How Small Must Mars Be Compressed to Become a Black Hole?

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Homework Help Overview

The discussion revolves around the concept of black holes, specifically focusing on the radius to which Mars must be compressed to become a black hole. Participants explore the relationship between mass, gravitational forces, and escape velocity in the context of black hole physics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the Schwarzschild equation and its implications for understanding black holes. There is an emphasis on the need to comprehend the reasoning behind the equation rather than just applying it. Questions about escape velocity and its relation to the speed of light are raised, indicating a search for deeper understanding.

Discussion Status

The discussion is active, with participants engaging in clarifying concepts and exploring connections between escape velocity and black hole formation. Some guidance has been provided regarding the relationship between Mars' escape velocity and the speed of light, although no consensus on a complete solution has been reached.

Contextual Notes

Participants express varying levels of familiarity with black hole physics and indicate that they are currently studying electromagnetism and thermodynamics, which may influence their understanding of the topic.

Seth Newman
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Homework Statement


To what radius do you need to compress Mars in order to turn it into a black hole?

Homework Equations


None given, but I am mildly familiar with Schwarzschild and his equation. I know that if we double the object's mass, multiply by the universal gravitational constant, and divide the entire thing by the speed of light squared we can technically turn anything into a black hole. In other words:

Per the text: R=(2GM)/(c^2)

The Attempt at a Solution


Obviously I can plug and chug with the equation, but I want to understand WHY this works, and maybe how to derive the equation (if that's even possible at my current understanding). I am fairly unfamiliar with black hole physics, but my instructor thought this would be an interesting problem for us to solve (currently in electromagnetism/thermo).

Thanks!
 
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Investigate: escape velocity.
 
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gneill said:
Investigate: escape velocity.

Ah. So, I should be looking for when the escape velocity of Mars is the speed of light?
 
Seth Newman said:
Ah. So, I should be looking for when the escape velocity of Mars is the speed of light?
That's the idea.
 
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gneill said:
That's the idea.

Great, thanks. That connection completely missed me. Appreciate it.

Edit: Turns out the radius needs to be 0.00094714 meters for Mars to be turned into a black hole!
 
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