Effects of a Modified Gravitation Law on the Perihelion Shift
The perihelion shift in a satellitenulls orbit has become an important measure of the effects of non- Newtonian contributions to the force of gravity. Historically important contributions have been ascribed to general relativity, and more recently there has been interest in using measurements of the perihelion to corntrain parameters for forces from darlc energy, as well as explaining anomalous motion of artificial satellites. The functional form of the perihelion shut seen in the cases of general relativity and dark energy, calculated in the literature, is seen in the present work to generalize to other forces. The present work h d s a generalized formula for the precession caused by any central force for small eccentricity, as well as an integral giving the precession for any force with any eccentricity that b not been encountered in previous literature. In the case of power law forces, this integral is performed analytically. These results are analyzed numerically, and the new formulas are applied to recent applications in dark energy, anomalous satellite motion, and gravitational contributions from higher-dimensional theories.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2007
- F&M Theses Collection