Question

The mass of earth is $6\times {10}^{24}Kg$. The distance between the earth and the sun is $1.5\times {10}^{11}m$. If the gravitational force between the two is $3.5\times {10}^{22}N$, what is the mass of the sun?
Use $G=6.7\times {10}^{-11}N{m}^2{Kg}^{-2}$

Answer 1

The gravitational force between the Sun and Earth can be found out using the formula,
$F=G\frac{M_e{M}_s}{R^2}$
where, $M_e$ and $M_s$ are the masses of the Earth and the Sun, respectively. Using all the given values, we have
$3.5\times {10}^{22}=(6.7\times {10}^{-11})\frac{(6\times {10}^{24})\times M_s}{(1.5\times {10}^{11}{)}^2}$
$\Rightarrow M_s=\frac{(3.5\times {10}^{22})\times (1.5\times {10}^{11}{)}^2}{(6.7\times {10}^{-11})\times (6\times {10}^{24})}=1.96\times {10}^{30}kg$