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