A planet moves around the sun in an elliptical orbit with semi-major axis a and time period T. T is proportional to

Answer: Option D

According to Kepler's third law, the square of the period of revolution (T) of a planet around the sun is proportional to the cube of the semi-major axis (a) of its elliptical orbit.

Thus, T²∝a³

Taking the square root on both sides, we get:

$$T\propto {\text{a}}^{\frac{3}{2}}$$

Hence, the time period (T) is proportional to $${\text{a}}^{\frac{3}{2}}$$ which corresponds to Option D.