Question

Consider 2 satellites A and B having time periods 16 hours and 1 hour, respectively. What is the ratio of the radius of their orbits?

(a) 4:1

(b) 8:1

(c) 16:1

(d) 64:1

I had been asked this question during an interview for a job.

This interesting question is from Gravitation in portion Gravitation of Physics – Class 11

Answer 1

The correct answer is (d) 64:1

The best I can explain: The time periods (T) of a satellite revolving around the earth of radius R and at height h is:

T = 2 x pi x [(R + h)^3 / (G X M)]^1/2

Hence, the time period is directly proportional to (R + h)^3/2

The ratio of orbits is, therefore, 64:1.