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Kepler's Laws & Planetary Motion question from NEET 2025

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Kepler's Laws & Planetary Motion

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

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Answer: (c)

Kepler's third law: $T \propto r^{3/2}$ .
$\dfrac{T_{Mars}}{T_{Merc}} = 4^{3/2} = 8 \Rightarrow T_{Merc} = \dfrac{687}{8} \approx 86\text{ days}$
Closest option is 88 earth days, so the answer is (c).

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