Stellar Radius & Effective Temperature

AI Thread Summary
To determine the relationship between stellar radius and effective temperature, the discussion focuses on using the luminosity equation L=4πR²σT⁴, assuming all Main Sequence stars have the same mean density. The attempt involves manipulating the solar version of the equation to express radius in terms of luminosity and effective temperature. However, it's suggested that incorporating mass is crucial to eliminate luminosity, indicating that the second relevant equation, L∝M³.⁵, may be key to finding the correct relationship. The guidance emphasizes the need to consider mass in the calculations rather than solely relying on radius and temperature. Understanding these relationships is essential for solving the homework question effectively.
Physics Dad
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I have a question for my Astro homework and I am a little unsure as to whether I am going in the right direction

Question
Using an expression that relates luminosity, size and temperature of a star, and assuming all Main Sequence stars have the same mean density, determine the relationship between stellar radius and effective temperature.

Relevant equations
L=4πR2σT4
L∝M3.5

Attempt at a solution
My thinking is to use the solar version of the above equation and this one, dividing one by the other to get rid of the 4π and σ and making...

R=RΘ(√(L/LΘ))(TeffΘ/Teff)2

However I don't know if I am supposed to just have R and T with no other variable.

Any guidance would be appreciated.
 
Last edited:
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Physics Dad said:
My thinking is to use the solar version of the above equation and this one, dividing one by the other
I don't think that is the right line. The information regarding density implies you are supposed to use some fact concerning mass to eliminate luminosity. Your second Relevant Equation looks useful in that regard.
 
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