Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit (which can be thought of as the orbital radius for circular orbits). Mathematically, this is often expressed as:
\[ \frac{T_1^2}{T_2^2} = \frac{a_1^3}{a_2^3} \]
Where:
- \( T_1 \) and \( T_2 \) are the orbital periods of the two planets,
- \( a_1 \) and \( a_2 \) are the orbital radii (or semi-major axes).
From this relationship, we can see that the correct correlation is:
The square of the ratio of the periods equals the cube of the ratio of the radii.
Thus, the correct response is: The square of the ratio of the periods equals the cube of the ratio of the radii.