Question

The Jupiter's period of revolution around the Sun is $12$ times that of the Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and the Sun.

• A. $5.2$ times
• B. $10.2$ times
• C. $6.4$ times
• D. $3$ times

Answer 1

Answer: (A)

$5.2$ times

Let, The time of revolution of Jupiter is $T_j$ and the radius of orbit of revolution of Jupiter is $r_j$

The time of revolution of Earth is $T_e$

The radius of orbit of revolution of Earth is $r_e$

According to Kepler's Law

$T^2\propto r^3$

$\Rightarrow T_j^2\propto r_j^3$ and $T_e^2\propto r_e^3$

$\therefore \frac{r_j^3}{r_e^3}=\frac{T_j^2}{T_e^2}$

$\therefore \frac{r_j}{r_e}={\left(\frac{T_j}{T_e}\right)}^{\frac{2}{3}}$

$\therefore \frac{r_j}{r_e}=(12{)}^{\frac{2}{3}}$ ...............................$($since, $\frac{T_j}{T_e}=12)$

$\therefore \frac{r_j}{r_e}=5.24$

Hence, the distance between the Jupiter and the Sun exceeds 5.2 times that between the Earth and the Sun.