Question

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

Answer 1

We have
`(Mv^2)/(r)=(gammaMm_s)/(r^2)` or `r=(gammam_s)/(v^2)`
Thus `omega=v/r=(v)/(gammam_s//v^2)=(v^3)/(gammam_s)`
(Hence `m_s` is the mass of the Sun.)
So `T=(2pigammam_s)/(v^3)=(2pixx6*67xx10^(-11)xx1*97xx10^(30))/((34*9xx10^3)^3)=1*94xx10^7sec=225` days.