Exact formula: $g_h$ = $\frac{GM}{R+h}$^2 = gR^$\frac{2}{R+h}$^2

Approximation (h << R): $g_h$ ≈ g(1 - 2h/R)

Derivation of approximation: $g_h$ = $\frac{g}{1+h/R}$^2 ≈ g(1 - 2h/R) using binomial approximation (1+x)^n ≈ 1+nx for x << 1.

When to use which:

• If h/R > 0.1 (i.e., h > 640 km), use the exact formula
• If h << R, the approximation is sufficient

At height h = R: $g_h$ = g/4 (not g/2! — inverse square, not inverse).