Question

Distance between a distant planet and the Sun is four times that of distance between Earth and Sun. Calculate the time taken by planet to orbit the Sun in respect of Earth years.

• A. $4$ Earth years
• B. $64$ Earth years
• C. $16$ Earth years
• D. $32$ Earth years
• E. $8$ Earth years

Answer 1

The correct option is E $8$ Earth years

Let the distance between the earth and the sun be $R$.

Thus distance between the planet and the sun $R^{\prime }=4R$
Time taken by earth to orbit the sun $T=1$ earth year

Using Kepler's 3rd law, $T^2\propto R^3$

$⟹$ $\frac{T^{\prime }}{T}=(\frac{R^{\prime }}{R}{)}^{1.5}$

$\therefore$ $\frac{T^{\prime }}{1}=(\frac{4R}{R}{)}^{1.5}=4^{1.5}$ $⟹T^{\prime }=8$ Earth years