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?
A.The semimajor axis of the planet's orbit is same as that of the Earth.
B.The semimajor axis of the planet's orbit is twice as compared to that of the Earth.
C.The semimajor axis of the planet's orbit is thrice as compared to that of the Earth.
D.The semimajor axis of the planet's orbit is four times as compared to that of the Earth.✓ Correct
Explanation
By Kepler's third law, T² ∝ a³, where T is the orbital period and a is the semimajor axis. If T_planet = 8 T_Earth, then (T_planet/T_Earth)² = 64 = (a_planet/a_Earth)³. Therefore a_planet/a_Earth = 64^(1/3) = 4. The semimajor axis of the planet's orbit is four times that of the Earth's.
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