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

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?

Professor PC Thomas Classes · Answer

(c) : Given, $R_{	ext {martian }}=4 R_{	ext {mercury }}$ $T_{	ext {martian }}=687$ \ Earth year $T_{	ext {mercury }}=$ ? \ By kepler's third law $ \\begin{aligned} & \left(\frac{T_{	ext {Mercury }}}{T_{	ext {Martian }}}ight)^2=\left(\frac{R_{	ext {Mercury }}}{R_{	ext {Martian }}}ight)^3=\left(\frac{1}{4}ight)^3=\frac{1}{64} \ & T_{	ext {Mercury }}=\frac{T_{	ext {Martian }}}{8}=\frac{687}{8}=85.8 	ext { days } \end{aligned} $ \ Nearest answer is 88 earth days.