Stars emit radiation whose spectrum is very similar to that of a blackbody. Imagine two stars identical in size, each of which is at the same distance from us. One of the stars appears reddish in color, while the other one looks distinctly bluish. Based on this information, what can you say about the relative temperatures of the two stars? Which is the hotter? How do you know?

Blackbody radiation refers to a theoretical object's emission of electromagnetic radiation that is solely dependent on its temperature. This hypothetical object, dubbed a 'blackbody', absorbs all incoming light and emits radiation in a pattern characteristic of its temperature. What's fascinating about a blackbody is that it is a perfect emitter; it radiates the maximum amount of energy at any given temperature and wavelength.

When scientists refer to stars or other celestial objects as blackbodies, they mean objects that closely mimic this ideal emitting behavior. In practice, no object is a perfect blackbody, but stars are good approximations because they emit a continuous spectrum of light that depends only on their surface temperatures.

This concept is crucial when observing the colors of stars, as their color is significantly a result of the radiation they emit due to their temperature—an insight provided by Wien's Displacement Law.

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from high-frequency gamma rays to low-frequency radio waves. In between, lies the visible spectrum, which is what humans can naturally perceive with the naked eye, containing all the colors of the rainbow. Each color corresponds to a different wavelength, with violet having the shortest wavelength and red having the longest.

In the context of stellar observations, this spectrum allows astronomers to determine various properties of stars. For example, the color of a star gives astronomers clues about its peak wavelength of emitted light, and therefore its temperature. Following the logic of Wien's Displacement Law, stars emitting blue light are generally hotter than those emitting red light because blue light has a shorter wavelength and therefore indicates a higher surface temperature.

Stellar temperatures can be deduced from the color of the stars, thanks to the principles behind blackbody radiation. Observing the color provides a first-hand impression of the star's temperature; typically, the hotter a star, the more blue it appears, while cooler stars exhibit a reddish hue. This characteristic stands in line with Wien's Displacement Law, which illustrates the inverse relationship between the peak wavelength of radiation and the temperature of the emitting body.

A blue star, like the one mentioned in the exercise, has a surface temperature that can reach up to 25,000 degrees Kelvin or more. In contrast, reddish stars have cooler surface temperatures, usually no more than 3,500 degrees Kelvin. By comparing the color of two stars, one can deduce that the bluer one is hotter, indicating not just a difference in appearance, but a fundamental difference in thermal characteristics.