The simple answer is by looking at them.
The technical answer is by analysing their bolometric luminosity with a bolometer.
Rigel is brighter than Betelgeuse. Rigel is a blue supergiant star and one of the brightest stars in the night sky, while Betelgeuse is a red supergiant and although it is one of the largest stars known, it is not as bright as Rigel.
Rigel is brighter than Betelgeuse. Rigel is a blue supergiant star that is one of the brightest stars in the night sky, while Betelgeuse is a red supergiant star that is dimmer in comparison.
Betelgeuse has an apparent magnitude of 0.42(v) and an absolute magnitude of -6.02. Rigel has an apparent magnitude of 0.12 and an absolute magnitude of -7.04. So Rigel is brighter.
Rigel appears as bright as Betelgeuse even though it is further away because Rigel is intrinsically brighter (has a higher luminosity) than Betelgeuse. Despite being further away, its higher luminosity compensates for the distance, making it appear similarly bright in the sky.
Betelgeuse is larger than Rigel. Betelgeuse is a red supergiant star with a diameter about 1,180 times that of the Sun, while Rigel is a blue supergiant with a diameter roughly 79 times that of the Sun.
Betelgeuse is larger in size than Rigel. Betelgeuse is a red supergiant star with a diameter about 800 times that of the Sun, while Rigel is a blue supergiant star with a diameter about 70 times that of the Sun.
Betelgeuse is around 10 times greater in diameter than Rigel.
You can tell if Rigel or Betelgeuse is hotter based on their color. Rigel appears blue-white, indicating a hotter temperature, while Betelgeuse appears orange-red, suggesting a cooler temperature. Additionally, the spectral class of Rigel (B8Ia) is hotter than Betelgeuse's spectral class (M1-2Ia).
No, Rigel is hotter than Betelgeuse. Rigel is a blue supergiant star with a surface temperature of around 12,000 Kelvin, while Betelgeuse is a red supergiant with a surface temperature of around 3,500 Kelvin.
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Rigel appears as bright as Betelgeuse because it is closer to Earth than Betelgeuse, even though Rigel is smaller and less luminous. The brightness of a star is determined by both its luminosity and distance from Earth, so a smaller, closer star can appear just as bright as a larger, more distant one.
It is common for astronomers to identify stars in a constellation with Greek alphabets. This is called the "Bayer designations". Bayer, a German astronomer, designated the stars in a constellation according to brightness, but this is not always the case. Here, Betelgeuse is not as bright as Rigel but it is called Alpha Orionis, rather than Beta Orionis. One reason for this is because 400 years ago, nobody could accurately determine which star was brighter, and it probably seemed that Betelgeuse was the brighter star.