Question

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6\times {10}^{24}$ kg and of the Sun $=2\times {10}^{30}$ kg. The average distance between the two is $1.5\times {10}^{11}m$. (Gravitational Constant $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$)

Answer 1

According to the question,
$M=$ Mass of the Sun $=2\times {10}^{30}kg$
$m=$ Mass of the earth $=6\times {10}^{24}kg$
$R=$ Average distance between the earth and the Sun $=1.5\times {10}^{11}m$
From the universal law of gravitation,
$F=G\frac{M\times m}{R^2}$
Therefore, putting all the values given in question in above equation we get
$F=6.67\times {10}^{-11}\frac{(2\times {10}^{30})\times (6\times {10}^{24})}{(1.5\times {10}^{11}{)}^2}=35.57\times {10}^{21}=3.56\times {10}^{22}N$