Stellar Radius & Effective Temperature

In summary, the question asks to determine the relationship between stellar radius and effective temperature using the expression L=4πR2σT4 and assuming all Main Sequence stars have the same mean density. The solution involves using the solar version of the equation and dividing it by another equation to eliminate variables. The information regarding density implies that mass should be used to eliminate luminosity. The second Relevant Equation, L∝M3.5, can be used to do so.
  • #1
Physics Dad
55
1
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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  • #2
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.
 

What is a stellar radius?

A stellar radius is a measure of the size of a star, typically measured in terms of the radius of our own sun. It is the distance from the center of the star to its outermost layer or surface.

How is stellar radius measured?

Stellar radius is typically measured using a combination of techniques, including spectroscopy, interferometry, and photometry. These methods involve analyzing the light emitted by a star and using mathematical models to determine its size.

What is effective temperature?

Effective temperature is a measure of the surface temperature of a star. It is not the actual temperature of the star, but rather the temperature at which a theoretical blackbody (an object that absorbs all radiation that falls on it) would emit the same amount of energy as the star.

How is effective temperature related to a star's color?

The effective temperature of a star is closely related to its color. Hotter stars tend to emit more blue light, while cooler stars emit more red light. This is because the temperature of a star's surface affects the types of atoms and molecules present, which in turn affects the colors of light that are emitted.

What is the relationship between stellar radius and effective temperature?

Stellar radius and effective temperature are related in that larger stars tend to have higher effective temperatures. This is because larger stars have more mass, which causes them to have stronger gravitational forces that compress their core and increase their temperature. However, other factors such as the star's chemical composition can also affect its effective temperature.

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