Question

The mass of the 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 $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

• A. $1.96\times {10}^{30}kg$
• B. $1.2\times {10}^{12}kg$
• C. $3.6\times {10}^{18}kg$
• D. $2.4\times {10}^{9}kg$

Answer 1

The correct option is A $1.96\times {10}^{30}kg$

From Newton's law of Gravitation,
$F=\frac{G{M}_1{M}_2}{r^2}$
where, $F$ is the force of attraction between earth and Sun, $M_1$ is the mass of the earth, $M_2$ is the mass of the Sun and $r$ is the distance between the earth and the Sun.
or, $3.5\times {10}^{22}=\frac{(6.67\times {10}^{-11})(6\times {10}^{24})M_2}{(1.5\times {10}^{11}{)}^2}$
or, $M_2=\frac{(1.5\times {10}^{11}{)}^2(3.5\times {10}^{22})}{(6.67\times {10}^{-11}{)}_6\times {10}^{24}}$
or, $M_2=1.96\times {10}^{30}kg$