Difficult star question (1 Viewer)

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Pllllease help me I have been stuck on this for ages:

[HRW5 14-57E] A star, with mass 3.29 1030 kg, revolves about the center of the Milky Way galaxy, which is 3.33 1020 m away, once every 2.17 108 years. Assuming that each of the stars in the galaxy has a mass equal to that of our star, that the stars are distributed uniformly in a sphere about the galactic center, and that our star is essentially at the edge of that sphere, estimate roughly the number of stars in the galaxy.

Answer needed ASAP
(working out would also be nice)
What have you tried so far?
Here's what I think, find the volume of the star sphere. Then divide that by the mass of the star.
Ive noticed a mistake in the question by the way. Where it says 3.29 1030kg, 3.33 1020m and 2.17 108 years it is supposed to say 3.39 x 10^30 kg, 3.33 x 10^20 m and 2.17 x 10^8.

Keep trying please

I think this may be a uni type of question.
You need to find the mass of the object that the star is orbiting such that it orbits at that speed at that distance. you can then divide that by the mass of your star to find how many stars
i think you would need Gauss's law. find out the acceleration of the star, then apply gauss's law to find out the mass enclosed by that sphere.

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