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Nobody can put the Earth on a scale, but we can find its mass from g…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Nobody can put the Earth on a scale, but we can find its mass from $g$ . On the surface $g = 9.8\ \text{m/s}^2$ and $R = 6.4 \times 10^{6}\ \text{m}$ . Find the Earth's mass.

Need a reminder? The key ideaShow

Near a planet, $g = \dfrac{GM}{R^2}$ ; at a distance $r$ from its centre, $g$ falls as $\dfrac{1}{r^2}$ . On the Earth's surface $g = 9.8\ \text{m/s}^2$ ; at $n$ Earth radii above the ground it is $\dfrac{9.8}{(1 + n)^2}\ \text{m/s}^2$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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