Newton assumes we use the center of mass to calculate F=G*(mM/r^2)
This is true in the sense that yes, with the mass of volume being considered as homogenous, the pull of gravity is definitely towards the Center of mass. But it doesn’t take into account the fact that mass is not all concentrated at a hypothetical center of volume. It, the mass, is spread across the volume. So how does this affect Newton’s orbital calculations when trying to model both planets orbital preccession and the flyby anomaly?
We already know Newtonian calculations can not account for the observed anomalous preccession, first noticed by Le Verrier, unless an additional gravitational force is added. Le Verrier assumed an additional mass inside its orbital path. Others including Einstein provided their own explanations. (Einstein invoked an additional 1/r^4 gravitational force as the source of the anomalous advance of preccession.) All supplied mathematical proofs.
I believe a non relativistic solution is still needed. And have found a simpler explanation based on the assumption that if the suns mass is spread across its volume, rather than concentrated at its center, this effects an outcome on perehilion that is slightly different from F=G(mM/r^2)
And this effect is related to the fact that an orbiting body will experience an additional gravitational pull from what Newtons formula predicts, the closer it is to the suns volume. Based on the assumption that some of the suns mass is closer to the orbitting body than the center of the sun is to the orbiting body at perehilion. And therefore must exert an additional increase in gravitational pull as defined by F in the Newtonian formula above.
But how can this be quantified without resorting to Le Verrier or General Relativity?
I believe I can supply not only the theoretical explanation but also the mathematical calculation to explain not only the anomalous preccession of the planets. But also the flyby anomaly.
The theoretical explanation is outlined above by assuming the suns mass is distributed across its volume. Not at its center. I call this the classical model seeing as it is a non relativistic explanation.
The calculations are as follows: Assuming this effect is greatest at perehilion than this neccessitates calculating the additional gravitational force at the perehilion. Not at the semi major axis as Newton, Einstein and others assume.
I have found that a simple 1/r^2 formula using r at perehilion instead of at semi major axis gives a reliable outcome that quantifies the additional preccession at least as well if not better than Le Verrier, Gerber or Einstein. Without needing to resort to fantasies about Vulcan or imaginary Spacetime. Altering distance r at perehilion slightly, by adding an additional distance R, gives an even more accurate formula that can be consistently applied to model all the planets anomalous preccessions.
Notice that in my version of the classic r^2 relationship between gravity and radius, the radius is not the radius of the sun. But the radius of the orbit at perehilion. The explanation for this is that the effect is based on the assumption that the anomalous preccession is directly related to the diameter of the sun vs the distance of the orbitting body from the suns center. Notice that the diameter of the sun as seen from the orbitting body is determined by r^2. (Its size in the sky as seen from the orbitting body gets smaller with distance using 1/r^2)
Where r is perehilion distance and R is radius of the sun, are the following “classical” formulae:
A)Preccessional advance in arc seconds=1/(r+R)^2
B)Preccessional advance in arcseconds= 1/(r+3R)^2
The following table shows column 1 planet, column 2 observed, column 3 predicted GRT (relativity), columns 4&5 predicted classical model.
Notice classical version B is more accurate even than GRT for predicting all the planets observed preccessions.
Observed. GRT. A B
Mercury. 43.1 43.5 45.85 43.24
Venus. 8.0 8.6 8.54 8.33
Earth. 5.0 3.87 4.5 4.49
Mars. *2.5 1.3 2.3 2.29
( Errors on Venus observed are 8.0 +-5.0)
(Source: Mon. Not. R. Astron. Soc. 403, 1381–1391 (2010)
[Table 1, column 9])
It is also worth pointing out that usually reference say Mars’ “observed” is 1.3. This is actually a theoretical assumption. Erroneously assumed to be consistent with the prediction made by GRT.
In fact it is commonly accepted that only Mercury, Earth and Venus orbits can be measured to a any sufficient degree of accuracy. Not Mars or any of the other planets.
What relativist revisionists fail to mention is that total of the best measured preccession of Mars which includes any anomalous contribution is 9.0arcseconds/Century.
Of which *2.5* is an unattributable “uncertainty”. Not 1.3
(https://link.springer.com/article/10.1140/epjc/s10052-017-4722-z)
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