The first constraint arises from the Earth-Moon system. A time variation of is then related to a
variation of the mean motion (
) of the orbit of the Moon around the Earth. A decrease in
would induce both the Lunar mean distance and period to increase. As long as the gravitational binding
energy is negligible, one has
The Lunar Laser Ranging (LLR) experiment has measured the relative position of the Moon with
respect to the Earth with an accuracy of the order of 1 cm over 3 decades. An early analysis of this
data [544] assuming a Brans–Dicke theory of gravitation gave that . It was
improved [365] by using 20 years of observation to get
, the main uncertainty
arising from Lunar tidal acceleration. With, 24 years of data, one reached [542]
and finally, the latest analysis of the Lunar laser ranging experiment [543] increased the constraint to
Similarly, Shapiro et al. [458] compared radar-echo time delays between Earth, Venus and Mercury with
a caesium atomic clock between 1964 and 1969. The data were fitted to the theoretical equation of motion
for the bodies in a Schwarzschild spacetime, taking into account the perturbations from the Moon and other
planets. They concluded that . The data concerning Venus cannot be used due to
imprecision in the determination of the portion of the planet reflecting the radar. This was improved to
by including Mariner 9 and Mars orbiter data [429]. The analysis was further
extended [457] to give
. The combination of Mariner 10 an Mercury and
Venus ranging data gives [12]
Reasenberg et al. [430] considered the 14 months data obtained from the ranging of the Viking
spacecraft and deduced, assuming a Brans–Dicke theory, . Hellings et al. [249
] using
all available astrometric data and in particular the ranging data from Viking landers on Mars deduced that
http://www.livingreviews.org/lrr-2011-2 |
Living Rev. Relativity 14, (2011), 2
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