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Chapter 17: Problem 10

Explain why the color ratios of a star are related to the star's surface temperature.

Short Answer

Expert verified
The color ratios of a star are related to their surface temperature due to the principles of black body radiation and Wien's Displacement Law. The temperature of a star determines the wavelength of light most intensely radiated by it. Thus, cooler stars appear reddish, while hotter stars appear bluish, indicating their relative surface temperatures.

Step by step solution

01

Explain Black Body Radiation

The first part of understanding this relationship is to know about black body radiation. A blackbody is an idealized physical body that absorbs all incident electromagnetic radiation. The energy radiated by a black body is given by Planck's Law, which indicates that objects of different temperatures emit spectra that peak at different wavelengths.
02

Introduce Wien's Displacement Law

Next, we need to be familiar with Wien's Displacement Law. This law states that the wavelength at which the radiation emitted by a black body is highest is inversely proportional to the temperature of the body. Mathematically, this can be written as: \(\lambda_{max}T = b\), where \(T\) is the temperature of the body, \(\lambda_{max}\) is the wavelength at which the radiation is highest, and \(b\) is a constant of proportionality known as Wien's constant.
03

Relate Wien's Law to Star's Color

The color of stars, like our sun, is directly related to their surface temperature. The temperature determines the wavelength of light that is most intensely radiated by the star. Still, stars radiate in all parts of the spectrum, from radio waves to gamma waves. However, the part of the spectrum that is radiated most intensively depends on the Star's surface temperature, which can be estimated using Wien's Displacement Law.
04

Relate color to temperature range

Stars cooler than the sun appear to be reddish due to the peak of their spectrum being in the red or infrared. Conversely, stars that are hotter than the sun will appear to be bluish because their spectrum's peak is in the blue or ultraviolet wavelengths. Thus, the observed color of stars can tell us about their surface temperature.

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Most popular questions from this chapter

Astronomers usually express a star's color using apparent magnitudes. The star's apparent magnitude as viewed through a B filter is called \(m_{\mathrm{B}}\), and its apparent magnitude as viewed through a V filter is \(m_{\mathrm{V}}\). The difference \(m_{\mathrm{B}}-m_{\mathrm{V}}\) is called the \(B-V\) color index ("B minus \(V\) "). Is the \(B-V\) color index positive or negative for very hot stars? What about very cool stars? Explain your answers.

Which is more massive, a red main-sequence star or a blue main-sequence star? Which has the greater radius? Explain your answers.

Would it be possible for a star to appear bright when viewed through a \(\mathrm{U}\) filter or a \(\mathrm{V}\) filter, but dim when viewed through a B filter? Explain.

A fellow student expresses the opinion that since the Sun's spectrum has only weak absorption lines of hydrogen, this element cannot be a major constituent of the Sun. How would you enlighten this person?

If a red star and a blue star both have the same radius and both are the same distance from the Earth, which one looks brighter in the night sky? Explain why.
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