Part of JME-05 — Gravitation

Variation of g with Depth

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Formula: gdg_d = g(1 - d/R) (exact, assuming uniform density)

This is a LINEAR decrease. At the centre (d = R): g = 0.

Physical reasoning: At depth d, only the sphere of radius (R-d) below contributes to gravity (shell theorem: the outer shell produces zero net field inside).

Comparison with height:

  • Height: g decreases as 1/r2r^2 (faster initially, then slows down)
  • Depth: g decreases linearly (constant rate)
  • At the same small distance delta from the surface: g decreases faster with height (2*delta/R > delta/R)

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