The equivalence principle and the gravitational constant in experimental relativity

Fischbach's analysis of the Eotvos experiment, showing an embedded fifth force, has stressed the importance of further tests of the Equivalence Principle (EP). From Galilei and Newton, the EP played the role of a postulate for all gravitational physics and mechanics (weak EP), until Einstein, who extended the validity of the EP to all physics (strong EP). After Fischbach's publication on the fifth force, several experiments have been performed or simply proposed to test the WEP. They are concerned with possible gravitational potential anomalies, depending upon distances or matter composition. While the low level of accuracy with which the gravitational constant G is known has been recognized, experiments have been proposed to test G in the range from few cm until 200 m. This paper highlights the different features of the proposed space experiments. Possible implications on the metric formalism for objects in low potential and slow motion are briefly indicated