Notice that we used the term "appears" in the definition. It is because magnitude, as we usually mean it, does not tell how bright that object really is. It refers to how bright it seems to be.
Astronomers divide magnitude into two general types: apparent and absolute.
¹A unit of distance in astronomy, 1 parsec equals 3.26 light-years or 3.09 × 10¹³ km (1.92 × 10¹³ miles).
It''s important to point out that an object''s absolute magnitude is measured without extinction (or dimming) of its light due to absorption by interstellar matter and cosmic dust.
So the apparent magnitude depends on an object''s intrinsic luminosity, its distance, and the extinction reducing its brightness. The absolute magnitude allows us to compare the intrinsic luminosity of objects (in a given range of the spectrum) by hypothetically placing all objects at a standard reference distance from the observer.
Let''s take our Sun and Rigel. The Sun appears way brighter than Rigel in our sky so its apparent magnitude is higher (magnitude −26.8 and 0.18, respectively). However, if we placed both the Sun and Rigel at 10 parsecs away from the Earth, Rigel would impressively outshine the Sun. That''s because the distant star has a higher absolute magnitude: -6.69 vs 4.83 for the Sun.
Here are some more examples:
Apparent magnitude values are expressed as a number without a unit; when you see something like "Antares has a magnitude of 1.09", it means that the apparent magnitude is implied. This can be written more concisely as "Antares (mag 1.09)", "Antares (1.09 m)" or "Antares (m = 1.09)". When referring to magnitude types other than apparent, astronomers specify the type by writing the magnitude type with a phrase or abbreviation letter: "Antares has an absolute magnitude of −5.28" or "Antares (M = −5.28)". They also use the letters in formulas.
By the way, apparent magnitude can be measured both with the naked eye and with a telescope; both in the visual range of the spectrum and in other ranges (photographic, UV, IR). In this case, "apparent" means "observable" and does not refer specifically to the human eye. If we''re only considering what the human eye can see, then we''re measuring visual magnitude. However, many popular science sources use these terms interchangeably.
In 137 CE, the ancient astronomer Ptolemy classified stars on a six-point scale from one (brightest) to six (faintest, barely visible to the naked eye) and coined the term magnitude. Initially, this system grouped stars into six distinct groups without distinguishing brightness within a group. Today, we use a refined version of this magnitude scale.
Ptolemy''s scale is a system of how relatively bright celestial objects appear to be. Such a system requires a zero point or a reference star. Traditionally, Vega, with an apparent magnitude of 0.0, was taken as this reference star.
Of course, with the development of telescopes, astronomers expanded this scale to include much dimmer celestial bodies, such as faint nebulae and distant galaxies.
Astronomers also extended the scale to cover brighter objects in the sky, like the Sun, the Moon, and some planets. Since Vega was considered the zero-magnitude star, astronomers assigned negative values to objects brighter than Vega. Here are some examples of apparent magnitude values for bright objects:
So this magnitude scale might be confusing, just remember that the larger the number, the dimmer the object. The brightest objects have negative magnitudes.
You might have noticed that there are far more dimmer stars than there are brighter ones in our night sky. Here''s a simplified breakdown of star numbers by their stellar magnitudes:
Note that these numbers represent all the stars visible to the naked eye in the entire sky. Since we can only see half the sky at any moment, the actual number of stars you can see at one time is different.
We know that a magnitude 1 star is brighter than a magnitude 2 star. But how much brighter?
The magnitude scale is logarithmic, where a difference of 5 magnitudes always corresponds to a brightness change by a factor of 100. This means that a star of magnitude 1 is 100 times brighter than a magnitude 6 star, and similarly, a star of magnitude 2 is 100 times brighter than a magnitude 7 star.
But if you use a calculator, you'll see that the numbers don't quite add up. That's because 2.5 is a simplification; the precise number is 100^(1/5) ≈ 2.51188643150958. In most sources, you'll see this number shortened to 2.5 or 2.512. Here is the change in magnitude between stars with differences of 1, 2, 3, 4, and 5 magnitudes:
A difference in magnitude 1 increases the brightness by about 2.512 times, so an increase in magnitude by 8.1 times will increase the brightness by (2.512)^8.1 times, which is ≈1,700.
So, the Full Moon is about 1,700 times brighter than Venus! If we use the general equation for comparing brightness based on stellar magnitudes, it can be expressed as:
Iᴬ / Iᴮ ≈ 2.512^(mᴮ – mᴬ)
Here Iᴬ and Iᴮ represent the intensities (or brightness) of objects A and B, respectively, and mᴮ, mᴬ are their magnitudes.
To define an object''s precise apparent magnitude, astronomers measure this object''s flux or intensity (the total amount of energy per unit area arriving at the telescope''s detector per second). Then, they compare how relatively bright the source appears to be by comparing it with the reference star, using the following formula:
where m is the magnitude (as we already know) and F is flux. I is used instead of F in many sources, as astronomers use the term "flux" for what is often called "intensity" in physics.
With the advent of accurate photometers and cameras, astronomers realized that even Vega wasn''t a perfect reference star. Its brightness varied over time by ~0.03 magnitudes. So, for the sake of accuracy, astronomers came up with the zero point based on a theoretical source with constant flux. However, for visual observations, Vega can still serve as a standard of zero magnitude.
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