Understanding the Relativity-Induced Precession of Mercury's Orbit

[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.