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

Q.10) 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 ?

A) $124 \text { earth days }$

B) $88 \text { earth days }$

C) $225 \text { earth days }$

D) $172 \text { earth days }$

 

Answers (1)

best_answer


Solution:
From Kepler's 3rd law, $T^2 \propto R^3$.
Let $T_M=687$ days (Mars), $R_M=4 R$, and $T_{M e}=$ ?
Using the ratio:

$$
\left(\frac{T_M}{T_{M c}}\right)^2=\left(\frac{R_M}{R_{M c}}\right)^3=4^3=64
$$


So,

$$
\frac{T_M}{T_{M e}}=8 \Rightarrow T_{M e}=\frac{T_M}{8}=\frac{687}{8}=85.875 \approx 88 \text { days }
$$


Hence, the answer is option (2) 88 Earth days.

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Dimpy

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