For the ascertainment of greater knowledge of the nature of gravity we need templates. The proton springs to mind because it is at the heart of all matter. Its role in the Bohr atom and the Rydberg series is ample proof that the link between gravity & electromagnetism lies with the proton. Take the Compton frequency of the proton wavelength, 2.2687314x10^23. You will find this number closely linked to most products involving numerical structures bonding planck units with Classical gravitational formulae.
In recent posts in Sonntag I've mentioned the Protonic Model. The Protonic Model is a hypothetical mass structure where the timescale mass is 1.080624035x10^35 local mass units. This figure is simply the Compton frequency taken to exponent 1.5 or (2.2687314x10^23)^1.5. The timescale mass is the total mass needed in a sphere to house a schwarzschild sphere measuring one light second in diameter. If we consider this mass structure to be measured in metres and its diameter one light second then its local Gravitational constant, G, will be 6.7360006x10^24 divided by its mass, 1.080624035x10^35, equal to 6.23343585x10^-11. 6.736x10^24 is our GM product where the Schwarzschild diameter is equal to one light second. If you divide it by G you wind up with just the timescale mass in local mass units. In this particular case protonic mass units will be about 1.07 times lighter than kilograms. One big difference in this model will be that local h, the Planck constant, will be bigger by about 1.07.
However, we can still make use of the constants we have even if we have to mix them. We have a Protonic G and our own h. So we can find a hybrid Planck mass. The formula for the planck mass is (ch/4G)^0.5. Using our mixed constants we arrive at a figure, 2.822570503x10^-8. This must differentiate from our own SI Panck mass by the square root of 1.07. As we don't know this value exactly let's call it (x), that is (x)= about 1.07.
Opposite numbers: I use this term to describe the situation where a particular mass has a Schwarzschild diameter equal to the Compton wavelength of another mass. A case in point is the proton. We know its Compton wavelength to be 1.3214x10^-15m. But we also know that the GM product with a Schwarzschild diameter equal to this has a GM product value of 29.6906036. And wherever we know a Compton wavelength we must find, also, the GM product of its opposite number.
In Planck gravitational structures two numbers constantly crop up: (1) h/4 turns up as a mass value and differentiates with the mass value for the proton by 1.009721668x10^7.
(2) The Quantum Adjustor crops up frequently and, amongst other things, is the differnce beween 1/(1.009721668x10^7) and the local planck mass. Its value in our own SI system is 3.62994678 which is worked out from the formula 4/(4(c/2)h)^0.33333r. What we don't know is how close any template is to the value of the proton in precise terms.
Now let's put it in to action: Remembering our hybrid Planck mass, 2,822570503x10^-8, Compton frequency 2.2687314x10^23 and, of course, the Quantum Adjustor, 3.62994678, we get:
2.2687314x10^23/2.822570503x10^-8 is equal to 8.03782012x10^30. 8.03782012x10^30/3.62994678 is equal to 2.21430798x10^30. This last value is not just an adjusted Planck frequency but a Sun like mass value. When divided again by our hybrid Planck mass we get: 2.21430798x10^30/2.822570503x10^-8=7.845005038x10^37. And, 7.845005038x!0^37/3.62994678=2.16119009x10^37. The square root of 2.16119009x10^37 is equal to 4.64886018x10^18. c/4.64886018x10^18 equals 6.44873x10^-11. Which is the value of the local G, of the particular time scale mass model where the Planck mass is equal to our hybrid mass, 2.822570503x10^-8. Working backwords from this we can find local h which is 6.854931784x10^-34. Obviously, because of the square root situation, if our own SI system is based on a difference of (x), then this in between model differs by the square root of (x) or (x)^0.5.
What we do have is the GM product of Gm^2, or the Planck mass squared, it is ch/4, or 4.966118653x10^-26. 1/4.966118653x10^-26=2.013645x10^25. 4(2.013645x10^24)^0.333r is equal to 1.08823066x10^9. (1.08823066x10^9)(2.833570503X10^-8)=30.71607783. This represents the difference between the SI proton GM opposite and the in between model's. But is the SI system's proton monitor based precisely on the proton?