Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2010-12-24
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
14 pages, 2 figures. Submitted to American Journal of Physics December 24, 2010
Scientific paper
Beginning with a Lagrangian that is consistent with both Newtonian gravity and the momentum-velocity relation of special relativity, an approximate relativistic orbit equation is derived that describes relativistic corrections to Keplerian orbits. Specifically, corrections to a Keplerian orbit due to special relativity include: precession of perihelion, reduced radius of circular orbit, and increased eccentricity. The prediction for the rate of precession of perihelion of Mercury is in agreement with existing calculations using only special relativity, and is one sixth that derived from general relativity. All three of these corrections are qualitatively correct, though suppressed when compared to the more accurate general-relativistic corrections in this limit. The resulting orbit equation has the same form as that derived from general relativity and is easily compared to that describing Kepler's orbits. This treatment of the relativistic central-mass problem is complementary to other solutions to the relativistic Kepler problem, and is approachable by undergraduate physics majors whom have not had a course dedicated to relativity.
Lemmon Tyler J.
Mondragon Antonio R.
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