Question

How will you 'weigh the sun', that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5\times {10}^{8}km$.

Answer 1

Orbital radius of the Earth around the Sun, $r=1.5\times {10}^{11}m$

Time taken by the Earth to complete one revolution around the Sun,
$T=1year=365.25days$
$=365.25\times 24\times 60\times 60s$

Universal gravitational constant,$G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$
Thus, mass of the Sun :
$M=\frac{4{\pi }^2{r}^3}{G{T}^2}$

$=\frac{4\times {3.14}^2\times (1.5\times {10}^{11}{)}^3}{6.67\times {10}^{-11}\times (365.25\times 24\times 60\times 60{)}^2}$

$\approx 2\times {10}^{30}kg$

Hence, the mass of the Sun is $2\times {10}^{30}kg$