Apparent brightness and ``magnitude''

In this class, we will describe how bright a star seems as seen from Earth by its apparent brightness.

The apparent brightness is how much energy is coming from the star per square meter per second, as measured on Earth. The units are watts per square meter (W/m²).

Astronomers usually use another measure, magnitude. (Our book calls it apparent magnitude.) Since magnitude is so commonly used, we need to understand a little about it too.

The magnitude system stems from ancient Greece. A very bright star was called ``first magnitude,'' a pretty bright star is ``second magnitude,''... a barely visible star is ``sixth magnitude.''

This system has been turned into a quantitative system

The apparent brightness of a star is described by a magnitude that is a positive number for most stars, but can be a negative number for, say, Venus.
Bigger magnitudes correspond to dimmer stars.
Suppoe that two stars have have magnitudes
- m₁ = 1.2 (bright)
- m₁ = 2.2 (pretty bright)
Then the magnitudes differ by 1:
m₂ - m₁ = 1.0
Then the ratio of apparent brightness for the two stars is
b₁/b₂ = 2.512

We can make this a little more concrete by supplying some numbers. The apparent brightness of the brighter star (magnitude 1.2) is

b₁ = 9.4 × 10^‒9 W/m²

The apparent brightness of the dimmer star (magnitude 2.2) is

b₂ = 3.8 × 10^‒9 W/m²

The ratio of these is b₁/b₂ = 2.512.

Notice, by the way, how small the apparent brightness of a star is. There is not much energy content in the light from a single star. Compare this to the apparent brightness of the sun, 1.4 × 10³ W/m². The sun can keep us warm, but starlight can't do that.

ASTR 122 course home page

Updated 29 Octobber 2007

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA