Luminosity and how far away things are

In this class, we will describe how bright a star or galaxy really is by its luminosity.

The luminosity is how much energy is coming from the per second. The units are watts (W).

Astronomers often use another measure, absolute magnitude. Absolute magnitude is based on a ratio scale, like apparent magnitued. I think it is confusing.

The luminosity of the Sun is

Lsun = 3.9 x 1026 W
We will often measure luminosities of stars in units of the luminosity. That is, we might say for a certain star Lstar = 5.2 x Lsun, meaning that the star has 5.2 times the energy output per second of the Sun.

Apparent brightness

In this class, we will describe how bright a star seems as seen from Earth by its apparent brightness. This is often called the intensity of the starlight. Sometimes it is called the flux of light.

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.''

Measuring luminosity

Since we can't go to a star to measure its luminosity, we have to be clever. If we know the distance to the star we can do it, because there is a simple relation between The relation is

This relation is based on conservation of energy. Consider an observer a distance d from the star. How much energy crosses a square meter detector that this observer has?

Note that the brightness decreases proportionally to the square of the distance as one moves away from the star. This can be demonstrated experimentally in the laboratory.

We can write the relation so that it gives L in terms of b and d.

Luminosities of stars

One finds

Using brightness and luminosity to get distance

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