Question

Calculate the period of revolution of Jupiter around the Sun. The ratio of the radius of Jupiter's orbit to that of the Earth's orbit is $5$.
(Period of revolution of the Earth is $1$ year)

Answer 1

According to Kepler's third law or law of harmonics, the ratio of orbital period to orbital distance for each planet is $1$. Thus, from the formula for the law of harmonics,
$1=\frac{T^2}{R^3}$ where, $T=$ orbital period and $R=$ orbital distance.

$\therefore \frac{T_e^2}{R_e^3}=\frac{T_p^2}{R_j^3}$

$T_p^2=5^3\times T_e^2$

$=125\times 1$

$T_p=\sqrt{125}=11.18$ year