## 17. Classical Mechanics (Stellar Dynamics)

##### Solution

InKeplar's Thrid law,the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. where is the orbital period, and is the semi-major axis of the planet. For system 1 the radius of the orbit is , and for system 2 the radius of the orbit is . The ratio of the period of system 1 and 2 can be described as Therefore,

##### Answer

(D)

##### Reference

https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law_Of_Kepler's