Astrophysics - Temperature of a star via flux and wavelength

In summary: I was thinking of v=lambda (I misspoke earlier calling it frequency instead of wavelength) but I wasnt sure how to use the wavelengths in the equation. I am guessing I can just substitute the values for lambda in the equation.In summary, the conversation discusses using the equation Flux = 2πhv3/c2 to determine the temperature of a star based on the measured flux at two different wavelengths. The equation used is Planck's law for blackbody radiation and the value 'e' represents the base for exponentials. The conversation also mentions the need to incorporate the wavelengths, which can be done by substituting the values for lambda in the equation.
  • #1
cwolfx2
8
0

Homework Statement



What is the temperature of a star if the flux at 450 nm is measured to be 1.3 times the flux at 650 nm.

Homework Equations



I tried to use the equation Flux = 2πhv3/c2

ex-1
x= hv/kt

making 2 of the equations equal each other and solve for T. However being out of practice for months now i do not remember what e represents and how to solve for an exponent.

Though I imagine I may have the wrong equation and not sure if i need to or how to incorporate the wavelengths.
 
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  • #2
cwolfx2 said:
What is the temperature of a star if the flux at 450 nm is measured to be 1.3 times the flux at 650 nm.

Homework Equations



I tried to use the equation Flux = 2πhv3/c2

ex-1
x= hv/kt

Your spacing wasn't preserved, but if you meant

[tex] F(\nu, T) = \frac{2\pi h\nu^3/c^2}{e^{h\nu/kT} - 1} [/tex]

then yes, this is Planck's law for blackbody radiation.

cwolfx2 said:
making 2 of the equations equal each other and solve for T. However being out of practice for months now i do not remember what e represents and how to solve for an exponent.

'e' is just a number. Granted, it's an irrational number, and it is often used as a base for exponentials because an exponential function with e as a base has certain special properties that are convenient.

In order to solve for x, you have to undo the raising of e to the power of it. In other words, you have to do the inverse operation of taking an exponential. That inverse operation is taking the logarithm to base e, which is also known as the natural logarithm.

cwolfx2 said:
Though I imagine I may have the wrong equation

Modelling the star as an ideal blackbody radiator seems like a reasonable approach.

cwolfx2 said:
and not sure if i need to or how to incorporate the wavelengths.

Of course you need to incorporate them. The Greek symbol 'nu' ([itex]\nu[/itex]) in Planck's law represents frequency. What is the relationship between frequency and wavelength?
 
  • #3
Apologies for not getting back sooner, I had the wrong email attached to this account. Thanks for the response, I feel silly on some of my oversights such as e (need to look on my calculator more).
 

1. How is the temperature of a star determined through flux and wavelength?

The temperature of a star can be determined through the relationship between the flux (or intensity) of light emitted by the star and its wavelength. This relationship is known as the blackbody curve, which describes the distribution of energy emitted by an object at a certain temperature. By measuring the peak wavelength of the blackbody curve, we can calculate the temperature of the star through the use of Wien's displacement law.

2. What is flux and how does it relate to the temperature of a star?

Flux is the amount of energy per unit area per unit time that is received from a star. It is directly related to the temperature of a star, as hotter stars emit more energy and therefore have a higher flux compared to cooler stars. This relationship is described by the Stefan-Boltzmann law, which states that the flux is proportional to the fourth power of the temperature of the star.

3. Can the temperature of a star be accurately determined using only flux and wavelength?

While flux and wavelength are important factors in determining the temperature of a star, they are not the only ones. Other factors, such as the composition and size of the star, can also affect the temperature. Therefore, while flux and wavelength can provide a good estimate of the temperature of a star, it may not always be completely accurate.

4. How does the temperature of a star affect its color?

The temperature of a star has a direct impact on its color. Cooler stars, with temperatures below 3,000K, appear red, while hotter stars, with temperatures above 10,000K, appear blue. This is due to the different wavelengths of light that are emitted by stars at different temperatures, with cooler stars emitting longer, red wavelengths and hotter stars emitting shorter, blue wavelengths.

5. Can the temperature of a star change over time?

Yes, the temperature of a star can change over time. This is particularly true for younger stars, which are still undergoing nuclear fusion and may experience fluctuations in temperature. However, for older, more stable stars, the temperature generally remains relatively constant throughout its lifetime.

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