The Period of Orbit as a Test of the General Theory of Relativity.
Abstract
The formalism of the General Relativity Hamilton Jacobi equation suggests four types of corrections due to General Relativity that might be the basis of a test of the predictions of General Relativity. Tests have been conducted on only three of these corrections. The fourth correction is to period of orbit of a test mass. The period of orbit is derived for the circular case using the geodesic equation. Using the HamiltonJacobi formalism and phase integral canonical transforms, the General Relativity form of Kepler's third law is derived and is valid for arbitrary eccentricities. The corrections due to General Relativity on the period of the planets are calculated. For Mercury the correction is 1.4 seconds. The timedelay experiment conducted at JPL and MIT numerically integrated the motion of six planets and least square adjusted the orbital constants over a period of 80 years. This experiment did not detect the period of orbit because of the particular formalism that is used in the least square adjustment procedure. A similar demonstration data reduction program was written and programmed. As anticipated, this demonstration program does not detect the period of orbit effect. A modification of the least square data reduction program is made and programmed. The modified program, as designed, will accurately measure the period of orbit. These modifications introduced into the timedelay experiment's data reduction procedures would result in a highly sensitive new test of the General Theory of Relativity.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT.........1P
 Keywords:

 Physics: Astronomy and Astrophysics;
 Formalism;
 HamiltonJacobi Equation;
 Prediction Analysis Techniques;
 Relativity;
 Canonical Forms;
 Data Reduction;
 Least Squares Method;
 Time Lag;
 Transformations (Mathematics);
 Astrophysics