Magnitude

Throughout the astronomical descriptions and event posts here on Darker View I use the term magnitude to describe the brightness of an object in the sky. Magnitude is a simple scale, but somewhat confusing without a quick introduction.

The origins of our current magnitude scale are as old as the science of astronomy itself. One of the first stellar catalogs, the Almagest, was compiled by Claudius Ptolemy in the 2nd century. To denote the brightness of stars the catalog assigned the brightest as being “stars of the first rank”, with a corresponding second rand, third rank, etc. The dimmest of stars, the faintest visible to the unaided eye, were assigned to the sixth rank. This system was used with little alteration for the next two millennium. Subsequent catalogs and observers used their own versions of the scale, perhaps adding a decimal place to denote finer differences in brightness. As there was no instrumental method of measuring the brightness, magnitude estimates varied widely from source to source.

With the dawn of modern photographic methods and later electronic methods, it became possible to systematize the scale. It was desirable to create a scale that approximated the old system and time honored traditions. Thus the current magnitude scale was developed, understanding the origins allows understanding of the modern system.

Magnitudes

  Magnitude
Sun -26
Full Moon -13
International Space Station     -6
Venus (max) -4.9
Jupiter (max) -2.9
Sirius -1.46
Saturn (max) -0.24
Vega 0.03
Capella 0.91
Polaris 1.97
Andromeda Galaxy 3.4
M42 The Orion Nebula 4.0
Vesta (max) 5.1
M13 The Hercules Cluster 5.8
M57 The Ring Nebula 8.8
Pluto (max) 13.6
Eris 18.7

Example magnitudes of celestial objects
With the current magnitude system the larger the number, the dimmer the object. While this may seem opposite the obvious solution, it keeps the order of the original rankings. To allow the same sort of scale each magnitude represents a change in brightness of 2.5x. Thus a 2.0 magnitude star is two and half times dimmer than a 1.0 magnitude star. The scale is not linear, rather it is exponential. For example, consider a first magnitude star and a fifth magnitude star, thus 4 magnitudes difference. The 5.0 magnitude star is 2.5 x 2.5 x 2.5 x 2.5 = 40x dimmer than the star of 1.0 magnitude. With the modern system a precise number can now be placed on the brightness of any given object, allowing for accurate measurements. Yet a correspondence to the old system is maintained.

The new system can be extended beyond the original 1-6 magnitudes of the ancient system. Very bright objects are assigned negative numbers. Thus the bright planet Venus can achieve magnitudes as bright as -4.9, while the Sun is measured at -26 magnitude, 63 trillion times brighter than the brightest stars. On the other end of the scale, astronomers regularly observe distant galaxies, with magnitudes well into the 20’s, millions of times fainter than the visual stars.

For a casual observer looking up at the night sky the ancient system still works. The brightest stars in the sky range from about -1 to 1 magnitude, with the dimmest stars visible from a dark site in the high fifth and sixth magnitudes. Just remember the two simple rules… A bigger number means fainter, and there is a 2.5x difference per magnitude.

Author: Andrew

An electrical engineer, amateur astronomer, and diver, living and working on Mauna Kea, Hawai'i.

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