What will be the ratio of gravity at depth \(h\) below the Earth's surface and at height \(h\) above the Earth's surface, where \(h << R\) (R is Earth's radius):
increases linearly with \(h\)
For h << R: gravity at depth h below surface: g_d = g(1 − h/R); gravity at height h above surface: g_h = g(1 − 2h/R).
Ratio g_d/g_h = (1 − h/R)/(1 − 2h/R) ≈ (1 − h/R)(1 + 2h/R) ≈ 1 + h/R (keeping first-order terms).
This is linear in h.
Hence, increases linearly with h.
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