# How to estimate star magnitudes

A clear night sky is awash with stars… we show you how to compare their brightness

#### By Dave Eagle

Even to casual stargazers it’s pretty obvious that the stars are of differing brightness. Astronomers always like to catalogue and classify objects in the sky, and the brightness of stars is no exception. Over 2,000 years ago, the Greek astronomer Hipparchus devised the system we use for this purpose, called the magnitude scale.

In Hipparchus’s magnitude scale, the brightest stars were known as first magnitude and the faintest stars were sixth magnitude. He gave a higher number to the faintest stars,
which sounds a little topsy-turvy until you swap the word ‘magnitude’ for the word ‘class’. Looking at it this way you start to see them as ‘first class’ stars, ‘second class’ stars and so on as the stars get fainter, putting the scale into perspective.

At the brighter end of the scale, magnitudes become a little awkward as some stars and other objects are brighter than first magnitude. There are stars with zero magnitude – wrongly suggesting they have no brightness – and in cases where the stars are even brighter, they have a negative magnitude, as you can see in these examples:

 The Sun –27 Full Moon –12 Venus (at its brightest) –4.4 Arcturus –0.04 Vega +0.03 Polaris +1.99 Pluto +13.9

With telescopes and imaging equipment like CCD cameras, you can go way beyond the sixth-magnitude objects on Hipparchus’s original scale and capture objects like Pluto, which is far too dim to be seen with the naked eye. The Hubble Space Telescope has managed to image objects as faint as magnitude +30. Don’t forget that the magnitude doesn’t tell you how luminous an object really is in itself; it’s a measure of the apparent brightness of a star as seen from our vantage point here on Earth.

The great thing about star magnitudes is that by getting to know the brightness of stars and carefully observing them, you’ll be able to estimate the magnitudes of other objects you see in the sky. This is handy when you see a meteor streaking across the sky, or a passing comet. You might also want to keep track of the changing brightness of a variable star so that you can let others know how bright it is.

The first step in learning how to estimate magnitudes is to make sure you know what you’re looking at. Print out a detailed star chart showing star magnitudes near your chosen star from planetarium software such as Redshift, or from one of the websites in ‘Find out more’ on page 80. You need to identify the field of view correctly. In our step-by-step guide using Ursa Minor over the page, this may seem easy, but when you’re tackling fainter stars in star fields that you haven’t observed much, it can take some time to find where you are.

When you’ve got to grips with what you’re looking at, use your chart printout to find two stars in the same field of view as the one you’re interested in, to compare it against. These ‘comparison stars’ need to be on either side of your target star in terms of brightness – one brighter and one fainter. You also need to make sure that both comparison stars are not variable stars, which change in brightness. Now decide how bright your target star is when compared to the two comparison stars. Is it halfway between them, or is it somewhere else in between, being of a more similar brightness to one than the other? Use your own judgement and be consistent in how you make your comparisons.

Once you’ve decided, it’s time to put a figure on the target star’s magnitude in comparison to your two other stars. Look up the magnitudes of the comparison stars on your star chart. Knowing this will help you make a reasonable estimate of your target star’s magnitude. Let’s say the two comparison stars are of magnitudes +4.0 and +3.0. If the target star is two-thirds of the way from the faintest star to the brightest, this gives you an estimated magnitude of about +3.3. Don’t worry if you’re a little unsure; practice makes perfect.

Give it a go
Now let’s try a real example. High up at this time of year is the constellation of Draco, the Dragon. The stars you’ll need are marked on it in the image below. It’s a constellation meandering between the two bears, Ursa Major and Ursa Minor, and it has a distinct pattern of four stars marking its head, known as the Lozenge. We’re going to estimate the magnitude of one of those stars, Grumium (Xi (ξ) Draconis). The comparison stars we’re going to use are Etamin (Gamma (γ) Draconis) and Kuma (Nu (ν) Draconis), at magnitudes +2.2 and +5.0 respectively.

#### The constellation of Draco is high this time of year. Use the stars Gamma (γ) and Nu (ν) Draconis to estimate the magnitude of Xi (ξ)

Observe carefully and try and work out where the brightness of Grumium lies between our two comparison stars. You should see that it’s roughly two-thirds of the way from Etamin towards Kuma, which will then give you a rough estimate for this star’s magnitude of about +4.0.

With your newfound skill you’ll be able to work out the brightness of a host of different objects, including variable stars. You’ll also be able to use binoculars or a telescope to estimate the brightness of really faint objects such as minor planets or comets. Make sure you record your findings in a log book – you never know what you might find.