Question

	Mass(Solar Masses)	Semi Major axis(AU)
Sun	1	0.004967199691804744
Jupiter	0.0009546133303706552	5.2033630099999995

Considering the following variables of the sun and jupiter. These bodies orbit their barycenter where the semi major axis is from the barycentre If jupiter has an orbital period of T=4331 days,what is the velocity of the sun around the barycentre

Answer 1

This is a two body central force problem.

When two bodies are moving due to a central force like gravity, their motion can be expressed as a revolution in an orbit around their center of masses.

The period of the two bodies will be same for such a problem.

Here, the period of Jupiter is 4331 days = 4331*3600*24 = 3.741*10⁸ s

So, period of sun = 3.741*10⁸ s

The semi major axis of the sun = 0.004967199691804744 AU = 7.4308*10⁸ m

Consider that the orbit of the sun and the Jupiter are almost circular.

The distance it travels in one period = = 2*3.14*7.4308*10⁸ = 4.6665*10⁹ m

So, the velocity of the sun is given by

v = distance/time = 4.6665*10⁹ /3.741*10⁸ = 12.474 m/s