomalies]; Ciufolini et al EPJP(12)-a1211 [constraints from the LARES satellite on deviations from geodesic motion]; Hees et al MG13(15)-a1301 [simulations of observations in alternative theories]; Ciufolini et al NPPS(13)-a1309 [LARES and LAGEOS satellites]; Sargsyan et al PS(14)-a1312 [non-gravitational perturbations on satellites]; Fienga et al a1409 [and Monte Carlo simulations]; Battista et al PRD(15)-a1507 [Earth-Moon Lagrange points]; Gurzadyan et al IJMPD(17)-a1709 [laser ranging, overview].
> Satellites: see Gravity Probe B; LAGEOS; LARES.
> Effects: see Geodetic Precession.

blue bullet Related subjects: see astrophysical and cosmological tests [strong-field tests, galactic center]; black-hole types [supermassive binary]; neutron stars [pulsars]; tests with spinning bodies [Lense-Thirring effect, Lense-Thirring-Schiff effect (frame dragging)].

Perihelion Advance / Precession > s.a. multipoles; Runge-Lenz Vector; solar system; test-body orbits; Two-Body Problem.
* Idea: In general relativity non-circular planetary orbits precess – their radial frequency is not equal to their angular frequency – and the magnitude can be used as a test of general relativity; Only in the newtonian limit a \(\gg\) RS we get no precession; In addition to the leading order term, there is a Thirring-Lense, gravitomagnetic term due to the Sun's rotation.
* Prediction: For Mercury, 43"/cy; For the binary pulsar, 4°/yr; In general,

ωprec ≈ 3 (GM)3/2 / c2(1−e2) a5/2 .

* Results: The value of β is consistent with general relativity to within σ(β) = 0.003; J2, Sun ≈ 10−7, from acoustic power spectra.
* Lense-Thirring term: The contribution from the Sun's angular momentum; 2005, The prediction is −0.0020, −0.0001 and −3 × 10−5 "/cy, for the three inner planets respectively, and are compatible with the measured perihelia corrections of −0.0036 ± 0.0050, −0.0002 ± 0.0004 and 0.0001 ± 0.0005, respectively; Smaller experimental errors for Mercury should be possible with the BepiColombo mission.
@ General references: Magnan a0712 [complete derivation]; Hioe PLA(09) [exact expression]; Lemmon & Mondragon AJP(09)oct-a0906 [alternative derivation]; Yamada & Asada a1105-wd [three-body-interaction effects]; Larrañaga & Cabarique a1202 [post-newtonian approximation, elementary derivation]; Hu et al AHEP(14)-a1312 [in a spherically symmetric spacetime].
@ Mercury: Moffat PRL(83) [and solar multipoles]; Stump AJP(88)dec, comment Doggett AJP(91)sep; Kurucz ap/06 [without general relativity?]; Iorio MG14(17)-a1601 [Lense-Thirring term]; Will PRL-a1802 + news sn(18)apr [new general relativistic contribution] + comment Zhou et al a1805, Iorio a1805.
@ With cosmological constant: Islam PLA(83); Freire et al GRG(01)gq/02 [+ conical defect]; Kraniotis & Whitehouse CQG(03)ap; Miraghaei & Nouri-Zonoz GRG(10)-a0810 [Newtonian limit of Schwarzschild-de Sitter]; Arakida IJTP(13)-a1212, comment Ovcherenko & Silagadze UJP(16)-a1511.
@ In other gravity theories: Iorio AHEP(07)-a0710 [f(R) theories and DGP models]; Biswas & Mani CEJP(08)-a0802 [in other gravity theory]; Schmidt PRD(08)-a0803 [modified newtonian]; Eingorn & Zhuk a0912 [with extra dimensions, problem with data]; Ridao et al CJP(14)-a1402 [in ETGR]; Özer & Delice CQG(18)-a1708 [modified gravity with a cosmological term]; De Laurentis et al a1801 [in f(R) gravity].
@ Related topics: Bolen et al CQG(01)gq/00 [McVittie spacetimes]; Stairs ap/01-MG9, LRR(03)ap [pulsar timing]; Dereli & Tucker MPLA(02)gq/01 [torsion]; Pireaux et al ASS(03)ap/01 [bounds on parameters]; Iorio PSS(07)gq/05 [LT term]; Kraniotis CQG(05)gq [Kerr, Kerr-AdS]; Iorio JCAP(05)gq [and brane world]; Pál & Kocsis MNRAS(08)-a0806, Jordan & Bakos ApJ(08)-a0806 [exoplanets]; Iorio AJ(09)-a0811 [anomalous precession of Saturn].

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