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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: g_h = gR^2/(R+h)^2. This is an inverse-square drop. Approximation: g_h ≈ g(1-2h/R) valid only for h << R. At h = R: g = g/4 (not g/2). At h = 2R: g = g/9.

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

With Latitude: g_eff = g - Romega^2cos^2(lambda). Maximum at poles (cos90 = 0), minimum at equator (cos0 = 1). The difference is only 0.034 m/s^2.

Key comparison: For the same small deviation from the surface, g decreases faster with height (factor 2h/R) than with depth (factor d/R). This means d = 2h gives the same g value.

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