Question

A satellite is revolving around earth in its equatorial plane with a period $T$. lf the radius of earth suddenly shrinks to half its radius without change in the mass. Then, the new period of revolution will be

• A. $8T$
• B. $2\sqrt{2}T$
• C. $2T$
• D. $T$

Answer 1

The correct option is D $T$

Time period of revolution is dependent on:

$1$. the mass of the planet around which the satellite is revolving $M$

$2$. the radius of the orbit of the satellite $r$

$T=2\pi \sqrt{\frac{r^3}{GM}}$.

Since, mass of earth is not changed and radius of orbit is not changed, time period will remain the same. Time period does not depend on the radius of the planet around which the satellite is revolving.