From "CosmoCoffee Blog"
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Greetings High School "Anonymous",
I am confused by your question. General Relativity already demonstrates how to calculate and understand the advance in the perihelion of Mercury.
General Relativity is the theory of gravitational interactions involving Stellar Scale systems [technically within a Stellar Scale system but exterior to any Atomic Scale system]. I really don't think I can improve upon GR in this context, especially with high school math.
If you ask me to model something on the Atomic Scale, it might be a more interesting request.
Have you thoroughly studied: http://arxiv.org/ftp/physics/papers/0701/0701132.pdf
Already published in ApSS, 2007.
This paper explains how, in a discrete self-similar cosmos, GR must be modified in order to model the dynamics of Atomic Scale or Galactic Scale systems.
Here's something really ironic. GR can be abreviated: R = kT. In groping for a unified theory that would apply in the microcosm as well as the macrocosm, theoretical physicists tinkered with the R and the T, but assumed that the k was inviolate and therefore of little interest.
Actually it is in the k = 8piG/c4 that the needed breakthrough was waiting all along. If you want to know how the discrete fractal scaling for k works, read the friggin' paper. But the key concept is that G is not scale invariant [even t'Hooft has finally figured that out. Well better 33 years late than never]; each Scale has its specific value of G and it only takes high school math, actually only elementary school math, to understand the scaling.
Please read the paper. Discrete Scale Relativity is the new paradigm for physics in the 21st century. When the physical characteristics of the dark matter are revealed, the new paradigm will be fully vindicated. So far we see mostly the high mass tail: neutron stars, BHs, gamma ray sources, RRATS, etc, and there are billions of these ultracompact objects, but the main DM components are in much lower states and are stellar mass black holes with 0.1 < M < 0.7 solar masses.
Any questions?
Yours in the new paradigm,
RLO
www.amherst.edu/~rloldershaw