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];
IJMPD(17)-a1709 [laser ranging, overview].

> __Satellites__:
see Gravity Probe B;
LAGEOS; LARES.

> __Effects__: see Geodetic Precession.

__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*
\(\gg\) *R*_{S} 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,

*ω*_{prec} ≈ 3 (*GM*)^{3/2}
/ *c*^{2}(1−*e*^{2})
*a*^{5/2} .

* __Results__: The
value of *β* is consistent with general relativity to within *σ*(*β*)
= 0.003; *J*_{2, 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 a1802 [new general relativistic contribution].

@ __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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