Question

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane.
Of the two, the planet that is farther from the star must have a:

• A. Larger acceleration due to gravity towards the star
• B. Larger orbital velocity around the star
• C. Greater Time period
• D. Larger gravitational attraction to the star
• E. A larger universal gravitational constant

Answer 1

The correct option is C Greater Time period

Time period of revolution of planet $T=2\pi \sqrt{\frac{r^3}{GM}}$ where $r$ is the radius of orbit

$⟹$ $T\propto r^{1.5}$

Thus time period is greater for the planet which is farther from the star.