Question

What is the work done by a planet revolving around the Sun?

Answer 1

1. When force is in the direction of displacement, work done is given as —

$$\begin{gathered} W=F\times s\times \cos \theta \\ where, \\ W\to Workdone \\ F\to Force \\ s\to Displacementofthepointofapplicationinthedirectionofforce \\ \theta \to Anglebetweenforceanddisplacement \end{gathered}$$

2. Based on the value of the angle between force and displacement work done can be positive, negative or zero.

Value of $\theta$	Value of $\cos \theta$	Nature of work done
$0\le \theta <90°$	$0<\cos \theta \le 1$	Positive
$\theta =90°$	$\cos \theta =0$	Zero
$90°<\theta \le 180°$	$-1\le \cos \theta <0$	Negative

3. The planets revolve in circular orbits around the Sun.

4. When we observe the motion of a planet around the Sun, we know that the gravitational force is exerted on the planet by the Sun, which acts towards the centre of the circle.

5. Also, we can say that the velocity of the planet acts tangentially as shown in the figure. So, the direction of displacement will also be the same as the velocity.

6. In this case, the force and displacement are perpendiculars (at and angle of $90°$) with each other, hence the work done will be zero.