Universum - 1888, Paris woodcut - C. Flammarion

"As you simplify your life, the laws of the universe will be simpler; solitude will not be solitude, poverty will not be poverty, nor weakness weakness." - Henry David Thoreau

The Pioneers Anomaly as measured shows a constant rate of acceleration towards the Sun at –a = ~8E-8 cm/s^2. This can be interpreted, in reverse order, as a gravitational phenomenon, whereby Newton’s ‘constant’ G is shown to grow at a steady rate over distance to cause this anomalous acceleration; which shows ‘as if’ G is growing at approximately 1 G per AU. This same result can be achieved in a modified Quantum equation, here called the Axiomatic Equation©, where Newton’s G grows in inverse proportion to solar energy received at a distance from the Sun, at about 1 G per AU. The resulting inertial mass acceleration towards the solar system’s largest mass, the Sun, is likewise shown per the Equivalence Principle to approximate the Pioneers Anomaly.

Mass is both a function of energy, as per Einstein's famous equation E = mc^2, and also a Quantum function of Planck's constant times c, divided by lambda l times the proton mass, also known as the Planck-DeBroglie equation. It will be shown that in addition to these, mass is also a gravity function, as defined by the Axiomatic Equation, derived here, as an extension of the DeBroglie-Planck-Einstein equation; where the proton mass is a variable, leading to a proton-to-proton gravitational coupling constant variable, which can then be computed into Newton's G gravity 'constant'. This Newton's G becomes a function of the Energy region where it is being measured, where for our solar system its delta G increases linearly at the rate of ~7.24E-11 Nm^2 kg^-2 per astronomical unit from the Sun, one AU = ~150E+9 meters. The hypothesis is that what happens to atomic mass at the quantum level is how it converts into Newton's G gravity at the macro level, per the Energy regions where G is measured.

I keep asking myself this question, because as described in this post on Boltzmann's Constant here, the numbers seem to work out (though one order of magnitude apart) to support the variability of Earth's known G from its calculated orbital Energy, per the Axiomatic. This is a perpetual question for me, can it be right? I don't know. There is always the danger of concidental mathematical results, so what appears right may not be. Another danger is the 'preloading' mathematically of values sought for, so that it becomes a self-fulfilling methodology. In the above referenced post, I might have done what is a pre-destined result, by taking Joules for Kelvin for Earth's black-body 255 K (or 2550 K for Boltzmann equivalent), and then reverse engineering it back to a hypothesized variation in Newton's G for Earth due to its black-body Kelvin temperature. So if this is all that was done, nothing was proved, except that 255 K is the same as ~0.15E+16 Joules for Earth's total mass (vs. 1.5E+16 for Axiomatic Energy equivalent). But if the numbers work out for Earth's gravity to be relative to its orbital Energy, viz. 9E+16 Joules, and by raising that energy, in Joules, by 255 K (times 10) equivalent matches the expected variance in Newton's G, from computed 7.24E-11 down to measured 6.67E-11 G, then perhaps the fact that these two separate calculations for 255 K black-body yield the necessary adjustment to G, i.e., minus ~0.57E-11 G, from its orbital computed G, then is there justification to think that perhaps this is not a mere coincidence?

What it shows is how deep space gravity G must be about 5 or 6 orders of magnitude greater than Earth's known G. Here's is the reprint of the original text (see original for additional links) to review this very interesting phenomenon, also pointing towards why the Pioneers are slowing in the outer solar system:

(Please note this below was derived from the Pound-Rebka Harvard experiment, showing how light redshifts gravitationally.)

G-deep space, is the "gravitational G" for hydrogen gas over the distance of 1z. In effect, this is the amount of gravitational G needed to make light redshift delta 1 z.

The answer is: G-deep space = 0.347E-6 m^3 kg^-1 s^-2

This is a continuation of the Physics Forum post: http://www.physicsforums.com/showthread.php?t=161315 where MOND (Modified Newtonian Dynamics) like effect may exist in our solar system, but at a much gentler rate. The two results for deep galactic space, per Milgrom's calculations is: a_0 = 1.2E-10 m/s^2, while per my calculations (shown below) in our solar system, it is 6 orders of magnitude lower: a_0s = 1.09E-16 m/s^2. If we find that within our solar system Newton's G is not a constant, but varies at the rather rapid rate of about 1G per 1AU, so that by Pluto's orbit, G is about 40 times what it is on Earth, but still of the order of magnitude 10^-10. However, per earlier work, out in deep space, this G grows (and perhaps levels off at) to a level of about 10^-6, which is about 5-6 orders of magnitude greater than here. But that was a rough 'guesstimate' and it may in fact be more like 6.

Wiki's http://en.wikipedia.org/wiki/Structure_of_the_Earth , says the inner structure of the Earth is taken from seismic shear waves, and at this time the figures for depths and size of inner core are 1210 km radius, and outer core is 2560 km thick (though this latter number may be inexact), which together give us a boundary of about 3770 km radius.

The reason I bring this up is that the inner core, from seismic wave shear refractions, remains a mystery. Why should the inner core show such incredible density? Why do seismic waves not penetrate it? It might be explainable in another way, that the micro-black hole at Earth's center acts 'as if' it were immense gravity. ...
Using the Schwarzchild equation for a black hole event horizon, for Earth's mass:

G=6.67E-11 m^3 kg^-1 s^-2
M=5.97E+24 kg
c^2=9E+16 m^2 s^-2

R_s=G2M/c^2 = 8.85E-3 meters

This could mean, not definitive, that Earth has a tiny micro-black hole at its center (per Axiomatic Equation, where when all energy lambda cancels, E=(1-g)c^2, so g=1 when E=0, and converting to Newton's G, where G^2= (g)(c^2)pi^2, so G=c if pi drops out), which may account for the inner core's strangeness.

If G equals its (hypothetical) maximum potential, G= 3E+8 (m^3 kg^-1 s^2), where G=c at its maximum (per Axiomatic), then if taking R_s and multiplying by this, 8.85E-3 times 3E+8 = 26.55E+5, or 2.655E+6 meters, which is the same as 2.655E+3 km, or 2655 kilometers. (This is about 40+% of Earth diameter.)

Notice how the Earth's spin slows a millisecond during Winter, and speeds up a millisecond during Summer, for a full variation of 2 milliseconds from trough to peak. In the earlier posted on planetary spin (Mar. 2, 2005) there was found a relationship between perihelion, where spin slows, to aphelion, where it speeds up, as a function of internal planetary heat and background space temperature. (Closer to Sun means warmer 'background' so spin slows.) All planets exhibit a distance to internal heat versus background space temperature spin ratios.

Earth is closer to the Sun during Winter (northern hemisphere). This is not insignificant, given the regularity shown in graph above. Please note this is most marked by Mercury's spin (Sept. 12, 2006), which slows at perihelion where it temporarily 'stands still' for a few days. This is more than mere coincidence?

EARTH: (@ E=9.0E+16 J) proton mass= 1.67E-27 kg, for G=6.67E-11
SATURN: (@ E=0.1004E+16J) proton mass= 1.498E-25kg, for G'=68.5E-11

Vs.
Earth's mass is 5.97E+24 kg

Titan's mass is 1.35E+23 kg

These are both in Earth kilograms, but the Saturn mass (roughly 10 AU, so 10 G equivalent to Earth's) is about 100 times equivalent mass for proton, for that orbital region (though Titan is so much smaller mass). Now look at Titan (moon), with an atmosphere similar to Earth's, largely nitrogen, the atmosphere is nearly 10 times taller than here. But the mass of Titan is less than 1/10th of Earth's! In fact, it is less than the total mass of Mars (all figured in Earth's kg at 1G). How can that be?

It seems there are other factors involved, as per Wiki's description of the Neutrino, though no lamda is mentioned there. However, checking on another paper: "Nonuniform Neutron- Rich Matter and Coherent Neutrino Scattering" by Horowitcz et al, I discovered it comes in femtometers in the range of one fermi = 1.0E-15 meters, so interesting. This is significant because I long puzzled over the Axiomatic Equation's lambda in E=hc/l*(proton mass) on the left side, where one kilogram of mass equals 90 petajoules, which makes l = 1.32E-15 m, at the output of our Sun (to give us proton mass of 1.67E-27 kg), which then translates into the proton-proton gravitational constant g = 5.9E-39 on the right side's E=(1-g)c^2; which itself translates into Newton's G, as per this paper: Variable G. So it all fits, except that Newton's G on Earth is only 6.67E-11, while per the Axiomatic calculations it should be 7.24E-11, but this was later found to be accounted for Earth's internal energy, using the Bolzmann constant, where Earth's interior works out to be about 2500K, probably close to its mean interior temperature.

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quote:

Pioneer anomaly put to the test
Sep 1, 2004
The European Space Agency is considering a unique experiment that could explain strange gravitational phenomena in the outer solar system.

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quote:

Like all good physical theories, GUTs make predictions. One is that the proton, the particle that inhabits all atomic nuclei, is unstable. For decades, experiments of increasing sensitivity have looked for decaying protons and failed to find them. As a consequence, the models have been tweaked so that protons decay so rarely as to be outside the current reach of detection. Another prediction fared no better: bundled-up interacting fields called magnetic monopoles have never been found.
For superstrings, the situation is even worse. In spite of its mathematical elegance, the theory is so detached from physical reality that it is exceedingly difficult to determine what a measurable string effect might be.

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F = k q₁ q₂/ r²

Coulomb's constant k = 1/4pie_o = 9x10⁹ N.m²/C² but can also be described as Volts per meter.

[This is somewhat similar to F=GMm/r^2 on a superficial level, but not directly the same, since charges are not only attractive but can also repel, so only superficially the same.]