Why does relativity cause Mercury's orbit to precess 43 arc seconds per century?

[MikeLizzi]

There is no trick. You can draw the ellipse directly opposite the cutout, just as shown in the picture. The lines will meet then, but not at zero angle. So the object will not continue on the old ellipse but a shifted one. That's precession.

I don't know what you are talking about.

If I draw a vertical ellipse on the upper part of a disc symetric to the y-axis and make a cutout in the lower part of the disc symetric to the y-axis and close the disc into a cone symetric to the y-axis my ellipse is still vertical and symetric to the y axis. I don't get any precession.

 

[Jonathan Scott]

I don't know what you are talking about.

If I draw a vertical ellipse on the upper part of a disc symetric to the y-axis and make a cutout in the lower part of the disc symetric to the y-axis and close the disc into a cone symetric to the y-axis my ellipse is still vertical and symetric to the y axis. I don't get any precession.

It's not an ellipse then - it's got a slight point at the join (at least in theory). If you follow the direction of the line from one side of the join it will diverge slightly from the line on the other side. In practice, you'd have to have a highly eccentric ellipse and a large angle missing to make this visible with ordinary pencil and paper.

 

[A.T.]

There is no trick. You can draw the ellipse directly opposite the cutout, just as shown in the picture. The lines will meet then, but not at zero angle. So the object will not continue on the old ellipse but a shifted one. That's precession.

If I draw a vertical ellipse on the upper part of a disc symetric to the y-axis and make a cutout in the lower part of the disc symetric to the y-axis and close the disc into a cone symetric to the y-axis my ellipse is still vertical and symetric to the y axis.

Being symmetric doesn't make it an ellipse. An ellipse is a smooth shape, but this will have a sharp corner, where you stitch the cone together.

I don't get any precession.

You get it, if you continue the path smoothly over the seam (dashed line in the picture). Eventually you have to make the cut-out-angle bigger and layout the seam area flatten out to see how the path will continue.

But it's easy to show mathematically. Just consider the angles between your original ellipse and your cuts. On the tip side they total less than 180°, so when you weld the cut lines, you don't get a smooth path.

 

[DrGreg]

Here's a very exaggerated version (not to scale) with 120° precession to get the point across.

 

[Bjarne]

OK I begin to understand, we can say that the deformation of space happens along the orbit with different values, and the result is that the angle defects whereby the ellipse cannot close. Simple…. When first the confusion first is gone. Thank’s .

However, I was told (and a quick estimation seemed to confirm it) that the purely spatial curvature causes just a small part of the 43 arc second relativistic contribution. While most of it is due to gravitational time dilation (time curvature) and effective potentials

Time and distance deformation should (as I understand it) not be able to cause the other part of the precession. Because time and distance dilation are (as I understand it) proportional to each other (?).

But what about the; - “relativistic resistances” ?.
It requires more and more energy to get a diminishing increase in speed.

So each time when Mercury accelerate towards perihelion, the planet need more potential energy to be able to reach that speed it should according to classis orbit mechanics, to overcome the increasing relativistic resistances (towards perihelion).
But Mercury do not get that extra speed from anywhere, which mean that each time heading perihelion, - speed must be a little too low, compared to what it must be according to classis orbit mechanics.
Does that too not also have an influence ?

 

[A.T.]

http://www.bun.kyoto-u.ac.jp/~suchii/eff.potent.html
[PLAIN]http://www.bun.kyoto-u.ac.jp/~suchii/eff.potent.jpg

The essence from this link is so far I understand Fig 2 > “precession because of extra dwell time at inner part.

According to classic understanding I don’t think there should be any extra “dwell time” – WHY should that happen due to general relativity?

I still do not understand the cause of that anomaly, (and do not have a mathematical background to do so).
Is there someone what can explain the cause in simple words?

I don't understand it well enough to explain it simply, yet still correctly. But here are more visualizations and explanations:
http://www.fourmilab.ch/gravitation/orbits/

 

[MikeLizzi]

Being symmetric doesn't make it an ellipse. An ellipse is a smooth shape, but this will have a sharp corner, where you stitch the cone together.


You get it, if you continue the path smoothly over the seam (dashed line in the picture). Eventually you have to make the cut-out-angle bigger and layout the seam area flatten out to see how the path will continue.

But it's easy to show mathematically. Just consider the angles between your original ellipse and your cuts. On the tip side they total less than 180°, so when you weld the cut lines, you don't get a smooth path.

Thanks for spending some time with me. I still don't know what you (or Dr Greg) are talking about. I will just assume I am too stupid to understand.

 

[A.T.]

Thanks for spending some time with me. I still don't know what you (or Dr Greg) are talking about. I will just assume I am too stupid to understand.

Dr Greg showed an extreme example where the trajectory precesses by 90° on each orbit. Start on the right end of the red ellipse going CCW, then it goes to the green, orange and finally blue one.

Try it yourself on paper, with different orientations of the initial ellipse. Make sure when you cross the seam, that the path keeps it's local orientation relative of the seam.