A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one

Question

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

TestHub · Accepted Answer

The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

$T^{2} \propto r^{3}$

Therefore, we can write

$\frac{T_{1}^{2}}{r_{1}^{3}} = \frac{T_{2}^{2}}{r_{2}^{3}}$

$\Rightarrow \frac{(200)^{2}}{r^{3}} = \frac{T_{2}^{2}}{{(\frac{r}{4})}^{3}}$

$\Rightarrow \frac{200 \times 200}{4 \times 4 \times 4} = T_{2}^{2}$

$\Rightarrow T_{2} = 25$ days

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