How does the magnitude scale measure star brightness?

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Astronomers describe brightness with a number called magnitude, and the smaller the number, the brighter the object. A difference of one magnitude is a brightness ratio of about 2.5, and five magnitudes is exactly a factor of 100. How bright something looks from Earth is its apparent magnitude; how bright it really is, compared at a standard distance, is its absolute magnitude.

A ranking that began with six classes

The scale goes back to ancient Greece. In the second century BCE, Hipparchus compiled a catalogue noting the brightness of stars, and Ptolemy later arranged stars into six classes. The brightest were called first magnitude and the faintest stars the eye could just pick out were sixth magnitude. Because it was a ranking, like coming first in a race, brighter meant a smaller number.

That backwards direction has survived to the present day. It is confusing at first, but it makes sense if you read a magnitude as a rank rather than an amount. The modern scale, however, is based on measured light rather than judgement by eye, so magnitudes are given to decimal places, such as 1.98 for Polaris or 0.03 for Vega.

Why one step equals about 2.5 times

In 1856 the English astronomer Norman Pogson put the old scale on a mathematical footing. Since first-magnitude stars appeared roughly a hundred times brighter than sixth-magnitude stars, he defined a difference of five magnitudes as exactly a factor of 100. One magnitude is then the fifth root of 100, about 2.512.

With that rule, a magnitude difference converts directly into a brightness ratio. Two magnitudes is about 6.3 times, three is about 16 times, five is 100 times, and ten magnitudes is 100 × 100, or 10,000 times. Adding magnitudes multiplies brightness, which suits the way the human eye responds to light in ratios rather than in equal steps.

Going the other way is just as simple: count one magnitude for every factor of 2.5. If one star is about 40 times brighter than another, then since 2.5 multiplied by itself four times is about 39, the two stars differ by roughly four magnitudes. Thinking of magnitudes as marks on a single ruler makes it possible to place the blazing Sun and a faint distant galaxy on the same scale, separated by more than 50 magnitudes.

Brighter than zero: negative magnitudes

Once the scale was fixed, objects far brighter than first magnitude needed a place on it, so the numbers continue past zero into negative values. Vega, at about +0.03, sits almost exactly at zero, and Sirius, the brightest star in the night sky, is −1.46.

Planets and the Moon go much further. Venus reaches about −4.9 at its brightest, Jupiter about −2.9, and the full Moon averages about −12.7. The Sun is about −26.7, a little over 25 magnitudes brighter than Sirius, which works out to roughly 13 billion times the brightness. Even the 14-magnitude gap between the full Moon and the Sun is a factor of about 400,000.

In practice, almost anything in the night sky brighter than about magnitude −1.5 is a planet or the Moon rather than a star. An exceptionally bright point low in the west after sunset, or in the east before dawn, is very often Venus. Selecting it in the Sky view shows its name and current brightness, a useful way to connect magnitude numbers with what the eye actually sees.

The naked-eye limit is about magnitude 6

On a clear night in a dark rural spot, the eye reaches stars of about magnitude 6, and under the darkest skies about 6.5. That limit depends heavily on the sky background. In a city, scattered artificial light brightens the whole sky, the fainter stars are lost in the glow, and far fewer stars remain visible.

Sirius is about 7.5 magnitudes brighter than a sixth-magnitude star, a factor of roughly 1,000. Binoculars and telescopes push the limit fainter by collecting light over a larger area. The Hubble Space Telescope can record objects near magnitude 31.5, some 25 magnitudes, or 10 billion times, fainter than the naked-eye limit.

By default the Sky view draws background stars down to magnitude 6.5, close to what the unaided eye sees under a dark sky.

Absolute magnitude: brightness at 10 parsecs

Apparent magnitude says nothing about distance: a faint star nearby can look brighter than a powerful star far away. To compare stars fairly, astronomers define absolute magnitude as the apparent magnitude an object would have if it were placed exactly 10 parsecs, about 32.6 light-years, away.

The Sun's absolute magnitude is +4.83. Seen from 32.6 light-years, it would be an ordinary star, visible only under a reasonably dark sky. Sirius has an absolute magnitude of +1.43, about 3.4 magnitudes or some 20 times brighter than the Sun, consistent with the measured luminosity of Sirius A at about 25 times the Sun's.

The gap between apparent and absolute magnitude, known as the distance modulus, depends only on distance. If the true brightness of a star can be worked out by some other means, comparing the two magnitudes gives its distance. Many of the methods astronomers use to measure the distances of far-off star clusters and galaxies rest on exactly this relationship, which is why magnitude remains a working tool and not just a historical curiosity.

Sirius and Rigel: a near star and a distant giant

Two bright stars of the northern winter sky show the difference well. Sirius shines at magnitude −1.46 from about 8.6 light-years, while Rigel in Orion shines at around 0.1 from roughly 860 light-years. In the sky, Sirius looks about four times brighter.

Their absolute magnitudes tell the opposite story: +1.43 for Sirius and about −7.8 for Rigel. That is more than nine magnitudes, so at equal distance Rigel would outshine Sirius several thousand times. At the other extreme, Proxima Centauri is the nearest star at 4.2 light-years, yet its apparent magnitude of about 11 keeps it invisible to the eye. Brightness in the sky alone says little about a star's true power or distance.

In the 3D Stars map, tapping a star brings up a card with its distance and brightness. Stars that look similar in the sky turn out to be scattered at very different distances from the Sun.

Try it in the simulator

  • Find Sirius →Opens the card and position of the brightest star in the night sky, magnitude −1.46.
  • Tonight's sky →Background stars are drawn down to magnitude 6.5, close to the naked-eye limit under a dark sky.
  • Sirius in 3D →Shows Sirius among nearby stars at their true distances.

FAQ

Is magnitude the same as a star's size?
No. Magnitude measures brightness, not diameter. A small star can appear bright if it is close or very hot, and a huge star can look faint if it is far away.
Does a star's magnitude ever change?
Many stars are nearly constant, but variable stars brighten and fade; even Rigel varies slightly, between 0.05 and 0.18. Planets change much more, because their distance from Earth and their phase keep changing.
How faint can I see when the Moon is up?
Bright moonlight raises the brightness of the whole sky and washes out faint stars. Around full Moon the limit drops noticeably even in the countryside, so nights near new Moon are best for faint stars and galaxies.

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