Wednesday, March 14, 2012

Mercury's orbit

can one explain the perihelion precession of Mercury's orbit with Newtonian gravity? what would be needed for this explanation? please keep in mind that at the time of Einstein's derivation (happy birthday, Prof. Einstein!) there was no real observational need for general relativity.

for bonus points: what's the order of magnitude of the perinigricon (point of closest approach to the black hole) precession of the stars orbiting the black hole at the centre of the Milky Way?

3 comments:

  1. perinigricon ist *really* the correct expression for referring to the point of closest approach of a celestial body to a black hole. an alternative term, perimelasma (which I think sounds way cooler), was coined by the scientist and science fiction writer G.A. Landis in his novel "approaching perimelasma".

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  2. I GUESS it should be possible. My ideas are very rough. I'll be happy to hear something more quantitative. The main reason I believe it is possible is:

    Realistically, scientists didn't have a whole "circle" of the perihelion, but rather a tiny curve that it described over the time of human observation. With 0.5'' shift per year, it would take thousands of years for a few percent of a circle to be traveled.

    That being said, I don't think they could distinguish the shift from the effect of a tiny motion of the ellipse center of mass. The most probable explanation of such shift seems the fact that we have a many body problem with the sun and many minor planets, whose effect can only calculated perturbatively.

    To create such shift, one could alternatively introduce an additional planet. But it should take a larger planet. Even Jupiter has only a thousandth of the solar mass. The new planet would somehow have to be unobserved and affect mainly Mercury. That seems odd.

    Therefore, if the perturbation theory was correct, one could study Mercury as part of a two-body system of which only the centre of mass moved on an ellipse. That way the unknown object could probably be small and close to Mercury. Whether the dynamics of a three body system could explain a large part of the shift curve, I have no idea.

    I'm really excited to hear other answers!

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  3. it was in fact proposed that an additional small planet called Vulcan was responsible for the perihelion shift of Mercury, by distorting the gravitational potential in a suitable way.

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