Apparent 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 'apparent magnitude', learn a few examples of the apparent magnitude of objects in the sky, and an equation to calculate apparent magnitude. A short quiz will follow.

What is Apparent Magnitude?

When you look at the sky at night, you see the stars and the moon. Perhaps some of those 'stars' turn out to instead be galaxies much further away. A dim star might appear dim because it isn't as bright as the Sun, or it might be dim because it's just a very long way away. But whatever the reason, some objects appear brighter than others.

Objects in the sky vary greatly in brightness.
Objects in the sky vary greatly in brightness.

Apparent magnitude is a number that represents how bright objects in the sky appear in the visible part of the electromagnetic spectrum. This scale is the opposite of how you might imagine -- high numbers are dim, and low numbers are bright.

One problem with such a scale is that it depends where you're standing on the Earth. If you live near a city, the stars might not seem nearly as bright as they would somewhere in the Rocky Mountains. So apparent magnitude ignores the atmosphere -- it relates to how bright an object in the sky would be if there was nothing to interfere with your view except the distance between you and the object.

Light Pollution - USA at Night
Light Pollution - USA at Night

Examples of Apparent Magnitudes

An apparent magnitude of zero is defined as the brightness of the star Vega. Stars with larger magnitudes appear dimmer than Vega, and stars with negative numbers as magnitudes appear brighter than Vega. Remember: lower is brighter!

Apparent magnitude follows a logarithmic scale, meaning that a magnitude 1 star is not twice the brightness of a magnitude 2 star. Instead, it is 2.512 times the brightness.

While Vega is only the 5th brightest star in the sky, it's important historically because it was the first star whose spectrum was analyzed and the first star to be photographed. Originally, the magnitude scale was based around the northern pole star, Polaris, but we discovered later that this star is variable in brightness. It was therefore changed to Vega, which is nearby. It actually was the nearest star to the North Pole back in 12,000 BCE.

Examples of Apparent Magnitudes
Examples of Apparent Magnitudes

Our Sun has an apparent magnitude of -27, a full moon can be as bright as -15, Mars has an average apparent magnitude of 1.8, the Andromeda galaxy is 3.4, and Pluto has a maximum brightness of 13.7. Most human eyes can only see objects that have an apparent magnitude of 6 or brighter.

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