Question

Calculate the force of gravitation between the sun and the earth if the average distance between them is $1.5\times {10}^{8}Km$, mass of the earth is $6\times {10}^{24}kg$, mass of the sun is $2\times {10}^{30}Kg$.

Answer 1

Step 1:Given data:

Mass of earth = $6\times {10}^{24}Kg$

Mass of sun = $2\times {10}^{30}Kg$

Step 2: Finding the distance between the sun and the earth

$$\begin{gathered} \text{Distance between sun and earth},r=1.5\times {10}^{8}Km \\ =1.5\times {10}^8\times {10}^{3}m \\ =1.5\times {10}^{11}m \end{gathered}$$

Step 3: Finding the value of Force

According to the universal law of gravitation “ Everybody in the universe attracts every other body exerting a force which is directly proportional to the masses of two bodies and inversely proportional to the square of the distance between them”.

$F=\frac{G{m}_1{m}_2}{r^2}N$

The value of the gravitational constant is specified and given as

$G=6.7\times {10}^{-11}N{m}^{2}K{g}^2$

Substituting the values into the formula,

$$\begin{gathered} F=\left(\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 2\times {10}^{30}}{{\left(1.5\times {10}^{11}\right)}^2}\right)N \\ =3.57\times {10}^{22}N \end{gathered}$$

Therefore, the value of force between the sun and the earth is $3.57\times {10}^{22}N$.

Hence, the force of gravitation between the sun and the earth if the average distance between them is $1.5\times {10}^{8}Km$, Mass of earth is $6\times {10}^{24}kg$,Mass of the sun is $2\times {10}^{30}Kg$ is $3.57\times {10}^{22}N$.