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 day…

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 which of the following is the length of 1 year on Mercury?

1. A. 88 earth days (Correct answer)
2. B. 225 earth days
3. C. 172 earth days
4. D. 124 earth days

Correct Answer

Option A — 88 earth days

Detailed Solution & Explanation

The correct answer is 88 earth days.

Key Points

• Kepler's third law: $T^2\propto R^3$.
• With $R_{Mars}=4R_{Mercury}$: $\left(\dfrac{T_{Mars}}{T_{Mercury}}\right)^2=\left(\dfrac{4R}{R}\right)^3=64\Rightarrow\dfrac{T_{Mars}}{T_{Mercury}}=8$.
• $T_{Mercury}=\dfrac{687}{8}\approx 85.9$ days, closest to 88 earth days.