Final answer:
The orbital period of Saturn, determined by applying Kepler's Third Law of planetary motion, is approximately 29.46 years, confirmed by the calculations showing that the square of the period approximates the cube of the semimajor axis (p² ≈ a³).
Step-by-step explanation:
To determine the orbital period of Saturn, we apply Kepler's Third Law of planetary motion, which states that the square of the orbital period, p², is proportional to the cube of the semimajor axis, a³, of its orbit. For Saturn, given the semimajor axis (a) to be 9.54 astronomical units (AU), we can calculate its orbital period (P) in years. Using the provided formula and Saturn's semimajor axis:
- a³ = 9.54 × 9.54 × 9.54 = 868.3
- p² should be approximately equal to a³
- Since p² = 867.9 ≈ 868.3, P ≈ 29.46 years (since p = P and we are looking for the period in years).
Therefore, the orbital period of Saturn is approximately 29.46 years, showing that Saturn adheres to Kepler's Third Law.