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? [2025]

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Solution

Q.
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 [2025]

1 172 earth days

2 124 earth days

3 88 earth days

4 225 earth days

Ans.
(3)

Given, $R_{martian} = 4 R_{mercury}$

$T_{martian} = 687$ Earth days

$T_{mercury} = ?$

By Kepler's Third Law

${(\frac{T_{Mercury}}{T_{Martian}})}^{2} = {(\frac{R_{Mercury}}{R_{Martian}})}^{3} = {(\frac{1}{4})}^{3} = \frac{1}{64}$

$T_{Mercury} = \frac{T_{Martian}}{8} = \frac{687}{8} = 85.8 days$

Nearest answer is 88 Earth days.

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