Question

Studies of the relationship of the Sun to our galaxy have revealed that the sun is located near the outer edge of the galactic disk, about 30, 000 lightyears (1 ly= 9.46 X 10^15 m) from the center. The Sun has an orbital speed of approximately 250 km/s around the galactic center.

(a) What is the period of the Sun's galactic motion?

(b) What is the order of magnitude of the mass of the Milky Way galaxy?

(c) Suppose the galaxy is made mostly of stars of which the Sun is typical. What is the order of magnitude of the number of stars in the Milky Way?

Answer 1

Hints:
(a) \(T = \dfrac{2\pi R}{v}\) (this is a distance divided by a velocity)
(b) Centripetal force is \(F = \dfrac{mv^2}{r}\), which is due to the gravitational force \(F = \dfrac{GMm}{r^2}\). Consider the mass of the Milky Way to be concentrated at the center.
(c) Use the answer to part (b).