10902

Mercury's Perihelion Precession

The observed precession in the orbit of the planet Mercury is 574.1 seconds of arc per century (relative to the International Celestial Reference Frame). According to Newtonian gravitational theory, taking account of the gravitational perturbations by the other planets (mainly Venus, Earth and Jupiter), a value of 531.6 is predicted. This anomaly of approximately 43 seconds of arc per century was first recognized by Le Verrier in 1859. The discrepancy was resolved by Einstein's general theory of relativity in 1915.
This Demonstration exaggerates the effect by making the mass of the Sun around times greater; also, you can change an orbital parameter.

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The general relativistic contribution can be approximated by the following model: is the perturbation parameter given by
,
where is the universal constant of gravitation, is the speed of light, and is the mass of the Sun. Here , where is the angular momentum per unit mass .
The perturbed solution, invoking the substitution is
,
where is the eccentricity of the orbit;
.
The relativistic analogue of the orbit trajectory in the two-body problem is
.
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