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

In summary, to turn Mars into a black hole, you would need to compress it to a radius of 0.00094714 meters. This can be calculated using the equation R=(2GM)/(c^2), which takes into account the mass of the object, the universal gravitational constant, and the speed of light. This method can technically turn any object into a black hole by doubling its mass, multiplying it by the gravitational constant, and dividing it by the speed of light squared. This is based on the concept of escape velocity, where an object must have a velocity equal to or greater than the speed of light to escape the gravitational pull.
  • #1
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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  • #2
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?
 
  • #4
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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  • #5
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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Related to How Small Must Mars Be Compressed to Become a Black Hole?

1. Can Mars realistically be turned into a black hole?

No, it is not possible to turn Mars into a black hole. Black holes are formed when a massive star collapses in on itself, and Mars is not massive enough to undergo this process. Additionally, the amount of energy and technology needed to artificially create a black hole is beyond our current capabilities.

2. Why would anyone want to turn Mars into a black hole?

The idea of turning Mars into a black hole is purely theoretical and is not a current goal or possibility for scientific research. It is often brought up as a thought experiment to explore the boundaries of physics and the capabilities of human technology.

3. Would turning Mars into a black hole affect Earth?

No, even if it were possible to turn Mars into a black hole, it would not have any impact on Earth. Black holes have a strong gravitational pull, but their effects are only felt within their immediate vicinity. Earth is far enough away from Mars that any changes to its mass or gravitational pull would not be noticeable.

4. What would happen to the rest of the solar system if Mars became a black hole?

If Mars were to somehow become a black hole, it would not have any significant impact on the rest of the solar system. The other planets would continue to orbit the sun as they do now, and the black hole would not have enough mass or gravitational pull to disrupt their orbits.

5. Is it possible to turn any other planets into black holes?

Similar to Mars, it is not possible to turn any other planets into black holes. The conditions necessary for a black hole to form are incredibly specific, and no other planets in our solar system meet those requirements. Additionally, artificially creating a black hole is currently beyond our technological capabilities.

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