Question
Download Solution PDFThe 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
The radius of Mars' orbit around the Sun, R′ = 4R, where R is the radius of Mercury's orbit.
The Martian year T′ = 687 Earth days.
First, apply Kepler's Third Law to find the ratio of the orbital periods:
(T′ / T)² = (R′ / R)³ = (4R / R)³ = 4³ = 64
From this, we can solve for the ratio of the periods:
T′ / T = 8
This means that Mars takes 8 times longer to orbit the Sun compared to Mercury. Therefore, the length of one year on Mercury is:
T = T′ / 8 = 687 / 8 ≈ 85.88 days
Hence, one year on Mercury is approximately 86 Earth days. The nearest option is 88 days.
Last updated on Jun 16, 2025
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