Question

5. Gas 2 pc from the center of the Andromeda Galaxy revolves at 100 km/s. Use Kepler’s third law (the aforementioned equation above) to find the velocity a star would have at the distance of 10 pc from the center (assuming the mass within 10 pc is the same). Now, assuming rigid body motion is in effect, what would the velocity be in this case?

Answer 1

We have from Kepler's 3rd law

where M is the mass of the Andromeda galaxy around which the gas is rotating , T is the time period taken by the latter to rotate once around the galaxy and R is the distance between the gas and galaxy. G is the universal garvitational constant.

Since the velocity of the rotating gas is the above equation reduces to .

Therefore .

In this case . i.e . Therefore .

Since the motion of the center of mass of the rotating object is the same whether it is a gas or a rigid body, the velocity must be same even for rigid body motion.