# GRE Physics GR 1777 Problem Solution

## 017. Classical Mechanics (Stellar Dynamics)

### Solution

In **Keplar’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