The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 10⁸ m/s . Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s . (d) Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?

Video transcript

Hey, everyone. So this problem is dealing with a galaxy very far away from earth. Its core mass is estimated to be about one times to the 38 kg. The average star in this galaxy has a mass that's similar to the sun's mass, which is 1.989 times 10 to the 30 kg. And we're asked to estimate the number of stars in the galactic core. Our multiple choice answers are a 9.34 times 10 to the B 9.7, sorry 7.91 times 10 to the eight C 9.45 times 10 to the 10 or D 5.3 times 10 to the seven. So this is a pretty basic or straightforward question as long as we can recall that the four mass is equal to the average mass of each star multiply drive the total number of stars. And so when we're solving for the total number of stars, we can rearrange the equation to be N sub X is equal to are four mass multiplied by the average mass of each star. And so from there, we can plug in the values given in the equation. So our core mass is one times 10 to the 38 kg. And the average mass of each star is 1.989 times 10 to 30 kg. And so our total number of stars, we plug that into our calculator. We get 5.3 times 10 to 7 and that aligns with answer choice D so D is the correct answer for this problem. That's all for this one. We'll see you in the next video.