The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The

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Question

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 the length of 1 year on Mercury is:

Accepted Answer

Correct Answer: B — 88 earth daysStep-by-step Solution using Kepler's Third Law:Kepler's Third Law: T² ∝ R³Let TMars = 687 days, RMars = 4RMercury(TMars/TMercury)² = (RMars/RMercury)³ = (4)³ = 64TMars/TMercury = √64 = 8TMercury = TMars/8 = 687/8 ≈ 85.88 ≈ 88 earth daysVerification: The actual orbital period of Mercury is 88 Earth days — this problem is physically grounded.Why Option A (124 days) is wrong: Does not correspond to any standard application of Kepler's law with RMars/RMercury = 4.Why Option C (225 days) is wrong: 225 days is the orbital period of Venus, not Mercury. A common confusion between the two inner planets.Why Option D (172 days) is wrong: Arises from using T ∝ R (instead of T ∝ R^{3/2}), giving TMercury = 687/4 ≈ 172 days. Incorrect power law.Key Concepts from Gravitation (NCERT Class 11, Chapter 8):Kepler's First Law: Planets move in elliptical orbits with the Sun at one focus.Kepler's Second Law: Equal areas are swept in equal times (conservation of angular momentum). Planet moves fastest at perihelion, slowest at aphelion.Kepler's Third Law: T² ∝ R³, or T² = (4π²/GMsun)R³. The proportionality constant depends only on the mass of the central body.Orbital velocity: v = √(GM/R). Greater radius → smaller orbital velocity.Escape velocity: ve = √(2GM/R) = √2 × vorbital. For Earth: ve ≈ 11.2 km/s.

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 the length of 1 year on Mercury is:

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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 the length of 1 year on Mercury is:

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