Question

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6\times {10}^{24}\mathrm{kg}$ and of the Sun $=2\times {10}^{30}\mathrm{kg}$. The average distance between the two is $1.5\times {10}^{11}\mathrm{m}$.

Answer 1

Step 1: Given data

The mass of the earth is $6\times {10}^{24}\mathrm{kg}$

The mass of the Sun is $2\times {10}^{30}\mathrm{kg}$

The average distance between the two is $1.5\times {10}^{11}\mathrm{m}$

Step 2: Formula used

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

Step 3: Calculation of force of gravitation

By substituting the values in the above formula,

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

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