Geostationary gravitational clock gain ($\Delta \tau =tGM(R^{-1}-r_g^{-1})/c^2$)

For spherical weak-field gravity, a stationary clock at radius $r_g>R$ gains the displayed proper time relative to a surface clock over coordinate interval $t$. A geostationary orbit has $r_g=(GM/{\Omega }_{\oplus }^2{)}^{1/3}$. This is the potential contribution only. Combining it with orbital and surface rotational special-relativistic terms requires a consistent reference frame and must not be silently included in a gravitational-only comparison.