Hertzsprung-Russell Diagram question

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In summary, the relationship between the luminosity, size, and surface temperature of a star can be expressed as $$ \frac{l}{l_0}=(\frac{R}{R_0})^2(\frac{T}{T_0})^4 $$ where $$L_0$$ is the luminosity of the sun, $$R_0$$ is the radius of the sun, and $$T_0$$ is the surface temperature of the sun. This can be derived from the equations $$F=\frac{L}{4 \pi R^2}$$ and $$F=\sigma T^4$$ by substituting in the values for the sun.
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Taylor_1989
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Homework Statement


From first principles show that the relationship between the luminosity, size
and surface temperature of a star can be expressed as:

$$ \frac{l}{l_0}=(\frac{R}{R_0})^2(\frac{T}{T_0})^4 $$

Homework Equations


$$L_0$$= Luminosity of sun
$$R_0$$=radius of sun
$$T_0$$=surface temp of sun

$$F=\frac{L}{4 \pi R^2}$$
$$F=\sigma T^4$$

The Attempt at a Solution


$$F=\frac{L}{4 \pi R^2}$$

$$L=4\pi R^2F =4\pi R^2\sigma T^4$$

So this is as far as I get. Is it just a matter of doing a luminosity for the sun and then just putting $$L/L_0 $$ or is there more to it. Have I got the wrong end of the stick. Any help would be very much appreciated. Thank in advance
 
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  • #2
Is it just a matter of doing a luminosity for the sun and then just putting [itex]\rm L/L0 [/itex] ?

Yes. That's really all there is to it.
 

FAQ: Hertzsprung-Russell Diagram question

What is a Hertzsprung-Russell Diagram?

A Hertzsprung-Russell Diagram is a graph that shows the relationship between the luminosity (brightness) and the temperature of stars. It is named after the two astronomers, Ejnar Hertzsprung and Henry Norris Russell, who independently created it in the early 20th century.

What is the purpose of a Hertzsprung-Russell Diagram?

The purpose of a Hertzsprung-Russell Diagram is to classify and understand the various types of stars in the universe. It helps scientists to identify the stage of a star's life cycle, its size, and its temperature.

How is a Hertzsprung-Russell Diagram constructed?

A Hertzsprung-Russell Diagram is constructed by plotting the luminosity of stars on the vertical axis and their temperature on the horizontal axis. The temperature scale is logarithmic, with the hottest stars on the left and the coolest stars on the right. The luminosity scale is also logarithmic, with the most luminous stars at the top and the least luminous stars at the bottom.

What can we learn from a Hertzsprung-Russell Diagram?

A Hertzsprung-Russell Diagram can tell us about the evolutionary stages of a star, its size, its temperature, and its composition. It also allows us to compare different types of stars and understand their similarities and differences.

What are the main types of stars shown on a Hertzsprung-Russell Diagram?

The main types of stars shown on a Hertzsprung-Russell Diagram are main sequence stars, red giants, white dwarfs, and supergiants. These categories are based on a star's luminosity and temperature, and each type represents a different stage in a star's life cycle.

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