For example, I showed the math to apply Milgromís MOND to our solar system here
, and here
computed the end result which approximates, however broadly, the Pioneer Anomaly. But I do not know that the math (which thus far remains unchallenged) is truly describing what is happening. The math postulated on a variable G, growing by a rather large measure of 1G per 1 AU with distance from the Sun, shows mathematically what happens with distance for a delta of acceleration (towards the Sun), but until this is measured empirically, it is just a story. A story made up mathematically is still just a story, until measured to verify its predictions. My math shows the Pioneer Anomaly, per modified MOND, predicts this acceleration delta is Ėa = 8.415E-7 m/s^2 (vs. Ėa = 8E-8 cm/s^2 for Pioneers) so not an exact match, but one which at least warrants a look. However, to date we have no measurements of what G is for the outer solar system, since we postulated Newtonís G to be a universal constant and measured ALL distant observations with this postulated G. Our mass measures, per Equivalence, may be off if G is not the same as here on Earth, but this would not show up in orbital dynamics, though it would show up in planetary density, something easily measured in atmospheric density. Why would Titanís atmosphere
, for example, be ten times taller than Earthís atmosphere, when Titan is smaller than Earth? So the story, using math as a tool with a constant G is one way, while math using a variable G makes the story another way. Which is true? This is easily resolved with an empirical measure of G away from Earthís known G. Then perhaps the story built up mathematically will have some more credence as a story.
I bring this up not to push for a variable G, but to illustrate that even with math we can weave any stories we like, as long as the math is right. But math is only a tool, and not in and of itself an a priori justification for theory being right. Theory is still just a story, until it is verified empirically, not within the domain of the math used, but with a Ďdouble blindí test type measurements, where the measurements are verified independent of the math used. Thatís when the story gets interesting. Copernicus, Keppler, Brahe, Galileo, all made our former stories of astronomy obsolete with real observations, supported by the math. The trouble I see, expressed by many on these ATM pages, is when the math paints the story first, and then is used to prove the story, the story gets muddled. Remember the Ptolemeic epicycles within epicycles? There were mathematically correct, but the story came out wrong, much to regret for all those who bought into the original story. It took empirical evidence, independent of the mathematical epicycles, to finally get the story right. That said, I agree that any story in physics, or astrophysics, must in the end find mathematical expression, since that is the only way we can use it for predictability of physics phenomena.
BTW, if G is variable with distance from the Sun, as I suspect (1 G per 1 AU), then at very great distances from the Sun, or any star and galaxy Ďhotí energy, say 50,000 AU and beyond, the G would be very high, and high enough to Ďgravitationallyí redshift all cosmic light passing through the gases and molecules of intergalactic space at about the Hubble constant. Take one hydrogen molecule per cubic centimeter of space and gravitationally redshift it per light year with G = ~10X-6, and see what you get. I worked out the math on these boards, like here
, and it comes in pretty close. Still, even if the math is correct, the whole idea of a variable G may be no more than a fine fiction. But if we accept a priori that all distant cosmic redshift is due to Doppler effect space expansion, are we not entertaining a similar fine fiction? How do you Ďdouble blindí test for space expansion? And if we donít test for an independent verification, independent of the math used, then how do we know it is real? BBT may be no more than another story, awaiting another Copernicus type to blow it away, with the math of course!
All we have to do is test empirically to see if the tools used were right for the story.