Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Abstract

Context. Forty years of lunar laser ranging (LLR) data provide an excellent basis to determine various parameters of the Earth-Moon system as well as parameters related to gravitational physics. Aims. We update the Institut für Erdmessung (IfE) LLR model taking the effect of a fluid lunar core into consideration. The temporal variation in the gravitational constantĠ/G 0 and the strong equivalence principle, parameterized by the Nordtvedt parameter η, are investigated. Methods. A set of LLR observations from 1970 to 2009 was analysed and the parameters were determined by a least squares adjustment in two runs. After solving for classical Newtonian parameters (e.g. initial conditions for the lunar orbit and rotation) in the first run, relativistic parameters were determined in the second run. Results. The upper limits to the gravitational constant and the Nordtvedt parameter were found to beĠ/G 0 = (−0.7 ± 3.8)×10 −13 yr −1 and η = (−0.6 ± 5.2) × 10 −4 .

A uniform treatment of the orbital effects due to a violation of the strong equivalence principle in the gravitational Stark-like limit

“…Our results are important also to accurately asses the overall uncertainty which can be obtained when constraints on ∆ are inferred by comparing them with the corresponding em- 7 If the polarizing external field is due to the Sun, our calculation are not strictly applicable to the Earth-Moon system since the temporal variations of g may not be neglected over the characteristic timescales of such a binary. 8 For exoplanets, see [37,38,39].…”

“…Potential SEP violations in the Earth-Moon system freely falling in the external gravitational field of the Sun, theoretically predicted by Nordtvedt long ago [3,4], are currently searched for with the Lunar Laser Ranging (LLR) technique [5,6,7] in the framework of the Parametrized Post-Newtonian (PPN) formalism. There are projects to test SEP with the Martian moon Phobos and the Planetary Laser Ranging (PLR) technique [8] as well.…”

Transiting planets as a precision clock to constrain the time variation of the gravitational constant

“…which is weaker by six orders of magnitude than those based on the pulsar timing (e.g., Williams et al 1976;Kaspi et al 1994;Zhu et al 2015) and the lunar ranging (e.g., Hofmann et al 2010). We would like to emphasize, however, that the conventional assumption of the constantĠ is not general, but has been introduced just for simplicity.…”

Parameterized post-Newtonian formalism for multimetric gravity

“…[8,9,[41][42][43][44][45][46]. Gravity theories whose parameters exceed these bounds are therefore experimentally excluded.…”