Final answer:
The correct order of star colors from hottest to coolest is Blue, White, Yellow, Red, but no given option lists this correctly. The hottest star among Archenar, Betelgeuse, and Capella is Archenar (blue), and the coolest is Betelgeuse (red). The color of a star, with blue being the hottest and red the coolest, is a rough indicator of its temperature.
Step-by-step explanation:
The question asks to list the four most common colors of stars in order from the hottest to the coolest. To answer this question correctly, we must understand that the color of a star is determined by its temperature, with blue stars being the hottest and red stars being the coolest. The order of colors indicating the temperature from hottest to coolest is Blue, White, Yellow, Red.
Therefore, the correct option is Option 1: Blue, Red, Yellow, White as it incorrectly lists the colors in the sequence from the hottest to the coolest stars. The right order should be Option 4: Blue, White, Yellow, Red, which is not listed among the given options.
Based on their colors, Archenar (blue) is the hottest among the given examples, and Betelgeuse (red) is the coolest, with Capella (yellow) having an intermediate temperature. A rough "thermometer" for measuring the temperatures of stars can be established based on the dominant color of light they emit, with blue indicating higher temperatures due to shorter-wavelength light.