Part of JME-05 — Gravitation

Variation of g — Complete Analysis

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g varies due to Earth's shape, rotation, and position:

With Height (h above surface): Exact: ghg_h = gR^2R+h\frac{2}{R+h}^2. This is an inverse-square drop. Approximation: ghg_h ≈ g(1-2h/R) valid only for h << R. At h = R: g = g/4 notg2\frac{not g}{2}. At h = 2R: g = g/9.

With Depth (d below surface): gdg_d = g(1-d/R) — linear decrease assuming uniform density. At centre (d = R): g = 0. This is exact for uniform density.

With Latitude: geffg_{eff} = g - R*omega2omega^2*cos2cos^2(lambda). Maximum at poles (cos90 = 0), minimum at equator (cos0 = 1). The difference is only 0.034 m/s2s^2.

Key comparison: For the same small deviation from the surface, g decreases faster with height factor2hR\frac{factor 2h}{R} than with depth factordR\frac{factor d}{R}. This means d = 2h gives the same g value.

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