Chapter 7, Problem 8TS

Calculate the force of gravity between the Earth $\left(6\times {10}^{24}\text{kg}\right)$ and the Sun $\left(2\times {10}^{30}\text{kg}\right)$ . The average distance between the two is $1.5\times {10}^{11}\text{m}$.

To determine

The force of gravity between the Earth and the Sun.

Answer to Problem 8TS

The force of gravity between the Earth and the Sun is .

Explanation of Solution

Given info: The mass of the earth is $6\times {10}^{24}\text{kg}$ , the mass of the sun is $2\times {10}^{30}\text{}\text{kg}$ and the average distance between the sun and the earth is $1.5\times {10}^{11}\text{m}$ .

Write the expression for the force of gravity.

$F=G\frac{m_1{m}_2}{d^2}$

Here,

$F$ is the force of gravity

$G$ is the universal gravitational constant

$m_1$ is the mass of the Earth

$m_2$ is the mass of the Sun

$d$ is the distance of separation

Substitute $6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}$ for G , $6\times {10}^{24}\text{kg}$ for $m_1$ , $2\times {10}^{30}\text{kg}$ for $m_2$ and $1.5\times {10}^{11}\text{m}$ for $d$ in the above expression to get $F$ .

$\begin{array}{c}F=6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}\times \frac{6\times {10}^{24}\text{kg}\times 2\times {10}^{30}\text{}\text{kg}}{{\left(1.5\times {10}^{11}\text{m}\right)}^2}\\ =35.6\times {10}^{21}N\end{array}$

Conclusion:

Therefore, the force of gravity between the earth and the sun is .