Finding mass of black hole once given the density

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SUMMARY

The discussion focuses on calculating the mass of a black hole given its density of 750 kg/m³ using the Schwarzschild radius formula. The relevant equation derived is D = (mass/(4/3π((2Gmass/c²)³)). The challenge lies in isolating the mass variable from within the complex fraction of the Schwarzschild radius. The solution requires careful algebraic manipulation to apply the exponent correctly across the entire bracketed term.

PREREQUISITES
  • Understanding of Schwarzschild radius and its implications in general relativity
  • Familiarity with algebraic manipulation and solving equations
  • Knowledge of gravitational constant (G) and speed of light (c)
  • Basic concepts of density and mass in physics
NEXT STEPS
  • Study the derivation of the Schwarzschild radius in detail
  • Learn advanced algebra techniques for isolating variables in complex equations
  • Explore the implications of black hole density on its mass and radius
  • Investigate the relationship between mass, density, and gravitational forces in astrophysics
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Students in physics, astrophysics enthusiasts, and anyone interested in the mathematical modeling of black holes and their properties.

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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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Apply the ^3 to everything inside the brackets to which it is attached.
 

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