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Nickelodeon
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Could someone explain in layman terms the current thinking on why the orbit of Mercury precesses? Presumably, it is not precessing in a gyroscope sense but the perihelion of the orbit just advances in the same plane.
Janus said:As mathman pointed out, the other planet's effect Mercury's orbit, as can the rotation of the Sun itself.
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Then Einstein, in his General Theory of Relativity, showed that the extra precession could be explained without an inner planet(in fact, the theory required the extra precession to exist), and the need for the planet Vulcan disappeared.(At least until the mid 1960's, where it provided a home for Mr. Spock)
Nickelodeon said:I'm having difficulty visualising how the planets could consistently nudge the Mercury's perihelion in the same direction. I would have thought that they could pull it one way then perhaps the other way depending on their relative positions.
The next thing I would like to know is regard to Einstein and how he explains the mechanics of what causes the small discrepancy. If the sun wasn't rotating would there be no discrepancy or is there something else going on?
Jonathan Scott said:The additional perihelion precession in Einstein's General Relativity is nothing to do with the rotation of the sun.
Nickelodeon said:This worries me because Janus says that the Sun's rotation does have an impact on Mercury's precession which introduces some doubt as to there being a definitive answer.
Jonathan Scott said:It is only relatively recently that the Sun's rotation rate and the resulting oblateness were known well enough to make an accurate calculation, and up to that point there was still some speculation that Einstein might be wrong when the rotation was taken into account.
If you followed the link in Janus' post you would have seen stuff involving J2, J4, etc. These are classical, non-spherical mass moments of the Sun about its center of mass. The Sun, because it rotates very slowly, is very close to spherical and thus has a very small J2 value: 2×10-7. There is no doubt that Mercury's relativistic recession results from relativity rather than the Sun's oblateness.Nickelodeon said:This worries me because Janus says that the Sun's rotation does have an impact on Mercury's precession which introduces some doubt as to there being a definitive answer.
D H said:If you followed the link in Janus' post you would have seen stuff involving J2, J4, etc. These are classical, non-spherical mass moments of the Sun about its center of mass. The Sun, because it rotates very slowly, is very close to spherical and thus has a very small J2 value: 2×10-7. There is no doubt that Mercury's relativistic recession results from relativity rather than the Sun's oblateness.
Ian said:Nickelodeon,
When calculating the precession of any planet make sure you calculate the length the body advances along the path of orbit - don't calculate the angular advance as Einstein did, or everyone else for that matter.
If the orbit of mercury was circular you would not observe an advance because Einstein's indicator (the perhelion) would not exist if the orbit was circular but the orbit would still advance.
Nothing wrong with converting to, or caculating for angular advance.Ian said:Nickelodeon,
When calculating the precession of any planet make sure you calculate the length the body advances along the path of orbit - don't calculate the angular advance as Einstein did, or everyone else for that matter.
Ian said:RandallB,
If you look at Einstein's original equation when he calculated the advance of mercury's perhelion you will see that he first deduced for a circular orbit and then he added the 'correction' for an elliptical orbit.
The units of the advance for a circular orbit are 'metres', as shown below:
(24pi3r3)/(c2t2) Metres.
and after adding the r(1-e2) correction for elliptical motion the equation becomes:
(24pi3r2)/(c2t2(1-e2)) radians
If you calculate the advance for any planet assuming the orbit is circular then the advance must be expressed in metres along the length of orbit. This figure will always be the same (~27833 metres) as the sun's mass is the only contributing factor.
The correction factor and change of units have made you think that the advance is different for all planets.
Ian said:Besides, Einstein didn't actually explain the advance, he only produced a calculation that agreed with observation.
Jonathan Scott said:The perihelion precession of Mercury depends on a second-order term in the complicated maths from that theory,
Nickelodeon said:The thinking man would look at the phenomenum (the precession discrepancy over and above planetary influencies) and decide on a probably cause, be it relative time, space curvature or relative mass variances then apply the maths accordingly. I'm sure Einstein did this but is there anyone out there who can shed some light on what those mechanical variance might be?
Jonathan Scott said:What do you mean "mechanical variance"?
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I’ve never cared for the term “geodesic” often used as though it were a magic bullet that explains how GR works.Nickelodeon said:by the "mechanical variance(s)" I was suggesting that for a planet not to be where it should be, as calculated by euclidean type maths, there has to be some influence acting on it, some imbalance. Given that it is following its local geodesic path (all the way round) I can't see where this imbalance is coming from unless the intensity of the geodesics are slightly assymetric somewhere along the line.
RandallB said:...
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Ian said:If you look at Einstein's original equation when he calculated the advance of mercury's perhelion you will see that he first deduced for a circular orbit and then he added the 'correction' for an elliptical orbit.
The units of the advance for a circular orbit are 'metres', as shown below:
(24pi3r3)/(c2t2) Metres.
and after adding the r(1-e2) correction for elliptical motion the equation becomes:
(24pi3r2)/(c2t2(1-e2)) radians
If you calculate the advance for any planet assuming the orbit is circular then the advance must be expressed in metres along the length of orbit. This figure will always be the same (~27833 metres) as the sun's mass is the only contributing factor.
The correction factor and change of units have made you think that the advance is different for all planets.
Jonathan Scott said:Yes, the precession distance is the same for all circular orbits around the sun. I'm not quite clear on your units; I'd write it as
6 pi Gm/c2
where m is the mass of the sun, and Google Calculator gives me 27.835km which agrees well enough with your numeric result.
A similar related feature applies to the curvature of space, in that in isotropic coordinates the "length deficit" in the circumference of any circle around the sun is one third of that precession distance.
RandallB said:I’ve only seen explanations that address different angles by planet, and did not know when measured as a distance in the circumference all would give the same value; very interesting.
I’ve not been able to find the original equation Einstein calculated the advance of mercury's perihelion with. I assume it also included a value that accounted for one full circumference or at some point a full circumference was removed from it to only show only the advancing distance portion.
Do either of you have a reference that shows the complete equation of calculating the Mercury orbit from the Einstein GR equations.
RandallB said:Also, do you have a reference that goes into some detail of what the isotropic circumference "length deficit" is or means? I don’t understand what that represents.
Thanks Jonathan seeing how GR treats the extra distance traveled really helps understand how the equations work.Jonathan Scott said:This is a standard result; I can find it for example in Rindler "Essential Relativity" section 8.4 (as I don't feel strong enough to get MTW out at the moment). After reinserting factors of G and c to get back to conventional units, equation 8.62 says that the precession angle per orbit is as follows:
[tex]\frac{6 \pi \, G m}{c^2 \, a \, (1-e^2)}[/tex]
where [itex]m[/itex] is the mass of the sun, [itex]a[/itex] is the semi-major axis and [itex]e[/itex] is the eccentricity. To convert this back to a distance for a circular orbit, multiply by [itex]a[/itex], giving [itex]6 \pi \, G m/c^2[/itex] as the distance.
RandallB said:Thanks Jonathan seeing how GR treats the extra distance traveled really helps understand how the equations work.
I was concerned with the focus or barrycenter of the ellipse; but I see when looking at the distance added by GR to the orbit circumference you must think of it relative to the center of the ellipse not one of the focus points – hence the use of “a” Semi-Major-Axis.
Getting the visualization right helps.
Another piece to the puzzle:
The two body circular orbit is not in fact actually circular in GR, since velocity is slowly increasing making the orbit grow smaller. Is there a part of the equations that reduce to how the obit radius reduces with each orbit?
Might it also be changing by a fix distance per orbit or maybe per unit of time.
Whatever it is I’m sure it is directly related to how the velocity is increasing over time with each orbit.
Thanks RB
Mercury's precession refers to the gradual change in the direction of its orbit around the sun. This means that over time, the point at which Mercury is closest to the sun (perihelion) will shift slightly from its original position.
Mercury precesses due to the influence of other planets in our solar system, particularly the massive planet Jupiter. This gravitational pull causes Mercury's orbit to shift over time.
Mercury's precession takes approximately 12 years to complete. This means that every 12 years, the point at which Mercury is closest to the sun will return to its original position.
Mercury's precession was first discovered by the German astronomer Johannes Kepler in the early 1600s. He observed that Mercury's orbit did not follow the predicted path based on his laws of planetary motion, and concluded that it must be due to the gravitational influence of other planets.
Yes, Mercury's precession can be observed from Earth through careful measurements and observations over time. This has been confirmed by modern technologies such as space probes and telescopes, which have provided more accurate data on Mercury's orbit and precession.