Magnitude: a Bright Idea

Anyone with good visual acuity can look up into the clear night sky and see that the stars vary greatly in brightness. In the 2nd century B.C., Hipparchus of Greece established a star brightness scale. He determined that the dimmest stars that could be seen with the naked eye were sixth magnitude (mag. 6), while the brightest stars were first magnitude (mag. 1).

This relationship was based merely on the visual, or apparent, brightness of the stars as determined by the observer. It did not take into consideration that some stars may be nearer to us than others, thereby making them appear to be brighter. In other words, a dim star close to the earth may appear as bright as a brilliant star that is further away. Only when a star's distance from the earth is determined can we truly know how intrinsically bright it is.

During more modern times a precise scientific method was employed to determine magnitudes. In 1856, an Oxford astronomer, N.R. Pogson, discovered a relationship between the brightness, or luminosity, of stars. A 1st mag. star was 100 times more luminous than a 6th mag. star. He could therefore compute the relationship between the change in brightness for different magnitude stars.

His relationship states that each whole magnitude jump represents a change in brightness of 2.512 times. He arrived at this figure by taking the 5th root of 100, the five being the range of magnitudes between 1st and 6th mag, and the 100 being the change in brightness over that entire range. Using this method, one can now determine that a 1st magnitude star is 2.512 times as bright as a 2nd magnitude star. A 1st mag. star would then be 6.3 times as bright as a 3rd mag. star (2.512 x 2.512).

It may take some time to fully understand this principle, and I'm now going to complicate the issue somewhat. There are stars dimmer than magnitude 6 and stars brighter than magnitude 1. The larger the positive magnitude the fainter the object. Also, the larger the magnitude in the negative direction the brighter the object is. Therefore, a star of magnitude of 1.4 is brighter than a star of magnitude 1.0. Confusing? Just remember, negative magnitudes represent a bright object (this also refers to planets, the moon, and the sun as well -- any object can be assigned a magnitude). Below is a small table to give you an idea on the magnitudes of some common sky objects and how they relate in brightness to each other.

• Stars: Sirius(1.4); Canopus(-0.7); Arcturus(0.0); Alpha Centauri(0.01);  Rigel(0.18); Antares(1.06); Regulus(1.36); Polaris (2.0)
• Solar System: Venus(-4.4); Full Moon(12.6); Sun(26.72); Mars at opposition(-2.8); Saturn(0.0)

Let's now take a look at a constellation that I'm sure is familiar to all of you, Ursa Major, and the Big Dipper asterism. On the next clear night locate this constellation and see if you can tell the difference between the stellar magnitudes of the seven stars that comprise this sky pictogram.

If you start with the bowl of the dipper and go clockwise from the pointer star nearest to the pole star (Polaris), the magnitudes are 1.9, 2.4, 2.5, and 3.4. The three stars that make up the handle starting from the bowl and extending outward are 1.7, 2.4, and 1.9 magnitude respectively. If you have difficulty seeing the 3.4 mag. star (called Megrez) in the bowl of the dipper, it is either a hazy or cloudy night. If the former, try observing any available bright planet or the Moon. If the latter, go inside and read a good book!

Furthermore, it is important to know what magnitude limits can be ssen by your eyes and with various instruments. The naked eye can see stars down to 6th magnitude under dark sky conditions, while a pair of binoculars can see down to about mag. 10. A six-inch telescope can show stars as dim as mag. 12.7, while the largest ground based telescopes with CCD cameras now push that limit to 25th mag. The Space Telescope peers deep into our universe by observing objects as faint as about 30th magnitude!! Soon we'll be seeing objects so far away that the light we detect began its journey soon after the birth of our universe.

I hope this explanation of the term magnitude will help you to more fully enjoy the night sky. On the next clear, moon-less night, with nontwinkling stars, use a star chart that provides star magnitudes to try to determine the dimmest star you can see at zenith using the naked eye. Your limiting magnitude will then be known. This new knowledge will be beneficial when the magnitude of a new comet, nova or supernova is announced. You will then know whether or not that celestial event can be seen in your sky.

Keep your eyes to the skies!