Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light-years and an orbital speed of about 200 km/s. (b) Observations of stars, as well as theories of the structure of stars, suggest that it is impossible for a single star to have a mass of more than about 50 solar masses. Can this massive object be a single, ordinary star?

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Welcome back everybody. We are looking at a discovered super massive black hole known as Sagittarius A. At the center of our galaxy and there's a star that is orbiting around Sagittarius A. We're told that the radius of the orbit is approximately 0. astronomical units. And we are told that its orbital speed is 2.1 times to the eighth meters per second. Now we are asked to find a what the mass of the black hole is and B. If the black hole was just formed from one star only, let's go ahead and tackle art A. Here we know that the orbital speed right of a of a planetary body around another is given by the square root of Newton's gravitational constant times the mass of the larger body all over the radius of the orbit, rearranging some things here we have that are desired mass that we're trying to find is the radius of orbit times the orbital speed squared all over Newton's gravitational constant. Let's go ahead and plug in some values here we have that. The mass of Sagittarius A is 0.8 astronomical units as its radius. But we really need to work with this in meters. So I'm gonna convert this real quick. It is given that there are 1.49 times 10 to the 11th meters in one astronomical unit. So these terms will cancel out giving us the right terms in the end. So that's the radius, times our orbital speed of 2.1 times 10 to the eighth squared All over Newton's gravitational constant of 6.673 times 10 to the negative 11. This is equal to 7.9 times 10 to the 36 kg. Now, if you actually divide by the mass of the sun, you get that this is approximately four times 10 to the six times times the mass of the sun. So with that in mind, let's move on to question B. Was Sagittarius A formed from only one star. Well, a good way to check is is the mass of our given black hole greater than, you know, 50 times are significantly greater than 50 times, You know, a smaller orbital body or or a star. Right? And we can just use the mass of our sun for our reference. So, plugging in our our mass here on the left side of this inequality, we get that four times 10 to the six times the mass of the sun is greater than 50 times the mass of the sun divided by the mass and Sons on both sides, we get that four times 10 to the six is significantly greater than 50 meaning that Sagittarius A could not or highly improbable that it was formed from just one star more. If you're if you're curious, probably more in the realm of probably like 8000 stars. If you do the math there. But with that being said, we found the answer choice to part A. And the answer choice to part B. Giving us a final answer choice of D. Thank you all so much for watching hope. This video helped. We will see you all in the next one.

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Key Concepts

Mass of Stars

Orbital Mechanics

Supermassive Black Holes