Question

The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius $3.84\times {10}^5$ km. Calculate the mass of the earth from these data.

Answer 1

$T=2\pi \sqrt{\frac{r^3}{GM}}27.3=2\times 3.14\sqrt{\frac{{(3.84\times {10}^5)}^3}{6.67\times {10}^{-11}M}}or27.3\times 27.3=\frac{2\times 3.14\times {(3.84\times {10}^5)}^3}{6.67\times {10}^{-11}M}orM=\frac{2\times (3.14{)}^2\times (3.84{)}^3\times {10}^{15}}{3.335\times {10}^{-11}\times (27.3{)}^2}=6.02\times {10}^{24}kg$
$\therefore$ Mass of earth is found to be $6.02\times {10}^{24}$ kg.