To find the value of the period of Neptune’s rotation around the Sun, we apply Kepler’s third law: Tn ^ 2 / Tz ^ 2 = an ^ 3 / az ^ 3, whence we express: Tn = √ (an ^ 3 * Tz ^ 3 / az ^ 3).
Constants: en – semi-major axis of the planet Neptune’s orbit (by condition an = 30.07 AU); Tz is the period of the Earth’s rotation (T = 1 year); az is the semi-major axis of the Earth’s orbit (az = 1 AU).
Calculation: Tn = √ (an ^ 3 * Tz ^ 3 / az ^ 3) = √ (30.07 ^ 3 * 1 ^ 3/1 ^ 3) = 164.89 years.
Answer: The orbital period of the planet Neptune, according to the calculation, is 164.89 years.
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