Phenomenological linear theory of gravitation : Part I. Classical mechanics
Abstract
Reasons are given why a linear theory of gravitation, if not the final word on gravity, yet is of considerable interest. Starting from a theory of considerable generality, we narrow down this generality by choosing the various constants in the theory on considerations of convenience as well as adjustment to experimental data; two of the constants are made zero. The number of facts predicted by the theory exceeds the number of adjustable constants appearing in it. Our theory differs from both Birkhoff's or Moshinsky's theory and from the linearization of Einstein's theory. In the present paper we explain the choice of the gravitational Lagrangian and discuss the choice of interaction of gravity with particles and other fields. We calculate the static gravitational field around the sun assumed to be at rest. Gravitational effects due to stresses inside the sun are taken into account as they are of a slightly larger magnitude than the relativistic effects leading to the advance of the perihelion. We discuss the equations of motion of a point mass in this gravitational field and consider both slow particles ( e.g. Kepler orbits of planets) and fast particles ( e.g. photons passing the sun). When the slow-particle case is expanded to second-order terms in v 2/c 2, the advance of the perihelion is found. The results are compared with available experimental evidence, and the choice of the constants of the theory is given as a function of the more accurate results which future experiments may procure. Some possible choices of the constants are indicated.
- Publication:
-
Annals of Physics
- Pub Date:
- May 1957
- DOI:
- 10.1016/0003-4916(57)90057-X
- Bibcode:
- 1957AnPhy...1..168B