🌍 Variation of g
📖 The Physics
We often treat gravity g as a fixed 9.8, but its strength actually depends on where you stand. Go up (a mountain, a plane) and it weakens as the inverse square of your distance from Earth's centre.
Go down a mine and only the mass beneath you pulls, so g falls roughly linearly to zero at the very centre. Earth's spinalso trims a little off near the equator.
Height h: g_h = g·R² / (R + h)² ≈ g(1 − 2h/R)
Depth d: g_d = g(1 − d/R)
Latitude λ: g_λ = g − ω²R·cos²λ
Notice g is largest right at the surface and drops off both above and below. It vanishes at the very centre (everything pulls equally in all directions), and it's smallest at the equator (λ = 0°) because of the rotation.
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