g at Height & Depth

Surface gravity: g₀ = GM/R² ≈ 9.81 m/s² at Earth's surface (R = 6.37 × 10⁶ m, M = 5.97 × 10²⁴ kg).

At height h above surface: g_h = g₀·(R/(R+h))² = g₀/(1 + h/R)². For h ≪ R: g_h ≈ g₀(1 − 2h/R).

At depth d below surface (uniform sphere): g_d = g₀(1 − d/R). Linear decrease; reaches zero at center.

g at the center of Earth = 0 (mass on all sides pulls equally).

g_h falls more slowly than 1/r² near the surface — only because surface gravity is the reference.

Real Earth: g varies from ~9.78 m/s² (equator) to ~9.83 m/s² (poles) due to rotation and oblateness.

Effect of Earth's rotation: g_apparent = g − ω²R cos²(latitude). Smallest at equator.

Altitude effect important for satellites, mountaineering, sensitive gravimetry.