Physics Question

Question

Our sun orbits around the centre of our galaxy (the Milky Way) once every 2.5 x 108 years. The radius of the sun’s orbit about the centre of the galaxy is approximately 3.15 x 1020 m. The sun has made only about 20 revolutions since the Earth was formed over 3 billion years ago! The centripetal force keeping our sun in orbit is supplied by the force of gravity.
a) Calculate the mass of the galaxy.

 

b) Assuming that the typical star contains ten times the mass of our sun, estimate the number of stars in our galaxy. Show all work.

 

having troubles with B

Answer 1

(a)

 

M = mass of galaxy = ?

G = universal constant of gravitation (get from tables)

T = sun's orbital period around center of galaxy (given)

R = radius of sun's orbit around center of galaxy (given)

v = speed of sun in orbit around center of galaxy

 

v = 2πR/T

 

Centripetal acceleration:

 

v²/R = GM/R²

 

v² = GM/R

 

M = Rv²/G, where v = 2πR/T

 

Plug in the numbers and work in consistent units (kg, m, s, etc.) to get M.

 

(b)  Assuming you got a good number for M from part (a), divide M by 10 times the mass of the sun.  That will be an estimate of the number of stars.