How Does a Star's Mass Affect its Properties and Position on the HR Diagram?

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A star's mass significantly influences its properties, including radiated power, surface temperature, lifetime, and position on the Hertzsprung-Russell (HR) diagram. Higher mass stars have greater fusion rates, leading to increased temperatures and luminosities, but shorter lifespans due to rapid fuel consumption. The relationship between these factors can be expressed mathematically, though clarity is needed on specific equations for temperature and radiated power. The discussion highlights the need for precise definitions and expressions to connect mass with these stellar characteristics. Understanding these relationships is crucial for interpreting a star's lifecycle and its placement on the HR diagram.
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1. A star in the main series. Explain how the radiated power, surface temperature, lifetime and location in the HR diagram depends on the star's mass.
2.E = 1/4Pi*r^2 (I think, need help with this)
3.I know that the lifetime of the star depends on its mass because of the fusion process, or how fast the atoms in the star fuses (which is connected to the stars temperature). I know that radiation power is L which is how much energi per time it releases. This is found by using
 
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Under 2, I don't see a temperature, radiated power (or is that E? If so, mention it!) lifetime, etc.
 
BvU said:
Under 2, I don't see a temperature, radiated power (or is that E? If so, mention it!) lifetime, etc.

What do you mean? An equation for the temperature, or radiated power?
 
Explain how the radiated power, surface temperature, lifetime and location in the HR diagram depends on the star's mass.
So the exercise is asking for a bunch of stuff, right? My naive idea would be that you need expressions for these things. If you want to do only one, fine with me!
Right now I see an expression for something called E with the dimension of m-2. What is it ?
 

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