g at Height & Depth
g(r) ∝ r inside, 1/r² outside — single curve across both regions.
Key Notes
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.
Formulas
At height h
Inverse-square dependence.
At depth d (uniform sphere)
Linear decrease to zero at center.
Surface gravity
Defines what we call 'g' on Earth's surface.
Apparent g (rotation)
λ = latitude. At poles: full g; at equator: less by ω²R.
Important Points
At the CENTER of Earth, g = 0. Counterintuitive but true.
Mt Everest peak (h ≈ 8.85 km): g drops by about 0.28%.
Going below Earth's surface DECREASES gravity LINEARLY in the uniform-density model.
Real Earth is denser near the core ⇒ true g(d) curve isn't strictly linear, but the principle holds.
International Space Station (h ≈ 400 km): g ≈ 8.7 m/s² (still ~90% of surface gravity). 'Weightlessness' = free fall in orbit, NOT zero gravity.
Geosynchronous orbit (~36,000 km): g ≈ 0.22 m/s² — much smaller, but not zero.
g at Height & Depth notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.