How is the Precession of Mercury's Perihelion Calculated and Explained?

[RandallB]

precession of perihelion for Mercury
(arc s/century)
5025".6 Coordinate
531".4 Gravitational tugs of the other planets
43".0 General relativity

The first two were well known with the unexplained 43” a problem until it was explained by GR.

Question is: What is “Coordinate precession” as how is calculated so accurately to have known that 43".0 was missing?

 

[Janus]

Coordinate precession is apparent precession due to the Earth's own precession. The coordinate system involved uses the Earth's vernal equininox as the reference point. Since this shifts due to the Earth's precession, Mercury would appear to precess relative to this point even if it had no precession of its own.

 

[RandallB]

Coordinate precession is apparent precession due to the Earth's own precession. The coordinate system involved uses the Earth's vernal equininox as the reference point. Since this shifts due to the Earth's precession, Mercury would appear to precess relative to this point even if it had no precession of its own.

Does this mean a more “fixed” coordinate like the stars or Gemini would give a “coordinate” precession of Zero for both the Earth and Mercury. That this coordinate adjustment is from the use of the earth’s alignment at Earth's vernal equinox, which moves as the north pole wobbles away from the north star, as a reference instead a more stable background?

If a more stable coordinate system was used there would be zero precession adjustments for this part. That is, it is not a “Newtonian” adjustment, Coordinate precession is only needed because of the frame of reference chosen for measurements.
Meaning all “Newtonian” precession comes solely from Gravitational tugs of the other orbiting objects.

Thus if we had a single plant system measure against a fixed background like the stars, it would have no “Newtonian” precession, only that precession caused by GR.
Correct?

 

[BobG]

The vernal equinox is measured against the stars. If you draw a line from the center of the Earth through the center of the Sun at the exact instant the center of the Earth lies on the ecliptic plane, and then keep on following that line to a star (or point in space referenced to some stars) you have a coordinate system with a reference that can be used all year long.

You actually have two types of precession you're talking about. The vernal equinox precesses relative to the stars. It precesses 360 degrees in about 26,000 years. If you talk to an astronomer, the first point of Aries is currently in the portion of the sky allocated to Pisces. If you talk to an astrologer, the first point of Aries is at the edge of Aquarius (hence the song "This is the dawning of the age of Aquarius").

Because of the gravitational tugs from the other planets and perhaps the oblateness of the Sun? (I'm sure it has to be oblate since it spins, but I'm not sure how the ecliptic plane is oriented relative to the Sun's equator), perihelion either precesses or regresses depending on the inclination of the orbit relative to the Sun's equator.

Edit: After thinking a bit, I'm not quite sure what you're getting at. You could have a fixed reference completely separate from the Earth (ECI, for example, where the location of the first point of Aries on some specific date is used instead of the current apparent location of the first point of Aries). That's good for analyzing the motion of orbiting objects, but eventually you're going to want to update to a more current location since virtually all of our observations are made from Earth. (The most prevalent inertial coordinate system used today is J2000, which is based on the location of the first point of Aries on 1 January 2000.)

 

[RandallB]

I'm not quite sure what you're getting at.

Mainly, I’m a little unclear on what the correct “Newtonian” precession calculations are required to get to the “Non General Relativity” number that didn’t match up with observations that took GR to explain.

The huge 5025 coordinate # thru me as I had no idea what is was.
It gives 360⁰ in 25,787 years so I figure that’s the same as your "about 26,000".

Meaning for a single planet case there is no “Newtonian” precession with no other planets to perturb it. The only precession would be from GR which I interpret to always be “Positive” or forward.
I think I’m good with understanding that coordinate precession has nothing to do with orbital dynamics, just measuring position.
That is the only “Newtonian” precession considerations are those caused by other plants – there is nothing inherent in a Newtonian elliptical orbit that should expect any precession or regressing.

Ignoring the oblate-ness of the Sun & its equator (precession here so small anyway). With the planets orbiting in a fairly flat plane; would I be correct in saying that the inner planets would always get precession effects from the other planets while the outer planets like Neptune would see negative precession forces (regresses) to their orbits.

Is there a Web site that might go over how those calculations are made and understand the effects of interplant gravitation tugs?

 

[BobG]

Is there a Web site that might go over how those calculations are made and understand the effects of interplant gravitation tugs?

The International Earth Rotation Service has enough information to occupy your time for quite a while.

(Actually, they have revised their name to International Earth Rotation and Reference Systems Service, but their old name still sounds so much more attractive. I've always thought it would sound incredibly cool and important to work for an organization whose name suggests you're responsible for the Earth's rotation. )

 

[RandallB]

Good resource of Earth info, plus some links to links leading to other orbital info like http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html" and the SOHO project.

Anyway I think I’m clear on mercury, BUT one last issue.

Normally for a Newtonian orbit to get it to change or precede would take some energy input to do the work of moving the orientation of the orbit. So most of the precession is due to energy being put into or taken away from mercury by tugs from other planets. Thus without the other planets it would maintain a ellipse with a fixed orientation, except for that precession caused by General Relativity.

I’m reasonably sure that precession would require energy going into the orbital system. So the question is; does GR somehow provide energy into the orbit of mercury??
OR would it be more accurate to say that orbit equilibrium and conservation of energy within the theory GR requires the precession for a net no change in energy. That is to say, that NOT having the GR precession happen, would require energy be extracted from the system.

 

[pervect]

Because the metric is static, there is an "effective potential". This means that energy is effectively conserved. You can see the GR equations for orbiting bodies online at

http://www.fourmilab.ch/gravitation/orbits/

(don't know if it's at a level where you can follow it, though, it takes calculus).

Orbital precession does not take an energy input, it only takes a force law that is not exactly inverse square.

 

[RandallB]

Orbital precession does not take an energy input, it only takes a force law that is not exactly inverse square.

So of my two options the second is the correct way to view the issue:
In the first the Newton Laws use “a force law that IS exactly inverse square” so for anyone to change an orbit to force a precession would require some work (like a torque on the entire orbit) to get it to change alignment. Thus the observed precession under Newton implied energy being used by the system from somewhere to effect that precession.

However the Newton law is not correct, where the Theory of GR uses “a force law that is NOT exactly inverse square”, here it would take some external input to deviate from the precession defined by GR. It only looks like energy is being used to move the orbit when viewed by Newton, GR laws demand that precession so that energy is conserved.

 

[pervect]

The observed precession doesn't imply that energy is being "used" as in "dissipated". For instance, if you could build a lossless, non-linear spring, and connect it from the Earth to the Sun, it would induce precession in the Earth's orbit in much the same way as relativity does.

The idealized spring would store energy, but it would be a passive devices that did not require a power source (and ideally one that did not dissipate energy, either).

 

[RandallB]

I don’t see how in a Newtonian view an idealized passive frictionless nonlinear spring would be able to create or change a precession positive or negative, without releasing energy from the spring into the elliptical orbit of the object. And with no automatic expectation for that energy to be returned to the spring. Thus leaving this view in a paradox.

It seems to me important to take the Newton the inverse square law as not being exactly correct as you suggested earlier.

 

[pervect]

I don’t see how in a Newtonian view an idealized passive frictionless nonlinear spring would be able to create or change a precession positive or negative, without releasing energy from the spring into the elliptical orbit of the object.

From some of our previous discussions, this has been something that has come up before and you didn't see it then, either.

Think about the issue some - is gravity (Newtonian gravity!) more like a motor (active), or like a spring (passive). Forget about the GR issues for the time being, you need to understand the Newtonian case first.

If you think gravity is active, like a motor, what happens when the batteries wear out?

 

[D H]

I don’t see how in a Newtonian view an idealized passive frictionless nonlinear spring would be able to create or change a precession positive or negative, without releasing energy from the spring into the elliptical orbit of the object. And with no automatic expectation for that energy to be returned to the spring. Thus leaving this view in a paradox.
It seems to me important to take the Newton the inverse square law as not being exactly correct as you suggested earlier.

Gravity is a conservative force, and so is this idealized frictionless spring. Energy is conserved.

I think you are confusing non-closed orbits with non-conservative forces.

Consider a central force field for which the potential energy is proportional to an integral power of the distance. There are only two integers that lead to closed orbits: U(r) ~ 1/r, which is how gravity works, and U(r) ~ r^2, which is how linear springs work. All other cases lead to paths that aren't closed (i.e., exhibit precession). Adding a non-linear spring to an inverse square law ensures that upon superposition the orbits are not closed.

 

[RandallB]

From some of our previous discussions, this has been something that has come up before and you didn't see it then, either.

I’d need a reference to see where we disagreed on this before.

Think about the issue some - is gravity (Newtonian gravity!) more like a motor (active), or like a spring (passive). Forget about the GR issues for the time being, you need to understand the Newtonian case first.
If you think gravity is active, like a motor, what happens when the batteries wear out?

Where did I imply gravity acted like a “motor”? – I said the Newton formulas define a passive system that conserves energy, only IF there is no precession. And that’s why Newton’s is wrong GR is correct.

Your claim is that you can duplicate the precession provided by the laws of GR with Newtonian laws applied to a non-linear spring. So yes let's use the Newton case. Just exactly what is the function of your spring that can perform this trick.

The best I can come up with is manually attaching a spring to the orbiting object where it crosses the MINOR access. Hooking up and disconnecting one degree before and after the crossing. On the way IN this would release energy out of the spring into the object.
The extra speed input into the object would also be at an angle that would input a precession.
But on the way OUT hooking and unhooking the spring would take energy out of the orbit and put it back into the spring. This gives passive energy conservation, but the vector here will give a negative precession canceling out the other.
Also the continued application of the counterbalancing non-liner pulses would not change to total energy in the orbit, but it would pull the max limit of orbit down (apogee) and push the perigee out until no eccentricity remained. Thus removing the minor axis, so points cannot be found to attach and detach the spring.

If you can show us a method for applying what ever kind of spring you like, however you like, that can with Newton’s laws duplicate the precession required by GR, without using a motor, I will be impressed. Let us know what you come up with when you think about it.
RB

 

[pervect]

I don't want to beat you over the head, but as in the last thread

https://www.physicsforums.com/showthread.php?t=99572

you don't seem to be "getting it", and I can't explain it any more clearly or simply. (The tie in with the last thread was that we were also talking about energy in that thread.)

Anyway, I'm talked out, so it will be up to someone else to continue this thread.

 

[RandallB]

I don't want to beat you over the head, but as in the last thread

That the tread where you and your kept changing the question to fit your answer rather than address the question I re-explained twice – no problem I’m still working on it and will find a better explain then any given there.

But it also where even after explain how the Pythagorean was involved some still couldn’t see it – not sure if you couldn’t either.

At some point I’ll go back to it and draw a picture for those that still conceptual aren’t "getting it", when it comes to seeing the Pythagorean inside a formula. But I understand how without using a little vision it can be hard for some to spot.

So we can leave that one be for now. But sticking with this one it doesn't relate that well to the other. You made the claim here that a non-linear spring in the Newtonian could match GR!
How is it you're talked out, you didn't put up I did. I’m the one that went to the trouble to design a non-linear spring to do something. Where’s your design that can match GR within the Newtonian?

All I said is that it cannot be done (provide precession and conserver energy in the spring at the same time). My statement is easily falsified – all you need to do is show the design that does the job, that all.
If you’ve tried but were unsuccessful (which must is the case) say so, don’t just say you don’t want to talk about it and walk away.

As for my nonlinear spring that only puts energy in and out of the ellipse at the MINOR access in pulses. That was with a spring under tension. It has the eccentricity decreasing, no precession, no energy change in orbit or spring long term.
The same can be done by using a spring in compression only the eccentricity will increase still no change in precession, or energy long term.

But if we only apply the tension spring for the in bound side and the compression spring on the outbound side we will get precession, but energy comes out of both spring long term.
Reverse sides for the springs - energy goes into the springs and you have a negative precession change. But you cannot conserve the springs energies and change the precession (Like GR does) as you claim.

It only takes some quite thoughtfulness to be able to see your concept of a non-linear Newtonian spring won’t do the job. If you cannot design one with a function that will at least say you couldn’t. If you can’t take the time to do that, you never will “get it”.