Finding mass of black hole once given the density

In summary, to calculate the mass and radius of a black hole with a density of 750 kg/m^3, you can use the formula D = (mass/(4/3pi((2Gmass/c^2)^3) and apply the ^3 to everything inside the brackets to solve for mass. However, there may be some difficulty with the algebra due to one of the "mass" variables being stuck inside the Schwarzschild radius in a complicated fraction.
  • #1
fifel85
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Homework Statement


Calculate the mass and radius of a black hole with density 750 kg/m^3.

Homework Equations


The Attempt at a Solution


In a previous question, I already used the Schwarzschild radius to come up with a formula for the density of a black hole:
D = (mass/(4/3pi((2Gmass/c^2)^3). I realize that this should be enough to solve for mass, but I am having difficulty with the algebra...How do I solve for mass when one of the "mass" variables is stuck inside the Scharzchild radius in a complicated fraction?
 
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  • #2
Apply the ^3 to everything inside the brackets to which it is attached.
 

FAQ: Finding mass of black hole once given the density

What is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. It is formed when a massive star dies and collapses in on itself.

How is the density of a black hole determined?

The density of a black hole can be determined by dividing its mass by its volume. The mass can be calculated using the orbital motion of objects around the black hole, and the volume can be estimated based on the size of the event horizon.

What is the relationship between density and mass of a black hole?

The density of a black hole is directly proportional to its mass. This means that as the mass of a black hole increases, its density also increases. This is because the gravitational pull of a black hole is determined by its mass, and as the mass increases, the gravitational pull becomes stronger, resulting in a higher density.

Can the mass of a black hole be accurately determined from its density?

No, the mass of a black hole cannot be accurately determined solely from its density. The density of a black hole can only provide an estimate of its mass, as other factors such as the spin and charge of the black hole also play a role in determining its mass.

How is the mass of a black hole calculated from its density?

The mass of a black hole can be calculated from its density by using the formula M = ρ x V, where M is the mass, ρ is the density, and V is the volume. However, this calculation will only provide an estimate of the black hole's mass and may not be entirely accurate.

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