- Finally climbing Pen-y-Fan after years of being beaten back (2012)
- Writing a FOL Resolution Theorem Prover from scratch in Lisp (2017)
- Calculating the advance of the perihelion of Mercury in General Relativity (2019).
The book uses algebra and calculus rather than tensors, and bases itself on the Schwarzschild metric rather than Einstein's field equations.
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| The Schwarzschild metric (Taylor and Wheeler) |
So that is some hand-holding! Nevertheless the conceptual analysis is clear and the result comes out, despite approximations, pretty accurately.
I did the calculations!
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Why does the elliptical orbit measurably precess? Because the metric isn't sufficiently flat at Mercury's orbital radius. As Mercury approaches the sun at perihelion it ventures into more deeply-curved spacetime. Locally radial distances increase and time slows.
Mercury dwells longer here than Newton thought.
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| Here's the PDF of the chapter on Mercury's anomalous precession. |
While it dallies, its constant orbital momentum is still swinging it around the sun. When it laggardly rises, it's moved farther around than it thought. The ellipse-axis has advanced.
Now I see it.
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What other items do I have on my bucket list? I have one, but it's secret.
It is good to see some Physics back on the Blog!
ReplyDeleteThis book looks like a "Space-farer's Navigation course". GR remains a paradigm of a cleanly presented (applied) mathematical Theory, to which other Theories (in so many subjects) continue to aspire!
Another part of the explanation for the GR orbitals is that there is now a 1/r^3 term, where Newton just has 1/r^2. This in turn comes from the fact that in Newton Gravitation is instantaneous, but in Einstein Gravitation takes time to get around.
Re-instating the "c"s in the Taylor-Wheeler equations is one simple project further project to do.
[Answer: as c --> infinity, precession -->0.]
Yes. The book is great! You can get a long way starting just with the metric! Even (just about!) Unruh radiation.
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