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

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To turn Mars into a black hole, it must be compressed to a radius of approximately 0.00094714 meters. This calculation is based on the principle that the escape velocity of Mars must equal the speed of light. The relevant equation used is R=(2GM)/(c^2), which relates mass, gravitational constant, and the speed of light. Understanding this concept requires familiarity with black hole physics and the relationship between mass and escape velocity. The discussion highlights the importance of grasping these fundamental principles in astrophysics.
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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