# Absolute Magnitude: Definition & Formula

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

In this lesson you will learn the meaning of the term 'absolute magnitude', a few examples of the apparent magnitude of objects in the sky, and an equation to calculate absolute magnitude. A short quiz will follow.

## What is Absolute Magnitude?

When you look at the sky at night, you see the moon, stars, planets, and even a few distant galaxies. Some objects are bright, and some are dim. But how bright are they really? The Sun is the brightest object in our sky, but it turns out that it isn't an especially bright star at all... it's just super close. Because the objects in the night sky are at different distances, it's hard to tell from their brightness how bright they really are.

Apparent magnitude is a number that represents how bright objects in the sky appear to our eyes. This scale is an inverted scale, meaning that high numbers represent dim objects, and low numbers represent bright ones. An apparent magnitude of -4 is brighter than an apparent magnitude of +8. Remember: lower is brighter!

Absolute magnitude is a similar measure that represents how bright an object actually is. This works by imagining we could place every object in the sky at a distance of 10 parsecs (190 trillion miles) away. Absolute magnitude is how bright stars would appear in our sky if they were all at that distance - or in other words, it's the apparent magnitude they would have if they were moved to that distance.

Magnitude scales ignore anything that would interfere with the observation of an object, like light pollution. The numbers represent what it would look like with no atmospheric effects.

## The Magnitude Scale

The brightness of the star Vega is used to define an apparent magnitude of 0. Stars with positive apparent magnitudes appear to our eyes to be dimmer than Vega, where as stars with negative apparent magnitudes appear brighter than Vega.

Originally, the North Pole star Polaris was chosen, but when it was discovered that Polaris is a variable star (its brightness changes), astronomers switched to nearby Vega. In fact, Vega once was the North star 14,000 years ago, and will be again in another 10,000 years or so.

So that's what 0 magnitude means. But is a 3 magnitude star twice as bright as a 6 magnitude star? Unfortunately not.

Magnitudes work on a logarithmic scale, where each number is a factor of 2.512 different to the number next to it. A magnitude 1 star is 2.512 times brighter than a 2 magnitude star. And a 1 magnitude star is 6.31 times brighter than a magnitude 3 star (2.512 x 2.512 = 6.31).

Many astrophysics students have wondered if this scale was designed purely to torture them. As likely as that may seem to them, in reality it's more of a historical quirk that we keep for the sake of tradition.

## Examples of Absolute Magnitudes

Our Sun has an apparent magnitude of -26, by far the brightest object in the sky. But its absolute magnitude is only 4.83. Compare this to the brightest star in the sky that our eyes can see, Sirius, which has an absolute magnitude of 1.4, or a much dimmer star called Ross 458, which has an absolute magnitude of 14.8. The brightest stars our telescopes have detected are around -10. Galaxies in the sky are extremely dim on the apparent magnitude scale, but the absolute magnitude of the M87 galaxy is -22, which makes sense because it contains hundreds of billions of stars.

## Equation

The following equation tells us the relationship between apparent magnitude and absolute magnitude:

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