Gravity Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

medium

At what height above Earth's surface would the gravitational acceleration be half of

g

? Earth's radius is

R = 6.37 \times 10^6 \text{ m}

1
Gravitational acceleration at distance $r$ from Earth's center: $g' = \frac{GM}{r^2}$ . At the surface: $g = \frac{GM}{R^2}$ .
2
Set $g' = \frac{g}{2}$ : $\frac{GM}{r^2} = \frac{GM}{2R^2} \implies r^2 = 2R^2 \implies r = R\sqrt{2}$
3
Height above surface: $h = r - R = R(\sqrt{2} - 1) = 6.37 \times 10^6 \times 0.414 \approx 2.64 \times 10^6 \text{ m}$

Answer

h \approx 2.64 \times 10^6 \text{ m} \approx 2640 \text{ km}

Gravitational acceleration decreases with the square of the distance from Earth's center. You must go about

0.41R

above the surface to halve gravity.

About Gravity

The universal attractive force between any two objects with mass, decreasing with the square of distance.

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