Two stars, whose spectra peak at 660 nm and 480 nm,...

Two stars, whose spectra peak at $660 \mathrm{nm}$ and $480 \mathrm{nm}$, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the $\mathrm{H}-\mathrm{R}$ diagram (Fig. $44-6$ ) to estimate the ratio of their diameters.

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Key Concepts

Wien's Displacement Law

This law connects the peak wavelength of a star's spectrum to its surface temperature through the relation ?max × T = constant. It allows one to determine the temperature of a star by measuring the wavelength at which its spectrum peaks, which is foundational when analyzing stellar properties from their light.

Stefan–Boltzmann Law

This law states that the total energy radiated per unit surface area of a blackbody is proportional to the fourth power of its temperature. In the context of stars, it is used to relate a star’s luminosity to its radius and temperature with the equation L = 4?R²?T?, making it essential for estimating stellar diameters given temperature information.

Main Sequence and Hertzsprung–Russell Diagram

The HR diagram is a graphical tool that plots stars based on their luminosities and temperatures, revealing patterns such as the main sequence where most stars, including the two in question, reside. For stars on the main sequence, their luminosity, temperature, and size follow empirical relationships that help determine parameters like the stellar radius when combined with physical laws like the Stefan-Boltzmann law.

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