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The difference between these concepts can be seen by comparing two stars. Betelgeuse (apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky than Alpha Centauri A (apparent magnitude 0.0, absolute magnitude 4.4) even though it emits thousands of times more light, because Betelgeuse is much farther away.
A difference of 1.0 in magnitude corresponds to the brightness ratio of , or about 2.512. For example, a magnitude 2.0 star is 2.512 times as bright as a magnitude 3.0 star, 6.31 times as magnitude 4.0, and 100 times magnitude 7.0.
The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100 n/5.
The apparent magnitude is the observed visible brightness from Earth which depends on the distance of the object. The absolute magnitude is the apparent magnitude at a distance of 10 pc (3.1 × 10 17 m), therefore the bolometric absolute magnitude is a logarithmic measure of the bolometric luminosity.
Factor ()Multiple Value Item 0 0 lux 0 lux Absolute darkness 10 −4: 100 microlux 100 microlux: Starlight overcast moonless night sky [1]: 140 microlux: Venus at brightest [1]: 200 microlux
The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account.
This is a consequence of the logarithmic magnitude scale, in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the whitish Sun has a B−V index of 0.656 ± 0.005, [2] whereas the bluish Rigel has a B−V of −0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B−V = −0.03). [3]
Once this distance is found, the distance away can be found via the arc subtended in the sky, giving a preliminary distance measurement. From this measurement and the apparent magnitudes of both stars, the luminosities can be found, and by using the mass–luminosity relationship, the masses of each star. These masses are used to re-calculate ...