Orbits and Kepler's Laws Question

[hardygirl989]

Homework Statement

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?

___________ yr

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

___________ kg

(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?

___________

Homework Equations

F=GMm/R^2
v=2∏Rf
GMT^2=4∏R^3

The Attempt at a Solution

a) I got the correct answer. I did:
v=2∏Rf=2∏R/T
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...

 

[Steely Dan]

If they're asking for an order of magnitude, they might just want $10^{41}$ and $10^{11}$, respectively (assuming those are the correct numbers, which they seem to be).

 

[hardygirl989]

That makes sense.

The website says only one thing about scientific notation on their formatting page:
Incorrect format: 1.2E15 Correct Format: 1.2e15

I tried typing in e41 and it told me that it cannot understand what I wrote. I understand that you probably are not able to access the website, but do you have any suggestions that I can try?

 

[Steely Dan]

In that notation, "e41" does not make sense, but "1e41" ($=10^{41}$) does make sense. I would recommend trying that, as well as 2.66e41. The only online homework submission site I am familiar with is WileyPlus, and on that system this notation would be accepted.

 

[hardygirl989]

1e41 was correct! Thank you so much for your help! =D

SOLVED.