From

Formula

Comments

Not dependent on G, ħ or c:

Light deflection

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{\sqrt{\delta R}}{2\sqrt{\overline{\lambda }}}$

$\delta$ light deflection

Advance of perihelion

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{\sqrt{\sigma a\left(1-e^2\right)}}{\sqrt{6\pi \overline{\lambda }}}$

$\sigma$ Advance of perihelion

Micro lensing

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{\theta \sqrt{\frac{d_S{d}_L}{d_S-d_L}}}{2\sqrt{\overline{\lambda }}}$

$\theta$ micro lensing

Not dependent on G or ħ, but on c:

Gravitational acceleration

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{R\sqrt{g}}{c\sqrt{\overline{\lambda }}}$

Orbital velocity

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{v_0\sqrt{R}}{c\sqrt{\overline{\lambda }}}$

Orbital time

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{2\pi \sqrt{R^3}}{Tc\sqrt{\overline{\lambda }}}$

Periodicity pendulum clock

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{2\pi R\sqrt{L}}{Tc\overline{\lambda }}$

L is length pendulum.

Velocity ball Newton cradle

$\frac{l_p}{\overline{\lambda }}=n_p\approx \frac{R{v}_{out}}{c\sqrt{2H\overline{\lambda }}}$

H hight of ball drop.

Cavendish apparatus

$\frac{l_p}{\overline{\lambda }}=n_p=\frac{L2{\pi }^2{R}^2{\theta }_c}{T^2{c}^3{l}_p}$

R distance from small to large ball.

L distance between small balls,

${\theta }_c$ angle, T pendulum periodicity.

Not dependent on G or c, but on ħ and H₀ and T_cmb:

Cosmology observations:

$\frac{l_p}{{\overline{\lambda }}_c}=n_p=\frac{T_{CMB}^2}{H_0^2}\frac{k_b^{2}16{\pi }^2}{{\hslash }^2}$

T_cmb: CMB temperature,

H₀: Hubble constant.