Astrophysics question

[MartenAndre]

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

 

[BvU]

Under 2, I don't see a temperature, radiated power (or is that E? If so, mention it!) lifetime, etc.

 

[MartenAndre]

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?

 

[BvU]

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 ?

 

[HalfLostAndSearching]

the Stefan-Boltzmann law, which states that the radiated power is directly proportional to the fourth power of the star's surface temperature and surface area. This means that the higher the surface temperature, the higher the radiated power.

As for the location of the star in the HR diagram, it depends on its mass because the HR diagram plots stars based on their luminosity (radiated power) and temperature. Stars with higher masses have higher luminosity and surface temperature, placing them in the top left corner of the HR diagram. On the other hand, stars with lower masses have lower luminosity and surface temperature, placing them in the bottom right corner of the HR diagram.

Additionally, a star's mass also determines its lifetime. The more massive a star is, the faster it will burn through its fuel and the shorter its lifetime will be. This is due to the higher pressure and temperature in the core, allowing for faster fusion reactions. On the other hand, lower mass stars have lower pressure and temperature in their core, resulting in slower fusion reactions and longer lifetimes.

In summary, a star's mass plays a crucial role in determining its radiated power, surface temperature, lifetime, and location in the HR diagram. The higher the mass, the higher the radiated power and surface temperature, but also the shorter the lifetime. This is all connected to the fusion process and the star's internal conditions.