Chapter 14, Problem 40A

Calculate the speed in m/s at which Earth revolves around the sun. Note: The orbit is nearly circular.

To determine

Speed of revolution of Earth around the Sun in m/s.

Answer to Problem 40A

  $v=3\times {10}^4\text{m/s}$ approximately

Explanation of Solution

Given:

Assume orbit of Earth nearly circular.

Formula Used:

The speed is given as,

  $v=\frac{d}{t}$

Where, $d$ is distance and $t$ is time.

Calculation:

The time taken by Earth to revolve around the sun is 365 days.

So,

  $\begin{array}{l}T=365\times 24\times 60\times 60\text{s}\\ \Rightarrow T=31,536,000\text{s}\end{array}$

Now, distance of earth from the sun is around $r=1.5\times {10}^{11}\text{m}$

So, distance travelled by earth in one revolution

  $\begin{array}{l}d=2\pi r\\ =2\pi \times 1.5\times {10}^{11}\text{m}\end{array}$

So, the speed of Earth in its orbit is

  $\begin{array}{l}v=\frac{d}{t}=\frac{2\pi r}{T}\\ =\frac{2\pi \times 1.5\times {10}^{11}}{31,536,000}\text{m/s}\\ \Rightarrow v=3\times {10}^4\text{m/s}\end{array}$

Conclusion:

Therefore, the speed of revolution of Earth around the sun is $v=3\times {10}^4\text{m/s}$ approximately.