Standard form/way

Planck form

Observed

Gravitational constant

$G\approx 6.67\times {10}^{-11}$

$G=\frac{\hslash c}{m_p^2}=\frac{l_p^2{c}^3}{\hslash }\approx 6.67\times {10}^{-11}$

indirectly only

Cavendish: Gravitational constant

$G=\frac{L2{\pi }^2{R}^2\theta }{M{T}^2}$

indirectly only

Cavendish: Planck mass

Only derived from G

$m_p=\sqrt{\frac{\hslash cM{T}^2}{L2{\pi }^2{R}^2\theta }}$

indirectly only

Cavendish: Planck length

Only derived from G

$l_p=\sqrt{\frac{\hslash L2{\pi }^2{R}^2\theta }{M{T}^2{c}^3}}$

indirectly only

Cavendish: Planck time

Only derived from G

$t_p=\sqrt{\frac{\hslash L2{\pi }^2{R}^2\theta }{M{T}^2{c}^5}}$

indirectly only

Cavendish: Schwarzschild radius

Normally dependent on G

$r_s=\frac{L4{\pi }^2{R}^2\theta }{c^2{T}^2}$

indirectly onlyo

Newton’s gravity force

$F=G\frac{mM}{R^2}$

$F=n_1{n}_2\frac{\hslash c}{R^2}$

indirectly only³

Gravitational acceleration field

$g=\frac{GM}{R^2}$

$g=N\frac{l_p}{R^2}{c}^2$ or $g=N\frac{\hslash c}{R^2{m}_p}$

Yes

Mass from acceleration field

$M=\frac{g{R}^2}{G}$

$M=\frac{g{R}^2\hslash }{l_p^2{c}^3}$

indirectly only

Orbital velocity

$v_o=\sqrt{G\frac{M}{r}}$

$v_o=c\sqrt{N\frac{l_p}{r}}$

Yes

Escape velocity

$v_e=\sqrt{2G\frac{M}{r}}$

$v_e=c\sqrt{N2\frac{l_p}{r}}$

indirectly only⁴

Time dilation

$t_2=t_1\sqrt{1-\frac{2GM}{r{c}^2}}$

$t_2=t_1\sqrt{1-N2\frac{l_p}{r}}$

Yes

Newton’s gravitational bending of light

$\delta =\frac{2GM}{r{c}^2}$

$\delta =N2\frac{l_p}{r}$

Twice of that

GR gravitational bending of light

$\delta =\frac{4GM}{r{c}^2}$

$\delta =N4\frac{l_p}{r}$

Yes

Gravitational red-shift

${\lim }_{r\to +\infty }z\left(r\right)=\frac{GM}{R^2}$

${\lim }_{r\to +\infty }z\left(r\right)=N\frac{l_p}{r}$

Yes

Schwarzschild radius

$r_s=\frac{2GM}{r{c}^2}$

$r_s=N2l_p$

indirectly only

Einstein’s field equation

$R_{\mu v}-\frac{1}{2}{g}_{\mu v}R=\frac{8\pi G}{c^4}{T}_{\mu v}$

$R_{\mu v}-\frac{1}{2}{g}_{\mu v}R=\frac{8\pi l_p}{m_p{c}^2}{T}_{\mu v}$

indirectly only