INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

August 15, 2017

Period of a Planet

Try this Problem, useful for Physics Olympiad, based on the period of a planet.

The Problem:

Suppose that the gravitational force varies inversely as the \(n^{th}\) power of the distance. Then, the period of a planet in circular orbit of radius \(R\) around the sun will be proportional to

(A) \(R^{\frac{n+1}{2}}\)


(C) \(R^n\)

(D) \(R^{n/2}\)

The gravitational force can be given as $$ \frac{GMm}{R^n}=mR\omega^2$$

Now, we know \(\omega=\frac{2\pi}{T}\),


$$\frac{GMm}{R^n}= mR(\frac{2\pi}{T})^2$$ $$ T^2= \frac{4\pi^2R^{n+1}}{GM}$$


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.