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 $3.5\times {10}^{2}N$, What is the mass of the sun ?

Answer 1

Given that,

Earth of mass $M=6\times {10}^{24}kg$

Gravitational force $F=3.5\times {10}^{2}N$

Distance between earth and sun $r=1.5\times {10}^{11}m$

Mass of the sun = $m$

Now,

The gravitational force is

$F=\frac{GMm}{r^2}$

$3.5\times {10}^2=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times m}{{(1.5\times {10}^{11})}^2}$

$m=\frac{3.5\times {10}^2\times 1.5\times {10}^{11}\times 1.5\times {10}^{11}}{6.67\times {10}^{-11}\times 6\times {10}^{24}}$

$m=0.1967\times {10}^{11}kg$

$m=1.97\times {10}^{10}kg$

Hence, the mass of the sun is $1.97\times {10}^{10}Kg$