Chapter 13, Problem 25A

Calculate the force of gravity between Earth and the sun ( $\text{sun’s mass}=2.0\times 1030\text{ kg}$; average Earth—sun $\text{distance}=1.5\times {10}^{11}m$).

To determine

Force of gravity between Earth and theSun.

Answer to Problem 25A

Force of gravity $F=3.56\times {10}^{22}\text{N}$

Explanation of Solution

Given:

The mass of Earth is, $m_1=6\times {10}^{24}\text{kg}$

The mass of Sun is, $m_2=2\times {10}^{30}\text{kg}$

Average Earth-Sun distance, $r=1.5\times {10}^{11}\text{m}$

Formula Used:

From Newton’s law of gravitation,

  $F=\frac{G{m}_1{m}_2}{r^2}$

  $F$ is force of gravity, $G$ is gravitational constant, $m_1$ and $m_2$ are mass of two objects and $r$ is distance between the two objects.

Calculation:

As gravitational constant $G=6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}$

On substituting the values in above relation, the force of gravity between Earth and theSun is

  $\begin{array}{l}F=\frac{\left(6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}\right)\times \left(6\times {10}^{24}\text{kg}\right)\times \left(2\times {10}^{30}\text{kg}\right)}{{\left(1.5\times {10}^{11}\text{m}\right)}^2}\\ =3.56\times {10}^{22}\text{N}\end{array}$

Conclusion:

Therefore, the force of gravity between Earth and the Sun is $F=3.56\times {10}^{22}\text{N}$ .