Perihelion Precession of Mercury

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(credit: http://en.wikipedia.org/wiki/Kepler_problem_in_general_relativity )

« In Newtonian physics, under “standard assumptions in astrodynamics” a two-body system consisting of a lone object orbiting a spherical mass would trace out an ellipse with the spherical mass at a focus. 

The point of closest approach, called the Periapsis [Perihelion, when Sun is the spherical mass], is fixed. 

There are a number of effects in our Solar System that cause the perihelions of the planets to precess, or rotate around the Sun. 

These are mainly because of the presence of other planets, which perturb the orbits. 

Another effect is solar oblateness, which produces only a minor contribution. 

For a long time the perihelion precession of Mercury was a problem in celestial mechanics. Careful observations of Mercury showed that the actual rate of the precession transits of Mercury disagreed with what calculated from the Newton’s theory by an amount of about 43” (arc-seconds) per century. 

A number of “ad hoc” unsuccessful solutions had been proposed, but they tended to introduce more problems. 

In general relativity, this remaining precession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of space-time. This was a powerful factor motivating the adoption of general relativity. » 
 
 
 
 

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Rate of Mercury’s Perihelion Precessions

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« Earlier measurements of planetary orbits were made using conventional telescopes. 

More accurate measurements are nowadays made with radar technology. 

The total observed precession of Mercury is 5600 arc-seconds per century, with respect to the position of the vernal equinox of the Sun. 

This precession is due to the following causes (numerical values are the updated ones): » 
 

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« Therefore, the general relativity (GR) prediction takes perfectly into account the missing precession (discrepancies are within the observational error). »

 
 
 
 
The other Planets experience inferior Perihelion Precessions ...

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« All the other planets experience a precession, but, as their distance from the Sun is greater and their velocity slower, their shifts are lower and harder to observe. 

For example, the perihelion shift of Earth’s orbit due to general relativity is about 5 arcseconds per century. The perihelion shift of binary Pulsar systems has also been measured with the use of radio-telescopes. These observations are consistent with general relativity 

G  = universal gravitational constant  
M = mass of the Sun  
c   = velocity of light in vacuum  
A  = semi major axis of Mercury  
e   = eccentricity of Mercury’s orbit  
 

The perihelion relativistic precession of Mercury is the first tested confirmation of the general relativity theory. 
 

Minor is A, major is - Major is eccentricity "e", major is

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Detailed calculation of - arcseconds per century - m.k.s. system... 
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"Over" animation of Mercury’s Perihelion Precession...

z ( credit:  http://commons.wikimedia.org/ )