Variation of g

At Earth's surface, $g = GM/R^2 \approx 9.81\,\mathrm{m/s^2}$. It varies with location.

Concept

Altitude $h$: $g_h = g\,(1+h/R)^{-2} \approx g(1-2h/R)$ for $h\ll R$.

Depth $d$: assuming uniform density $g_d = g\,(1-d/R)$.

Latitude $\lambda$: Earth's rotation reduces effective g: $g_{\rm eff} = g - \omega^2 R\cos^2\lambda$. Max at poles, min at equator.

Shape: Earth is oblate; equatorial radius > polar radius, so g is smaller at equator (compounded with rotation effect).

Worked Example

At $h=R$ (one Earth radius up): $g_h = g/4 \approx 2.45\,\mathrm{m/s^2}$.

Common Confusions

• At the centre of Earth, $g=0$ (not infinity).
• Both rotation AND oblateness make g smaller at equator.

Key Takeaways

• g decreases with altitude and depth.
• g is maximum at the poles, minimum at the equator.
• At very high altitudes use the exact $1/(1+h/R)^2$ form.