Finding the mass of our Galaxy and the number of stars in it.

[seizureboi]

Homework Statement

The sun rotates around the center of the Milky Way Galaxy at a distance of about 30,000 light-years from the center (1 light year=9.5x10^15 meters). If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our sun (2x10^30 kg), how many stars would there be in our Galaxy?

Homework Equations

The Attempt at a Solution

For the mass of the Galaxy I got 3.44425x10^41 and I got a total of 1.72213x10^11 stars. I don't think these answers are correct. HELP!?

 

[ideasrule]

172 billion stars looks pretty close. How did you get those answers, and why do you think they're wrong?

 

[seizureboi]

Turns out I am right. What I did was first convert 200,000,000 years to seconds which gave me 6.3072x10^15 seconds/revolution around the center of the galaxy. Then I plugged the given items into the formula (4pi^2r^3)/(GxT^2), where "r" stands for radius (2.85x10^20), "G" standing for the gravitational constant (6.67x10^-11), and "T" standing for the period (6.3072x10^15). This gave me the mass of the galaxy (3.44425x10^41) and then I took that number and divided it by the mass of the sun since the question says to assume the mass of all other stars to be the same as the sun's, thus giving me the amount of stars in the galaxy (1.72213x10^11).

 

[mgb_phys]

Exactly correct method - however if you count the number of stars in the galaxy it's <10% of this.
We are trying to work out what the rest of the dark mass is.

 

[ideasrule]

Actually, 172 billion is pretty close to the number of stars in the galaxy. The reason the OP didn't get 10 times this value is because the question assumes the mass of the galaxy is uniformly distributed in a spherical fashion. That's dead wrong: the galaxy is more like a disk than a sphere, and a disk doesn't behave as if all its mass is concentrated at its geometrical center.