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One year at a planet is 8 times as large as compared to the one year at the Earth. Which one of the following is correct about the planet's orbit?
Explanation
This question is based on Kepler's Third Law of Planetary Motion (the Law of Periods), which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit: T2 ∝ a3.
Given that the orbital period of the planet (Tp) is 8 times that of Earth (Te), we can set up the ratio:
(Tp / Te)2 = (ap / ae)3
(8 / 1)2 = (ap / ae)3
64 = (ap / ae)3
To find the ratio of the semi-major axes, we take the cube root of both sides:
ap / ae = 3√64 = 4
Thus, the semi-major axis of the planet's orbit is four times that of Earth. Options A, B, and C are incorrect based on this mathematical relationship.