dwarf stars
-Sydney-
Objects with absolute magnitudes of one or less are extremely bright, and typically include objects like the Sun, the Moon, and certain major planets like Venus and Jupiter when viewed from Earth. These objects appear very bright in our sky because they reflect or emit a lot of light towards us.
Spica has a surface temperature of 22,400K and an absolute magnitude of -3.55Rigel has a surface temperature of 11,000K and an absolute magnitude of -6.7So the question is incorrect.
supergiant
According to Wikipedia giants have absolute magnitudes around 0 to -1 while supergiants have absolute magnitudes around -5 so they are 50-100 times brighter (5 magnitudes difference equals 100 times brighter).
It is a rational number which is less than 1. If the absolute value of the numerator is less than the absolute value of the denominator then the fraction is a proper fraction.
If the radius of Betelgeuse varies by 60% within three years, its luminosity will also change proportionally. Since absolute magnitude is related to luminosity, the ratio of the two absolute magnitudes will be the square root of the ratio of the luminosities. So, the ratio of the two absolute magnitudes will be approximately 1.22.
ble
Red giants have typical absolute magnitudes which are 10-15 magnitudes below white dwarfs, which means that the red giants are 10,000-1,000,000 times brighter, after due allowance for distance.
Yes, if the matter surrounding one star is more dense than that surrounding the other it would appear to be less bright.
Cassiopeia is a constellation, not a single star, so it does not have a specific absolute magnitude. The stars within the constellation Cassiopeia have a range of absolute magnitudes depending on their distance and luminosity.
Magnitudes require distance and luminosity. Therefore a specific star is required.
The less luminous one is closer to the observer, just as a candle in the same room can seem as bright as a sodium vapor lamp down the street.