JEE MainPhysicsGravitation
A satellite is revolving in a circular orbit around the earth. Its orbit is slightly adjusted such that its time period of revolution increases by 3 % . The approximate percentage change in its orbital speed is
Options
- ADecreases by 1.5 %
- BDecreases by 2 %
- CIncreases by 1 %
- DDecreases by 1 %
Correct answer
D. Decreases by 1 %
Step-by-step solution
According to Kepler's third law, the time period T and orbital radius R are related by T R^ 3/2 . For small changes, the fractional change is given by: T T = 3 2 R R Given that the time period increases by 3 % , we have: 3 % = 3 2 R R R R = 2 % The orbital speed v of a satellite is given by v = GM R , which means v R^ -1/2 . The fractional change in orbital speed is: v v = - 1 2 R R Substituting the value of R R : v v = - 1 2 (2 %) = -1 % The negative sign indicates that the orbital speed decreases by 1 % . Answer: