Gravitation — Formula Sheet

F = G·m₁·m₂ / r²

F₁₂ = −F₂₁ (Newton's 3rd Law pair)

g = GM/R²

gₕ = g / (1 + h/R)² ≈ g(1 − 2h/R) for h << R

g_d = g(1 − d/R)

gλ = g − Rω²cosλ

W = mg

U = −GMm/r

V = −GM/r

T² ∝ r³ → T₁²/T₂² = r₁³/r₂³

v_orb = 2πr/T = √(GM_s/r)

F = G m₁m₂/r² — the fundamental equation of gravitation

G = 6.67 × 10⁻¹¹ N m² kg⁻² is the Universal Gravitational Constant

Value of g at Earth's surface ≈ 9.8 m s⁻²

g decreases with altitude

g_h = g/(1 + h/R)² ≈ g(1 − 2h/R) for small h

g decreases with depth

g_d = g(1 − d/R); g = 0 at Earth's center

Therefore

g_h = GM/(R+h)² = g/(1 + h/R)².