g variation (depth)

Question

For depth d inside Earth (uniform density) g_d ≈ g(1 - d/R). Depth where g halves?

RankGuru · Accepted Answer

1. **Depth Formula**: $g_d = g_s (1 - \frac{d}{R})$, where $g_s$ is surface gravity.
2. **Condition**: We want the gravity to be half of the surface value: $g_d = \frac{1}{2} g_s$.
3. **Equating**: $\frac{1}{2} g_s = g_s (1 - \frac{d}{R})$.
4. **Solve for d**:
   - $\frac{1}{2} = 1 - \frac{d}{R}$
   - $\frac{d}{R} = 1 - \frac{1}{2} = \frac{1}{2}$
   - $d = \frac{R}{2}$.
5. **Conclusion**: Halfway to the center of the Earth, gravity is half the surface value.

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g variation (depth)

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