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 the velocity of Jupiter in the heliocentric reference frame.

• A. $68km/s$
• B. $106km/s$
• C. $8km/s$
• D. $13km/s$

Answer 1

The correct option is D $13km/s$

Given, $\frac{R_j}{R_e}=12$

As we know, $\frac{{\omega }_j}{{\omega }_e}={\left(\frac{R_e}{R_j}\right)}^{1.5}$
$\frac{V_j}{V_e}=\frac{{\omega }_j{R}_j}{{\omega }_e{R}_e}=\frac{(R_e{)}^{1.5}{R}_j}{(R_j{)}^{1.5}{R}_e}={\left(\frac{R_e}{R_j}\right)}^{0.5}\to V_j=\frac{V_e}{{12}^{0.5}}=13km{s}^{-1}$