Einstein's Explanation of Mercury's Precession

[stevmg]

Einstein used General Relativity to explain the aberrant precession of the planet mercury in its orbit around the Sun and was shown to be correct.

What the dickens , in 10th grade English, does the "precession of mercury" mean?

 

[George Jones]

From revolution to revolution, Mercury's point of closest approach (perihelion) moves. An animation that show this:

http://faraday.physics.utoronto.ca/PVB/Harrison/GenRel/Flash/Precession.html.

 

[stevmg]

From revolution to revolution, Mercury's point of closest approach (perihelion) moves. An animation that show this:

http://faraday.physics.utoronto.ca/PVB/Harrison/GenRel/Flash/Precession.html.

Thank you George. It appears from the animation that the closest and furthest points of the "ellipse" (not a true ellipse, of course) moves or precesses but the closest and furthest distances remain about the same.

Is this due to the relatively "fast" (tangential) linear speed of mercury as compared to the other planets which don't "precess"

Also, by Newtonian and Kepler theory, if the mass of the Sun and the planets remains constant are their orbits "perfect" ellipses? Seems like the differential positions of the planets at different points in time would shift the "center of gravity" of the solar system and alter the mechanics and throw the planets off their elliptical orbits - just using Newton theory alone.

 

[George Jones]

It appears from the animation that the closest and furthest points of the "ellipse" (not a true ellipse, of course) moves or precesses but the closest and furthest distances remain about the same.

Yes.

Is this due to the relatively "fast" (tangential) linear speed of mercury as compared to the other planets which don't "precess"

Newtonian gravity is an approximation to Einsteinian gravity that gets worse as gravity gets "stronger".

Also, by Newtonian and Kepler theory, if the mass of the Sun and the planets remains constant are their orbits "perfect" ellipses? Seems like the differential positions of the planets at different points in time would shift the "center of gravity" of the solar system and alter the mechanics and throw the planets off their elliptical orbits - just using Newton theory alone.

I am not sure what you mean, so I will give an (attempted) answer in two parts.

According to Newtonian gravity, if the solar system consisted just of Mercury and the Sun, both the Sun and Mercury would orbit their common centre of mass in ellipses, with the Sun's orbit much smaller than Mercury's. Consequently, in a reference frame for which the Sun is stationary, Mercury's orbit is not quite an ellipse, but this effect is very, very small.

The solar system, however, consists of more than than two masses, each of which exerts a Newtonian gravitational force on all the others. This perturbs the orbits away from perfect ellipses. Jupiter gives the largest effect, and Newtonian gravity predicts that Jupiter's perturbation should cause a precession of Mercury's orbit of 5557.6 arc seconds per century. The observed precession of Mercury's orbit is 5600.7 arc seconds per century. General relativity accounts for the 43 arc second difference.

 

[Matterwave]

Newtonian theory has no precession, the orbits are "perfect" ellipse's.

EDIT: Right, I should have specified that I was only considering the 2 body problem. George's answer is more complete.

 

[bcrowell]

Is this due to the relatively "fast" (tangential) linear speed of mercury as compared to the other planets which don't "precess"

All of the orbits have such an effect, but it's strongest for Mercury, both because Mercury's orbit is fairly elliptical and because it's closest to the sun. It's an effect that gets stronger as the gravitational field gets stronger. A nice way to understand it is to consider the extreme case of a strong field, which would be a black hole. If on orbiting object comes within the event horizon of a black hole, it never comes back out. In the less extreme case where the field is strong, planets spend more time near perihelion than predicted by Newton's laws. Since Mercury spends extra time close to the sun, it has more time to wrap around.

 

[SinghRP]

Stevmg: What the dickens , in 10th grade English, does the "precession of mercury" mean?
My answer: Planet Mercury is going around the sun in an elliptical orbit. The farthest point is called aphelion; the closest perihelion. Mercury is supposed to arrive at its exact perihelion point once in its own year. But it does not! It goes a little farther. This phenomenon is called in precise words: "the advance of the perihelion of Mercury."
All other planets do it but at varying degrees.
There is another type of precession. Right now the erth's spin vector is pointing to the North Star; in 2000 years it will point to Vegas.

 

[stevmg]

Gentlemen:

Thank you!