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The validity of General Relativity, after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here we focus our attention on the equivalence principle, in particular the strong form. The results of ground experiments and lunar laser ranging have provided the best upper limit on the Nordtvedt parameter {eta} that models deviations from the strong equivalence principle. Its uncertainty is currently {sigma}[{eta}] =4.4 $times$ $10^{-4}$. In the first part of this paper we will describe the experiment, to measure {eta}, that will be done by the future mission BepiColombo. The expected precision on {eta} is $approx$ $10^{-5}$. In the second part we will consider the ranging between the Earth and a spacecraft orbiting near the Sun-Earth Lagrangian points to get an independent measurement of {eta}. In this case, we forecast a constraint similar to that achieved by lunar laser ranging.
We present in detail the scientific objectives in fundamental physics of the Space-Time Explorer and QUantum Equivalence Space Test (STE-QUEST) space mission. STE-QUEST was pre-selected by the European Space Agency together with four other missions f
General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on one of the m
We briefly summarize motivations for testing the weak equivalence principle and then review recent torsion-balance results that compare the differential accelerations of beryllium-aluminum and beryllium-titanium test body pairs with precisions at the
The Lunar Laser Ranging (LLR) experiment provides precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of highly accurate measurements of the distance between the Earth and Moon
We consider the problem of testing the Einstein Equivalence Principle (EEP) by measuring the gravitational redshift with two Earth-orbiting stable atomic clocks. For a reasonably restricted class of orbits we find an optimal experiment configuration