# 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.

$T^2 \propto a^3$

where $T$ is the orbital period, and $a$ is the semi-major axis of the planet.

For system 1 the radius of the orbit is $a$, and for system 2 the radius of the orbit is $4a$.

The ratio of the period of system 1 and 2 can be described as $\Big( \frac{T_1}{T_2} \Big)^2 = \Big( \frac{a_1}{a_2} \Big)^3 = \Big( \frac{a}{4a} \Big)^3 = \Big( \frac{1}{64} \Big)$

Therefore, $\frac{T_1}{T_2} = \frac{1}{8}$