Astrophysics in a Nutshell Problem

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The discussion focuses on finding the temperature profile T(r) of a hypothetical star with a constant density, composed of a classical, non-relativistic ideal gas of fully ionized hydrogen. The relevant equation provided is a differential equation relating the temperature gradient to luminosity, density, and other constants. The poster expresses confusion about how to approach the integration by assuming which values can be treated as constants. There is a request for a clearer explanation of the principles and equations involved in solving the problem. Understanding the temperature profile is crucial for analyzing the star's physical properties.
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Homework Statement



Consider a hypothetical star of radius R, with density ρ that is constant, i.e. independent of radius. The star is composed of a classical, non relativistic, ideal gas of fully ionized hydrogen,
Find the the temperature profile (T(r))

Homework Equations


dT(r)/dr = ( (-3*L(r)*k(r)*ρ(r)) / (4∏*(r^2)*4*a*c*(T(r))^3)
so sorry this is written poorly

The Attempt at a Solution


So what I did is try and assume which of the values on the right side are constant so I could take them outside of the integral, but I'm not sure.Please explain principles and equations fully. I really want to understand this!
 
Last edited:
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Maybe you could state the problem?
 
Oh sorry. I thought I did!
I edited it. I says find the temperature profile (T(r))
 
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