# Turning Mars into a Black Hole

1. Mar 17, 2017

### Seth Newman

1. The problem statement, all variables and given/known data
To what radius do you need to compress Mars in order to turn it into a black hole?

2. Relevant 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)

3. 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!

2. Mar 17, 2017

### Staff: Mentor

Investigate: escape velocity.

3. Mar 17, 2017

### Seth Newman

Ah. So, I should be looking for when the escape velocity of Mars is the speed of light?

4. Mar 17, 2017

### Staff: Mentor

That's the idea.

5. Mar 17, 2017

### Seth Newman

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!

Last edited: Mar 17, 2017