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Gravitation and Black Holes

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At the Galaxy's Core. Astronomers have observed a small, massive object at the center of the Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 17.0 light years and an orbital speed of about 130 km/s. (See attached file for full problem description)

A) Determine the mass of the massive object at the center of the Milky Way galaxy. Give your answer in kilograms.
M =

B) Give your answer in solar masses (one solar mass is the mass of the sun).
Take the mass of the Sun to be 1.99 x 10^30 kg
M =

C) 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?
yes
no

D) Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what must the Schwarzschild radius of this black hole be?
Take the speed of light to be 3.00 x 10^8 m/s
Rs =

E) Would a black hole of this size fit inside the earth's orbit around the sun?
yes
no

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https://brainmass.com/physics/galaxies/gravitation-black-holes-73025

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Solution Summary

This in-depth solution contains step-by-step calculation and brief explanations to determine the mass of the object and what it is. All formulas and workings are shown.

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Find the equation that is used to calculate the Schwarzschild radius of a black hole. Calculate the Schwarzschild radius of this candidate black hole.

Black holes are strange astronomical objects that are formed from collapsed stars. These fascinating stellar objects are named "black holes" because the gravitational pull due to the collapsed star is so large that they do not even allow light to escape once it has entered the black hole. There is a "point of no return" in the black hole called the event horizon of the black hole. Its distance from the center of the black hole (the location of the collapsed star) is called the Schwarzschild radius and it is the largest radius that a body with a specific mass can have and still keep light from escaping. It is named after the German astronomer, Karl Schwarzschild, who first conceived of the idea of a black hole. Interestingly, while Scharwzchild was the first to theorize about black holes, he never believed that it was physically possible for them to exist.
Questions.
1. Execute the necessary research to find the equation that is used to calculate the Schwarzschild radius of a black hole. Hint: This equation should only involve the mass of the collapsed star, the speed of light, and a physical constant known as the Universal Gravitational Constant (this constant was also used in Unit 1).

2. After many different types of astronomical measurements, it is now believed that Cygnus X-1 is a black hole.
a. Execute the necessary research to find the location of this black hole relative to earth.
b. Using the equation from Question 1 and any/or additional required research, find/calculate the Schwarzschild radius of this candidate black hole.
3. Solve the equation found in Question 1 for each of the following variables:
a. the Universal Gravitational Constant
b. the mass of the star that collapsed to form the black hole
c. the speed of light

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