Apparent Magnitude, Absolute Magnitude and Luminosity

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How bright is bright? There are several ways in which we describe a star's brightness. Apparent magnitude, Absolute magnitude and Luminosity.

Apparent magnitude describes how bright a star, planet or moon appears to be. Stars visible to the naked eye in the night sky range in order of about six magnitudes from 1 to 6 with the one being brightest and six being faintest. There are many stars and objects in the sky beyond six magnitude but you will need a telescope or a good pair of binoculars to see them.

What is magnitude?

Magnitude is a ratio or light from one level to the next. The differences in magnitude is 2.5 times brighter per change in level. For Example a magnitude star of 1 is 2.5 times brighter than a 2 in the sky. A first magnitude star is one hundred times brighter than a sixth magnitude star.

What is a parsec?

A parsec is a angular distance in space measured using parallax. 1 parsec equals 3.26 ly

Absolute magnitude is how really bright a star is. Absolute magnitude is the apparent visual magnitude of a star 10 pc away. Absolute magnitude is calculated by knowing the stars distance verses it's apparent magnitude.

The formula for absolute magnitude is:  mv - Mv = -5 + 5 log 10 (d)  or d = 10 exponent (mv -Mv =5)/5

mv = Apparent magnitude

Mv = Absolute magnitude

d = parsecs

Example Problem: What is the Absolute magnitude of 61 CYG A ?

Sample Problem information gathered

1 parsec equals 3.26 light years

d = parsecs

mv = 61 CYG A Apparent visual magnitude is 5.2

Mv = Absolute magnitude which is the unknown

61 CYG A distance is 11.2 light years (ly) so 11.2 ly/3.26 = 3.43 pc

Sample Problem:

mv - Mv = -5 + 5 log10 (d)

5.2 - Mv = -5 + 5 log (3.43 pc)

5.2 - Mv = -5 + 5 (.54)

5.2 - Mv = -5 + 2.68

5.2 - Mv = -2.32

-Mv = -2.32 - 5.2

-Mv = -7.52

(-1)Mv = -7.52 (-1)

Mv = 7.52 absolute magnitude for 61 CYG A!

Luminosity is the measure of how much energy a star is emitting each second. Knowing that luminosity depends on two things its size and its temperature the formula

L/L sun = (R/R sun) exp 2 (T/T sun) exp 4

L = luminosity

R = Radius

T = Temperature

Sample Problem:

What is the luminosity of a star whose radius 20 times larger than the Sun but only a fourth as hot?

L/L sun = (20/1) exp2 (1/4) exp4

L/ L sun = (400/1) (1/256)

L/L sun = 400/256

L = 1.56 times the (L sun luminosity)