Question

The Earth may be considered to be a uniform sphere of radius 6.38 × 106 m. Its mass is assumed to be concentrated at its centre.

Given that the gravitational field strength at the Earth’s surface is 9.81 N kg–1, show that the mass of the Earth is 5.99 × 1024 kg.

Answer 1

$F_1=F_2,$

$mg=\frac{GMm}{R^2},$

$g=\frac{GM}{R^2},$

$M=\frac{gR^2}G,$

$M=5.99\cdot 10^{24}~kg.$