The distance of Neptune and Saturn from the sun is nearly `10^(13)m " and "10^(12)m` respectively. Assuming that they move in circular orbits, then what will be the ratio of their time periods.

Explanation

To find the ratio of the time periods of Neptune and Saturn, we can use Kepler's Third Law of Planetary Motion, which states that the square of the time period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit around the sun. Mathematically, this can be expressed as:

\[ T^2 \propto a^3 \]

### Step-by-Step Solution:

1. **Identify the distances from the sun:**
- Distance of Neptune from the sun, \( a_n = 10^{13} \, \text{m} \)
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