You start with a dimensionless formula, just the raw proportions as Newton used. These are the units for non reduced length, mass, and force:
F_Newtons/F_P = (m1*m2 / m_P²) * (l_P² / r²)
Then you solve for S_I units for force:
F_Newtons = (m1*m2 / m_P²) * (l_P² / r²) * F_P
This shows you how the math works. It converts the mass and length to the planck values, calculates the ratio at the planck scale and then scales that value from planck scale to SI Newton units.
The simplification by definitions.
G_SI = (l_P² / m_P²) * F_P
G_SI = ( (c*t_P)² / (Hz_kg/t_P)² ) * (c * Hz_kg / t_P²)
G_SI = ( c²t_P² / (Hz_kg²/t_P²) ) * (c * Hz_kg / t_P²)
G_SI = ( c²t_P⁴ / Hz_kg² ) * (c * Hz_kg / t_P²)
G_SI = c³ * t_P² / Hz_kg
G is just a simplified composite of these Planck scale units being simplified. :D
Sunday, June 8, 2025
How G works in gravity law.
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