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Viral theorem for the age of a star of constant luminosity

Please see attached, but the basic problem is how to rearrange the viral theorem into a form that describes the time taken for a star of uniform density and constant luminosity to reach its current radius. on the attachment are some of my notes on what i need to consider, please can you show me the full working to help me understand.


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Your assignment talks about a star of CONSTANT LUMINOSITY.

Therefore you cannot use the Stefan-Boltzmann Law for luminosity, as then it WOULD NOT BE CONSTANT

In my understanding of your assignment, you are given the ...