Gravitational potential energy released in core collapse

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SUMMARY

The gravitational potential energy released during the core collapse of a 1.2 solar-mass star, transitioning from an initial density of 10^9 g/cm^3 to a final density of 10^15 g/cm^3, can be estimated using the formula PE = -GM/r. The mass is calculated as the product of density and volume, with the volume determined by the formula (4/3)πr^3. The discussion highlights the need to determine the radius, which can be approximated using the solar radius for calculations.

PREREQUISITES
  • Understanding of gravitational potential energy concepts
  • Familiarity with the equations of state in astrophysics
  • Knowledge of density and volume calculations
  • Basic proficiency in using physical constants such as the gravitational constant (G)
NEXT STEPS
  • Research the derivation of gravitational potential energy in astrophysical contexts
  • Learn about the implications of core collapse in stellar evolution
  • Study the relationship between density, mass, and volume in astrophysical objects
  • Explore the application of the equation PE = -GM/r in different astrophysical scenarios
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in stellar dynamics and core collapse phenomena will benefit from this discussion.

creepypasta13
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Homework Statement



Estimate the gravitational potential energy released in the collapse of a 1.2 solar-mass core from an initial density of 10^9 g/cm^3 to a final 10^15 g/cm^3.

Homework Equations


The Attempt at a Solution



The book doesn't provide much guidance on this. I was thinking of using q= 3/5 assuming the density is constant. Then manipulate M^2/R to Rho*(M)*(R^2)*(4pi/3). And plug in the values for Rho that are given and substitute 1.2 for M. But there's no mention of what the radius is. Do I just use the solar-radius?

Never mind the above. I think I computed it correctly.

Mods, feel free to close this thread
 
Last edited:
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Maybe you can apply: PE = - GM / r.

Use mass = density X volume. Mass is given (1.2 X mass of sun). Densities are given.

Volume = (4/3) Pi r^3. You can find the change in radius.
 

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