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.

$latex T^2 \\propto a^3$

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

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

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

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

Answer

(D)

Reference

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