What is the period of Neptune’s revolution around the Sun, if it is at a distance of 30 AU from the Sun?

According to Kepler’s third law (T2 / a3) = const, where T and a are in years and astronomical units, respectively. Substituting the value for the Earth as a const, we find that the constant is 1. Substituting the value of the semi-major axis of Neptune into the expression (T2 / a3), we obtain that the period T = (a) 3/2 ≈ 164 years.

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