Question

The mass of sun is $2\times {10}^{30}$ kg and the mass of earth is $6\times {10}^{24}$ kg. If the average distance between the sun and the earth be $1.5\times {10}^8$km, calculate the force of gravitation between them.

Answer 1

Given :

mass of sun $M_{Sun}$ = $2\times {10}^{30}$ kg

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

Average distance r = $1.5\times {10}^{8}km$

= $1.5\times {10}^{8}km\times 1000\frac{m}{km}$

= $1.5\times {10}^{11}m$

According to the universal law of gravitation,

$F=\frac{G\times M_{Earth}\times M_{Sun}}{r^2}$

Plug in the given values to the formula,

$F=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times 2\times {10}^{30}}{{(1.5\times {10}^{11})}^2}$

$F=\frac{6.67\times 6\times 2\times {10}^{(-11+24+30)}}{({1.5}^2\times {10}^{(11\times 2)})}$

$F=\frac{80.04\times {10}^{43}}{2.25\times {10}^{22}}$

$F=35.57\times {10}^{(43-22)}$ = $35.57\times {10}^{21}$

$F=3.57\times {10}^{22}N$.