Calculating Escape Velocity of a Planetary Body

AI Thread Summary
To calculate the escape velocity of a planetary body with a radius five times its Schwarzschild radius, the relevant equations are the Schwarzschild radius, given by (2GM)/c^2, and the escape velocity formula, √(2GM/r). The attempt at a solution simplifies to v=√(c^2/5) after substituting the radius into the escape velocity equation. It is confirmed that the mass "M" in both formulas represents the same quantity. The discussion emphasizes the relationship between the two equations and the simplification process.
btpolk
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Homework Statement



Determine the escape velocity of a planetary body that has a radius 5 times greater than its Schwarzschild radius.

Homework Equations



Schwarzschild radius=(2GM)/c^2

escape velocity=√(2GM/r)

The Attempt at a Solution



v=√((2GMc^2)/(10GM))=√(c^2/5)

Is this right?
 
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Looks okay, but you can simplify a bit further: pull the c2 out of the square root.
 
Is the "M" in the Schwarzschild radius formula represent the same thing as the "M" in the escape velocity formula?
 
btpolk said:
Is the "M" in the Schwarzschild radius formula represent the same thing as the "M" in the escape velocity formula?

Yes, it does.
 
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