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PhysicsNEET 2025Kepler's laws, satellites, escape velocity

Gravitation

The radius of the 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?

  1. A.88 Earth days✓
  2. B.225 Earth days
  3. C.172 Earth days
  4. D.124 Earth days

Solution

Kepler's third law: T2∝r3T^2 \propto r^3. TMercuryTMars=(14)3/2=18\frac{T_{Mercury}}{T_{Mars}} = \left(\frac{1}{4}\right)^{3/2} = \frac{1}{8}, so TMercury=6878≈86T_{Mercury} = \frac{687}{8} \approx 86 — nearest option 88 Earth days.

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