Physics
Scientific paper
Feb 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..15...21r&link_type=abstract
Celestial Mechanics, vol. 15, Feb. 1977, p. 21-33.
Physics
10
Equations Of Motion, Gravitational Effects, Particle Motion, Relativity, Satellite Orbits, Schwarzschild Metric, Celestial Mechanics, Disturbing Functions, Eccentricity, Kepler Laws, Newton Theory, Planetary Orbits
Scientific paper
The motion of a satellite of negligible mass about a massive spherically symmetric object in a space of Schwarzschild geometry is calculated by using ordinary Newtonian methods for an inverse-square gravitational field acted upon by an inverse-cube disturbing function. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted in the Lagrange planetary equations. The equations can be integrated to calculate the displacement in position of the satellite due to the relativistic potential. For example, the Beacon Explorer C satellite is found to be displaced by about 17.4 cm after one revolution. For Mercury the advance of the perihelion is about 85 km after one orbit, and the maximum periodic displacement is about 13 km.
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