Correct Answer  Option 2 : n
1^{2}d
13 = n
2
The correct answer is option 2) i.e. n12d13 = n22d23
CONCEPT:

Kepler's laws of planetary motion
 The first law (Law of orbits): All the planets revolve around the sun in elliptical orbits having the sun at one of the foci.
 The second law (Law of areas): The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
 The third law (Law of periods): The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semimajor axis.
EXPLANATION:
From the third law of Kepler, the square of the time period (T) is directly proportional to the cube of the mean distance (d).
⇒ T2 ∝ d3
We also know that, time period, \(T =\frac{1}{frequency} = \frac{1}{n}\)
\(\Rightarrow\frac {1}{n^2} \propto d^3\)
For the two planets revolving around the sun,
\(\Rightarrow\frac {n_2^2}{n_1^2} \propto \frac{d_1^3}{d_2^3}\)
\(\Rightarrow n_1^2d_1^3 = n_2^2d_2^3\)