# Introduction

• Ephraim Fischbach
• Carrick L. Talmadge
Chapter

## Abstract

There has been renewed interest in recent years in the possibility of deviations from the predictions of Newton’s “inverse-square” (1/r2) law of universal gravitation: For two point massesm i andm j located a distance r apart, the magnitude of the force that one exerts on the other is given by
$$F = \frac{{{{G}_{N}}{{m}_{i}}{{m}_{j}}}}{{{{r}^{2}}}},$$
(1.1)
where GN = (6.67259 + 0.00085) x 10-11m3kg-1s-2is Newton’s gravitational constant. This interest stems from a number of sources, which include the following: Equation (1.1) is the expression one recovers by starting from Einstein’s theory of General Relativity (GR) and passing to the limit of nonrelativistic velocities and weak fields. Hence GR shares with Newtonian gravity the feature, contained in Eq. (1.1), that the acceleration of a test mass (say mi) is independent of mi(both its magnitude and chemical composition). As an experimental statement this is often referred to as the universality of free-fall(UFF), and tests of UFF have recently gained increased prominence, as we describe below. In GR the fact that all objects fall at the same rate in the same gravitational field is elevated to a fundamental assumption known as the equivalence principle [WEINBERG, 1972; MISNER, 1973; WILL, 1993; CIUFOLINI, 1995]. Although it is beyond the scope of the present book to discuss the various forms of the equivalence principle and their implications, suffice it to say that a breakdown of UFF (and hence of the equivalence principle) would pose a challenge for both GR and Newtonian gravity.

## Keywords

Equivalence Principle Test Mass Distance Scale Newtonian Gravity Newtonian Constant
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© Springer Science+Business Media New York 1999

## Authors and Affiliations

• Ephraim Fischbach
• 1
• Carrick L. Talmadge
• 1
1. 1.Department of PhysicsPurdue UniversityWest LafayetteUSA