SOLUTION: The Schwarzschild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole. R = 2GM/c^2 G= gravitational constant 6

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Question 251086: The Schwarzschild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole.
R = 2GM/c^2
G= gravitational constant 6.7x10^-11
M= mass of object
C= speed of light 3x10^8
The sun has M=2x10^30. What is the Schwarzschild radius for the sun? (Note its true radius is 700,000)
I have worked and reworked this problem and just cannot come up with the right answer. Please help.Inserting the values for the sun into thi
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
R+=+2GM%2Fc%5E2
Inserting the values for the sun into this equation we get:
R+=+%282%286.7%2A10%5E%28-11%29%29%282%2A10%5E30%29%29%2F%283%2A10%5E8%29%5E2
Now we simplify. In the numerator I am going to use the Commutative and Associative Properties for Multiplication to rearrange the factors to gather the powers of 10 together and the other numbers together. This will make the simplification easier:
R+=+%28%282%2A6.7%2A2%29%2A%2810%5E%28-11%29%2A10%5E30%29%29%2F%283%2A10%5E8%29%5E2
R+=+%2826.8%2A10%5E19%29%2F%289%2A10%5E16%29
R+=+%2826.8%2F9%29%2A10%5E3 which is approximately 3000.

I did some investigating and 700,000 is the actual radius of the sun. The answer we have of 3000 tells us that if the sun had the same mass but was only 3000 km is radius it would be a black hole.