Studies of the relationship of the Sun to our galaxy—the Milky Way—have revealed that the Sun is located near the outer edge of the galactic disc, about 30 000 ly (1 ly = 9.46 1015 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?
The Attempt at a Solution
a) I got the correct answer. I did:
T = 2∏R/v = 2∏(2.84x10^17Km)/250Km/s = 7.13x10^15 s
T = 7.13x10^15 s(1/3600)(1/24)(1/365) = 2.26x10^8 yr
b) I got this one wrong...
F = GMm/R^2 = Mv^2/R
M = v^2R/G = (250000 m/s * 2.84x10^20)/6.67x10^-11 = 2.66x10^41 Kg
c) I also got this wrong...
Number of Stars = 2.66*1041kg / 1.99*1030kg= 1.336*1011 stars
Can anyone help me out with the last two parts? I am not sure why they are wrong...