On Einstein's Theory of Gravitation and its Astronomical Consequences. First Paper

Sitter, W. de

doi:10.1093/mnras/76.9.699

Cited by 271 publications

(170 citation statements)

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“…In GR, the Kerr metric [84,85] at large distance gives the constants H = −F = G = −2. The result G = −2 can also be derived more generally as shown by de Sitter [86] and Lense & Thirring [87]. As above, J = ma denotes the magnitude of Earth's rotational angular momentum.…”

Section: Around Earthmentioning

confidence: 89%

Constraining torsion with Gravity Probe B

et al. 2007

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It is well-entrenched folklore that all torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally, and consider non-standard torsion theories in which torsion can be generated by macroscopic rotating objects. In the spirit of action=reaction, if a rotating mass like a planet can generate torsion, then a gyroscope would be expected to feel torsion. An experiment with a gyroscope (without nuclear spin) such as Gravity Probe B (GPB) can test theories where this is the case.Using symmetry arguments, we show that to lowest order, any torsion field around a uniformly rotating spherical mass is determined by seven dimensionless parameters. These parameters effectively generalize the PPN formalism and provide a concrete framework for further testing GR. We construct a parametrized Lagrangian that includes both standard torsion-free GR and HayashiShirafuji maximal torsion gravity as special cases. We demonstrate that classic solar system tests rule out the latter and constrain two observable parameters. We show that Gravity Probe B is an ideal experiment for further constraining non-standard torsion theories, and work out the most general torsion-induced precession of its gyroscope in terms of our torsion parameters.

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Section: Around Earthmentioning

confidence: 89%

Constraining torsion with Gravity Probe B

et al. 2007

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“…We adopt the value of  =´-S 190 10 kg m s 39 2 1 from helioseismology (Pijpers 1998;Mecheri et al 2004), which gives a Mercury perihelion precession rate of about −0 002/century for γ=1 (Iorio 2005). For earlier theoretical calculation of the LT effect on the perihelion precession of Mercury based on previous estimates of Mercury's orbit and the Sun's angular momentum (see de Sitter 1916;Barker & O'Connell 1970;Cugusi & Proverbio 1978;Soffel 1989). The Earth-induced LT effect has been detected for the LAGEOS satellites in Earth orbit (with 10% stated uncertainty, but with ongoing evaluation; Ciufolini & Pavlis 2004;Ciufolini et al 2011;Iorio 2011b;Renzetti 2014) and contributed to the precession of gyroscopes measured by Gravity Probe B (19%) (Everitt et al 2011).…”

Section: Dynamical Effects On Precession Of Mercury's Perihelionmentioning

confidence: 99%

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

et al. 2017

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The perihelion of Mercury's orbit precesses due to perturbations from other solar system bodies, solar quadrupole moment (J 2 ), and relativistic gravitational effects that are proportional to linear combinations of the parametrized post-Newtonian parameters β and γ. The orbits and masses of the solar system bodies are quite well known, and thus the uncertainty in recovering the precession rate of Mercury's perihelion is dominated by the uncertainties in the parameters J 2 , β, and γ. Separating the effects due to these parameters is challenging since the secular precession rate has a linear dependence on each parameter. Here we use an analysis of radiometric range measurements to the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft in orbit about Mercury to estimate the precession of Mercury's perihelion. We show that the MESSENGER ranging data allow us to measure not only the secular precession rate of Mercury's perihelion with substantially improved accuracy, but also the periodic perturbation in the argument of perihelion sensitive to β and γ. When combined with the γ estimate from a Shapiro delay experiment from the Cassini mission, we can decouple the effects due to β and J 2 and estimate both parameters, yielding ( ) ( ) b -= -´-1 2.7 3.9 10 5 and J 2 =(2.25±0.09)×10 −7. We also estimate the total precession rate of Mercury's perihelion as 575.3100±0.0015″/century and provide estimated contributions and uncertainties due to various perturbing effects.

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“…without fixing the radial coordinate, like Combridge and Janne did long ago [16], [17], one ends up to write de Sitter's line element [18] …”

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confidence: 99%

Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

Antoci¹,

Liebscher²,

Mihich³

2001

Class. Quantum Grav.

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Abstract. When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force four-vector. The norm of this force is calculated for Bach's twobody solution, that is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l ′ is made to vanish. In the limit when, say, l ′ → 0, the norm of the force divided by l ′ and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms happen thus to grow without limit when the test body (respectively the vanishing mass l ′ ) is kept at rest in a position closer and closer to Schwarzschild's two-surface.

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On Einstein's Theory of Gravitation and its Astronomical Consequences. First Paper

Cited by 271 publications

References 0 publications

Constraining torsion with Gravity Probe B

Constraining torsion with Gravity Probe B

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

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