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NEET UGPhysicsModerateNEET 2025

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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Sol. Applying Kepler's 3rd law : T2∝R3T^2 \propto R^3
Radius of Martian orbit, R′=4RR' = 4R
(T′T)2=(R′R)3=(4RR)3=43=64⇒T′T=8\left( \frac{T'}{T} \right)^2 = \left( \frac{R'}{R} \right)^3 = \left( \frac{4R}{R} \right)^3 = 4^3 = 64 \Rightarrow \frac{T'}{T} = 8
∴\therefore Length of 1 year on Mercury = T=T′8=6878=85.88T = \frac{T'}{8} = \frac{687}{8} = 85.88 days

Source: geekyrakshit/indian-exam-questions / neet2025-code45

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