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quote:Originally posted by Jim
Dr Joe, ...gold has many more protons(and neutrons)than hydrogen for example? ...[/quote]
Hi Jim, Thanks for mentioning this. The volume of a nucleus, is roughly proportional to the number of nucleons. The binding energy is usually 0.8 - 0.9% of the total mass-energy, so in a nucleus, the smallest possible gaussian protons, as calculated above, could be slightly lighter, larger and have slightly less internal gravity. On the other hand, the tidal gravitational force due to the other nucleons cancels about a third of the difference between free protons' and bound protons' internal gravity. (This tidal force is about the same within all nuclei because they all have about the same density.)
My hypothesis, in my 2002 paper on the Pioneer probes, published in "Aircraft Engineering and Aerospace Technology", was that when macroscopic gravity = microscopic gravity, the radio frequency anomaly charted by Anderson at 53 AU, occurs. Indeed the two regions where the anomaly occurred, correspond to the distance at which the Sun's gravity equals either the maximal internal gravity of a proton in a hydrogen-1 or lithium nucleus, or of a proton in other nuclei.
The only other significant source of macroscopic gravity, was the probe itself. Using the mass and average radius of the probe (including antennas but not booms) I find that the probe's self-gravity at its surface, is about half that needed to explain the range of distance over which the anomaly occurred (when it occurred the first time, at the distance corresponding to the internal gravity of a lone proton). The internal arrangement of the probe is rather like what's under the hood of my car. So it's believable that in some places, near large dense components, the internal gravity would be twice that on the surface. If so, then the duration of the anomaly perfectly matches the range of gravitational forces existing within the probe.
The second time the anomaly occurred, at the slightly greater distance corresponding to protons within nuclei, it occurred over a longer distance interval. The extra interval, corresponded to the range of proton masses due to different binding energy in common nuclei such as oxygen and iron.