Question

A planet of mass M moves along a circle around the Sun with velocity v = 34.9 km/s (relative to the heliocentric reference frame). Find the period of revolution of this planet around the Sun.

Answer 1

In this case, $\frac{Mv^2}{r}=\frac{\gamma Mm_s}{r^2}\implies r=\frac{\gamma m_s}{v^2}$

Therefore, $\omega=\frac{v}{r}=\frac{v^3}{\gamma v_3}$

$\implies2\pi\gamma m_s/V^3=1.94\times10^7 sec=255$ days