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Corrections of General Relativity to the Orbit of the Planet Mercury

Project #5 21SS-50

The orbit of the planet mercury is strange in that the major axis of the planet “precesses”, i.e, rotates about the sun as the planet moves in an elliptical orbit.  This could not be explained until Einstein found that Newton’s Law of Gravity was not correct when the planet was near a very massive object.  He found that in those cases the gravitational potential was given by

A mathematical equation

where the second term is the correction.

Use this expression in the polar form of the integral for the orbit

A second mathematical equation

to solve for the orbit and show that it is a precessing ellipse. In this equation

l is the angular momentum (a constant), E is the total energy of the system (a constant), M is the mass of the sun, m is the mass of Mercury, λ is a constant