Calculating Escape Velocity of a Planetary Body

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Homework Help Overview

The problem involves calculating the escape velocity of a planetary body, specifically one with a radius that is five times greater than its Schwarzschild radius. The context includes concepts from gravitational physics and general relativity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive the escape velocity using the relationship between the Schwarzschild radius and escape velocity. Some participants suggest simplifications to the expression provided. There are questions regarding the consistency of the mass variable "M" in both formulas.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempt and clarifying the meaning of variables used in the equations. There is no explicit consensus yet, but some productive guidance has been offered regarding simplifications.

Contextual Notes

Participants are exploring the definitions and relationships of variables in the context of gravitational physics, specifically regarding the Schwarzschild radius and escape velocity. The original poster's calculations are based on the assumption that the radius is directly related to the Schwarzschild radius.

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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