Calculating Schwarzschild Radius at Galaxy's Core

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In summary, astronomers have observed a small, massive object at the center of our Milky Way galaxy, believed to be a black hole. The object has a mass of 4.26 x 10^37 kg and a ring of material orbits it with a diameter of 15 light years and a speed of 200 km/s. By using the equation R_S = [2Gm]/c^2 and the given constants, the Schwarzschild radius of the object is estimated to be 1.89 x 10^19 m.
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mantillab
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Homework Statement



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. Take the distance of one light year to be 9.461 X 10^15 m. Mass of object = 4.26 X 10^37 kg. Speed of light (c) = 3 X 10^8 m/s. G = 6.67 x 10^(-11).

Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what is its Schwarzschild radius R_S?

Homework Equations



From Wikipedia, I got the equation for the Schwarzschild radius to be R_S = [2Gm]/c^2.

The Attempt at a Solution



Using the above equation and the above constants, I got 1.89 x 10^19 m, which is wrong.

Other wrong answers: 1.90×10^19 and 1.89x10^35.

Any help would be appreciated! Thanks!
 
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  • #2
Well it looks like you divided by c instead of c^2.
 
  • #3
Doh! Thanks so much.
 

1. What is the Schwarzschild Radius and what does it represent?

The Schwarzschild Radius is a theoretical concept in physics that represents the distance from the center of a black hole at which the escape velocity exceeds the speed of light. It is also known as the event horizon, as it marks the point of no return for any object or light attempting to escape the gravitational pull of the black hole.

2. How is the Schwarzschild Radius calculated at a galaxy's core?

To calculate the Schwarzschild Radius at a galaxy's core, you would need to know the mass of the black hole at the center of the galaxy. This information can be obtained through various methods such as observing the orbital motions of stars or analyzing the effects of gravitational lensing. Once the mass is known, the Schwarzschild Radius can be calculated using the formula 2GM/c^2, where G is the gravitational constant and c is the speed of light.

3. Can the Schwarzschild Radius change over time?

No, the Schwarzschild Radius is a fixed value determined by the mass of the black hole and the speed of light. It does not change over time, but the size of the event horizon may appear to change as the black hole consumes more matter and grows in mass.

4. What is the significance of calculating the Schwarzschild Radius at a galaxy's core?

Calculating the Schwarzschild Radius at a galaxy's core can provide valuable information about the properties of the black hole at the center of the galaxy. It can also help scientists understand the dynamics of the galaxy and the effects of the black hole's gravity on its surrounding environment.

5. Is the Schwarzschild Radius the same for all black holes?

No, the Schwarzschild Radius is directly proportional to the mass of the black hole. Therefore, larger black holes will have a larger Schwarzschild Radius, while smaller black holes will have a smaller Schwarzschild Radius. Additionally, the Schwarzschild Radius can also be affected by the spin and charge of the black hole, but these factors are typically negligible for most black holes.

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