# What is the apparent magnitude limit for the naked eye?

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If you only read the question, you will answer:"That depends on the light pollution". Yes, it does, but if you are in the darkest night sky (Bortle class 1), what magnitude would have the faintest star? In the Wikipedia article about the magnitude, it's written that +6.0 would be the typical limit, but in the article about the Bortle scale, I saw the fainter magnitude +8.0. So, what is the real limit?

The apparent magnitude classification was done arbitrarily by Ptolemy. His thought was to set the 20 brightest stars to the first position, the less bright stars to the second position and so on up to the faintest stars which were given the sixth position. After the use of Pogson's law we were able to give to stars not only natural numbers, but also numbers with decimal digits. When we started to use the first telescopes, we realised that the numbers which are greater than 6 have meaning. So the natural limit of naked eye is the apparent magnitude of +6. Here you can find a nice work from the italian Light Pollution Science and Technology Institute which shows as the typical limit of naked eye compared to the light pollution of each area.

## What is Magnitude in Astronomy? Definition, Examples

Magnitude (in astronomy, stargazing, and astrophotography) is simply a measure of the brightness of an astronomical (celestial) object (e.g. a star like Betelgeuse or a galaxy like Andromeda galaxy).

Why it's so important for an amateur (professional too) astronomer, stargazer and astrophotographer? It's very simple - the brighter the object, the easier to spot, gaze, and photograph!

## Characteristics [ edit | edit source ]

The star is of apparent magnitude 5.49, and so is visible with the naked eye under suitable viewing conditions.

51 Pegasi has a stellar classification of G5V, which indicates that it is a main sequence star that is generating energy through the thermonuclear fusion of hydrogen at its core. The effective temperature of the chromosphere is about 5571 K, giving 51 Pegasi the characteristic yellow hue of a G-type star. It is estimated to be around 6.1 to 8.1 billion years old, which makes it somewhat older than the Sun, with a radius 24% larger and 11% more massive. The star has a higher proportion of elements other than hydrogen/helium compared to the Sun a quantity astronomers term a star's metallicity. Stars with higher metallicity such as this are more likely to host planets. In 1996 astronomers Baliunas, Sokoloff, and Soon measured a rotational period of 37 days for 51 Pegasi.

Although the star was suspected of being variable during a 1981 study, subsequent observation showed there was almost no chromospheric activity between 1977 and 1989. Further examination between 1994 and 2007 showed a similar low or flat level of activity. This, along with its relatively low X-ray emission, suggests that the star may be in a Maunder minimum period during which a star produces a reduced number of star spots.

7.6 limit is an extreme, one-in-a-million limit that can be achieved by a person with excellent visual acuity in perfect conditions (perhaps at sea 200 km from the nearest coast, on a moonless night in a cloudless sky). An average person is not likely to see beyond magnitude 4 in the cities and beyond magnitude 6 in the country.

Notice that the table gives maximum apparent magnitudes of 5.1 and 5.5 for Uranus and Vesta, considerably brighter than Neptune's 7.78, and even those weren't discovered before the age of telescope.

Here's another reason. Do you know how many objects of magnitude less than 7.6 are there in the sky? The answer is, approximately 30 thousand! It is relatively easy to notice "the big 5" and to identify them as planets, because there are only two stars in the whole sky brighter than Saturn at opposition. But, unless you have photographic memory or you make detailed star charts for a living, you won't be able to recognize Uranus, Vesta, and Neptune as planets, at best you'll notice them and consider them regular stars.

I had the opportunity tonight to spend some time looking at the field including Neptune in Capricornus. I first plotted the planet on the Tirion atlas then looked quickly with 6x30mm binoculars to see that this was correct. The planet is well placed in the sense of being uncrowded and within an asterism of convenient stars so that further reference to the atlas was unnecessary.

In brief, I couldn't see it. A star presently not far southeast of the planet, HD 202890, was visible on numerous occasions. This is a K0 giant with V=6.9. I also got more intermittent glimpses of nearby 31 Cap, at V=7.1. Neptune, at V=7.7, I think won't be visible from this latitude until it gets north of the Equator. Gonna have to wait awhile! It ought to be straightforward with patience from Chile or elsewhere in the south.​

Sylas, thanks for digging this up!

Hamster, I agree that people would certainly not have noticed Neptune without actively searching for it. However, there are many amateur astronomers who try to spot faint objects with the naked eye.

For some years Brent Archinal and I have wondered about the naked-eye limiting magnitudes determined by Heber Cutis at Lick Observatory at the turn of the Century. He claimed to see down below mag. 8, but we wondered what the modern standard V magnitudes of those stars were. I've dug out the relevant publication (1901 Lick Obs. Bulletin, 2, 67), and have looked up the stars (fortunately a short and well-identified list). The names are given below along with V and B-V from the Hipparcos/Tycho catalogues, and the magnitude Curtis gave for the same stars. I use the H/T data for convenience they ought to be reliable to within a couple percent, and comparison with data collected in SIMBAD from ordinary sources suggest these numbers are fine for the present purpose. Curtis's comments are also shown for most of the stars.

As can be seen, the faintest star he saw reliably is V = 8.44, and two others below V=8.0 and one at 7.98 were seen as well. As might be expected, he did rather better overall on the near-overhead field around T UMa than on the T Vir field, several degrees south of the Equator (Lick is at about latitude +37.4). Just that alone tells you a lot about observing other than close to the meridian.

These in essence reproduce the results of Dave Nash at the Nebraska Star Party several years ago, when he did a double-blind test using stars in the head of Draco, and saw down to about V=8.2. On winter and spring nights at our Anderson Mesa site, I use a star in Coma at V=7.8 as a transparency test, and usually see it.

Star V B-V Curtis remarks
HD 106384 6.56 0.28 6.52 [FG Vir, sl var]
HD 107830 7.19 0.43 7.20 seen easily
HD 105654 7.23 0.40 7.31 seen quite easily
HD 106515 7.34 0.82 7.42 seen easily
HD 106622 7.47 0.93 8.1 seen without difficulty on last two nights
HD 106579 8.44 0.44 8.3 seen with considerable difficulty perhaps
one-fifth of trials failed

HD 110275 7.98 0.24 8.1 seen one or two failures
HD 110408 8.08 0.53 8.2 seen
HD 110104 8.21 1.12 8.3 seen with difficulty
BD+60 1415 8.98 1.35 8.5 glimpsed at intervals very doubtful

## Stellar apparent magnitude vs exposure times

Trollmannx wrote:

alexisgreat wrote:

I'm not sure I've ever seen this asked before, but what kind of exposure times are necessary to capture stars of a given stellar apparent magnitude?

As an example, let's saxy ISO 3200 f/2.8 1 second shutter speed? 2nd mag? 5th? And how much does light pollution factor into it? In the above example, let's say we are talking about limiting mag 4 NYC vs limiting mag 7 Poconos Mountains?

Visually the formula Log D * 5 + 7 is what manufacturers clinging to (meaning that you can see a 12 mag star with a 10 cm telescope). The real limit vary with observer, how high in the sky the star is, transparency and turbulence in the atmosphere. D is the aperture in cm.

Example: a telescope with 10 cm aperture

Calcuating log (10) * 5 + 8.5 = 1 * 5 + 7 = 12 mag.

With my Atik and a 110/620 mm telescope the formula Log D * 5 + 15 (that is 20 mag) will do for a few images taken under good conditions with several five minute subs, near perfect focus, splendid transmission and a steady atmosphere).

I just dis a quick check from my backyard using Vega (high in the sky), Nikon D3200 50mm f/1.8 at f/2.8 on a Los Mandy GM100 mount. Shown below is the result with a single 30 second exposure (right) next to the corresponding sky chart (on the left). Stars as faint as +11.4 are clearly visible in the image.

The 50 mm stopped down to f/2.8 has an aperture of 1.8 cm. Log(1.8)*5+8.5=9.8. For my setup, the equation predicts 1.6 magnitudes too low.

I then repeated the shot with the iso800 with 50mm f/2.8, but with 9x4 sec and stacked the results together. This produces 32 seconds of total exposure compared to the previous 30 sec, but reached "only" +11.1. So the stacking algorithm loose a little. There are many other factors.

In May 1975 Thomas Fowler published &ldquoA Nomogram for Astrophotographers&rdquo in Sky and Telescope (page 353). It lists the faintest stars recordable with Kodak&rsquos 102a-O emulsion with telescopes of various focal lengths and apertures, based on work by George Abell. The article also states that these equations apply only to film where the reciprocity failure has been eliminated, i.e. the 102a-O emulsion. It claims that sky glow limits the maximum usable exposure time, t_max=1.6*f#**2 and that the faintest star recordable, m_lim=5*log(f[inch])+10, is a function of the focal length only.

CCD cameras have no reciprocity failure, the quantum efficieciency of CCD is about 0.4 and the maximum length of the total exposure is not limited by the limitations of the individual exposures. Fowler's equation predicts +11.5 as the limit for a 50mm (f=2 inch) lens. hmm.

rnclark wrote:

alexisgreat wrote:

This is a very intriguing subject (for me anyway and it seems like for you also.) On Cloudy Nights we had a long discussion about what the darkest locations in the world are, and how dim humans can go in seeing starlight. The 8.5 figure is the one I found in my research also, and just to get some idea of what seeing that might be like, I fired up my Starry Night program and set the limiting magnitude to 8.5 and saw my desktop littered with 100,000 stars (I believe 8.5 is also the limit for a famous star atlas called Uranometria.) I was told on Cloudy Nights however, that with larger FOV the visual limiting magnitude is much brighter, but that 8.5 is only attainable when looking at small FOV's visually. In other words, over, say 100 degrees of sky, even from the darkest sites, that 6.5 is still the limit.

Yes, it does help to restrict the field of view. The night sky is pretty bright, so reducing that light from the whole sky helps the eye adapt to even fainter signals. So looking through a telescope one can usually reach fainter stars than whole sky eye view and projecting from the eye's aperture to telescope aperture.

Then we went on to discuss the locations where, over narrow fields of view, seeing down to magnitude 8.5 is possible for some eagle eyed observers, and the locations mentioned were Mauna Kea, Hawaii, The Andes, SW Africa (Namibia), The Outback of Western Australia, Dome C in Antarctica and some locations in the western US that are high up in the Rockies, or in the Desert Southwest (or perhaps in the High Plains like Nebraska.)

I have observed dozens, perhaps hundreds, of nights on Mauna Kea on the big telescopes, and when I had the opportunity, I would try some visual observations (including naked eye and binoculars). In my experience, the oxygen deprivation in the body at such high altitude sites reduces how faint one can reach. Breathing oxygen can help.
I always did better when going down to the 9,000 foot level.

I would add the Serengeti to very dark sites. But.

We have the wild life to worry about!

Another thing to consider is airglow. There is an equatorial airglow and polar airglow. Airglow is a minimum (of course depends on the night) around 40 to 50 degrees latitude. So western US in remote areas, including Colorado, Utah, Nevada, eastern Oregon, eastern Washington, Idaho, Wyoming and Montana are ideal.

Of course going south is better if you are trying to image southern objects. Ideal would be go to 45 degrees south.

As a matter of fact, I dug up a report from an observer who was exploring the Outback and who was carrying a device with him that measures light pollution (or lack thereof) and he reached the device's limit out there and was able to discern mag 8.5 stars in the Large Magellanic Cloud and something called "The Light Bridge" which is very difficult to see visually. The description got me really excited and perhaps plan a trek out there one day to see what truly transparent skies look like! He mentioned there were no inhabited villages within 100 miles of him in any direction!

I've posted about it before, here:

Another interesting thing that was mentioned was how young children can often see much better than adults can. Some children are even able to see the moons of Jupiter with their unaided eyes and can even detect the motion of the moon in the sky!

Yes. The Moon moves about 12 degrees /day, so 1/2 degree per hour, so when near a star the change in position is apparent very quickly.

## Astronomy - The Night Sky

Astronomy Coordinate Systems

It is helpful (though incorrect) to imagine all the stars to be fixed onto the inside of a vast crystalline dome - the celestial sphere.

Absolute distances between stars are of less importance than their angular separation in the sky. Adopting the Babylonian system of angular measure, the distance from horizon to zenith (directly overhead) is 90°. From North to South along the horizon is 180°.

The constant proportions of the human body give fairly accurate references that you can use to estimate angular separations in the night sky:

The Azimuthal angle is the number of degrees measured clockwise from True North to the star's position projected onto the horizon (ranging from 0 to 360°).

The Altitude of the star is its elevation in degrees from the horizon (ranging from -90° to +90°).

This co-ordinate system can only be used if the precise time is also stated, since stars move about the observer.

The most obvious thing about stars is that they are all different brightness or apparent magnitudes. We must distinguish this from the absolute magnitude of the star (the brightness if it were exactly 32 light year away). It is tempting to believe that the fainter stars are the most distant and the brighter ones are close by. This is untrue, in fact Sir Arthur Eddington stated that most of the bright stars we can see are the "Whales among the fishes". There are many nearby stars that are too faint too pick out.

In 130 B.C. Hipparcos devised a scale of apparent magnitude where the brightest stars were of the 1st magnitude (1M) and the faintest visible with the naked eye were 6th magnitude. It so happens that a 1M star is 100 times as bright as a 5M star. Since this is a logarithmic scale, the difference between one magnitude and the next is nearly 2.5 times

The limit of naked eye visibility is 6.5M.

10 x 50 binoculars can show stars down to 9M

Larger telescopes can detect greater magnitudes.

The scale is extended backwards for objects brighter than 1M. For instance

Larger telescopes can detect greater magnitudes.

Some of the brighter stars appear to form groups in the sky, these we call constellations. Most constellations were named a very long time ago by the Greeks or Arabs. People thought they could see the shapes of animals or their gods and named the constellations after them. In most cases it is very hard to imagine how they saw the shape that the star pattern is supposed to represent but we still use the same names today.

Registered Charity Number 1149774 WYRE FOREST & DISTRICT UNIVERSITY OF THE THIRD AGE

## Contents

Visible to
typical
human eye [ 1 ]
Apparent
magnitude
Brightness
relative
to Vega
Number of stars
brighter than
apparent magnitude [ 2 ]
Yes −1.0 250% 1
0.0 100% 4
1.0 40% 15
2.0 16% 48
3.0 6.3% 171
4.0 2.5% 513
5.0 1.0% 1 602
6.0 0.40% 4 800
6.5 0.25% 9 096 [ 3 ]
No 7.0 0.16% 14 000
8.0 0.063% 42 000
9.0 0.025% 121 000
10.0 0.010% 340 000

The scale now used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the night sky were said to be of first magnitude (m = 1), whereas the faintest were of sixth magnitude (m = 6), the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered twice the brightness of the following grade (a logarithmic scale). This somewhat crude method of indicating the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to originate with Hipparchus. This original system did not measure the magnitude of the Sun.

In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 is known as Pogson's Ratio. [ 4 ] Pogson's scale was originally fixed by assigning Polaris a magnitude of 2. Astronomers later discovered that Polaris is slightly variable, so they first switched to Vega as the standard reference star, and then switched to using tabulated zero points for the measured fluxes. [ 5 ] The magnitude depends on the wavelength band (see below).

The modern system is no longer limited to 6 magnitudes or only to visible light. Very bright objects have negative magnitudes. For example, Sirius, the brightest star of the celestial sphere, has an apparent magnitude of –1.4. The modern scale includes the Moon and the Sun. The full Moon has a mean apparent magnitude of –12.74 [ 6 ] and the Sun has an apparent magnitude of –26.74. [ 7 ] The Hubble Space Telescope has located stars with magnitudes of 30 at visible wavelengths and the Keck telescopes have located similarly faint stars in the infrared.

## Magnitude and Brightness Settings

In astronomy, how bright an object appears to an observer is called the object's apparent (visual) magnitude, and is denoted in SpaceEngine by m . Magnitude values follow an inverse logarithmic scale the lower the value, the brighter the object, and a decrease of 5 magnitudes equals an increase in brightness of 100 times. The dimmest stars visible with the naked eye from very dark skies on Earth have a magnitude around 6-7 m , and the brightest stars have a magnitude less than 1 m the brightest star, Sirius, has a negative magnitude: -1.44 m . The sun as seen from Earth has a magnitude -26.7 m .

The limiting magnitude for any light-receiving device (like an eye or a camera) is the magnitude of the faintest objects than can be registered by the device. The limiting magnitude of the unaided human eye is 6-7 m , while the most capable ground-based telescopes can detect objects up to 28 m . SpaceEngine has an option to increase the limiting magnitude, similar to the naked eye having super-sensitive vision, thus making it possible to see more stars and other celestial objects more clearly. This is the only way to see distant galaxies and nebulae at their best.

Information about the limiting magnitude is displayed in the lower-right corner of the screen «Limit: 7. m 00». If the limiting magnitude for all objects is the same, only one value will be displayed. If galaxies, stars, and planets each have different settings, then the current value for each will be displayed independently.

Magnitude and lighting settings can be adjusted in the Magnitude/brightness settings menu, which can be opened by pressing [F7], or by clicking on the gear icon on the lower-right toolbar. You can change the limiting magnitude for all objects by pressing the '[' and ']' keys, or by using the buttons on the lower-right toolbar. To change the limiting magnitude value for planets, stars, and galaxies/nebulae/star clusters separately, use the menu shown above, or press the '[' and the ']' keys while holding down [Shift] for galaxies/nebulae/clusters, [Ctrl] for stars, or [Ctrl]+[Shift] for planets. Values can be reset to default by pressing the Default button in the magnitude limit section of the menu, or by pressing the button on the lower-right toolbar.

Increasing the limiting magnitude to large values will lead to a reduction in PC performance.

The checkbox for [Auto increase galaxies magnitude] enables the automatic increase of the limiting magnitude of galaxies up to 16 m while the camera is in intergalactic space. This allows for easier visual navigation among galaxies and obseration of the larger scale structure of the universe.

The overall brightness of the scene can be changed by adjusting the exposure setting, the brightness of galaxy and nebula models can be changed using the glow magnitude limit setting, and uniform white light, called ambient light, can be used to illuminate planets and spacecraft this is especially useful for viewing the dark sides of planets.

Exposure can be increased or decreased by using the slider in the menu, the buttons on the lower-right toolbar, or the [<] and [>] keys. The glow magnitude limit can be changed by using the galaxies model lighting slider in the menu, or by using the [Ctrl]+[<] and [Ctrl]+[>] keys. The ambient light level can be changed by using the slider in the menu, or by using the [Shift]+[<] and [Shift]+[>] keys. Exposure can be reset to default by using the button on the lower-right toolbar, and all values can be reset by pressing the Default button in the models lighting section of the menu.

For information about the Overbright and Desaturate dim stars options, see Graphics.

Sadalsuud / Beta Aquarii is a yellow supergiant star of spectral type G0 lb. It is 2,046 times brighter than our Sun, having an apparent magnitude of 2.87, and an absolute magnitude of -3.04.

Sadalsuud is around 100 K cooler than our Sun, having surface average temperatures of around 5,608 K. The star’s corona is also a known X-ray emitter.

The Chandra X-ray Observatory reported X-rays being emitted from this star. It is among the first supergiant G-type stars to have its X-rays detected.

Sadalsuud’s spectrum has served as one of the stable anchor points by which other stars are classified since 1943. This star has a radial velocity of 6.5 km / 4.0 mi per second, while its rotational velocity is 6.3 km / 3.9 mi per second. The surface gravity on this star has been recorded at around 2.05 cgs.

##  Explanation

The scale upon which magnitude is now measured has its origin in the Hellenistic practice of dividing those stars visible to the naked eye into six magnitudes. The brightest stars were said to be of first magnitude (m = 1), while the faintest were of sixth magnitude (m = 6), the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered to be twice the brightness of the following grade (a logarithmic scale). This somewhat crude method of indicating the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This original system did not measure the magnitude of the Sun.

In 1856, Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 is known as Pogson's Ratio [1] . Pogson's scale was originally fixed by assigning Polaris a magnitude of 2. Astronomers later discovered that Polaris is slightly variable, so they first switched to Vega as the standard reference star, and then switched to using tabulated zero points for the measured fluxes [2] . The magnitude depends on the wavelength band (see below).

The modern system is no longer limited to 6 magnitudes or only to visible light. Very bright objects have negative magnitudes. For example, Sirius, the brightest star of the celestial sphere, has an apparent magnitude of 𕒵.47. The modern scale includes the Moon and the Sun the full Moon has an apparent magnitude of 󔼔.6 and the Sun has an apparent magnitude of 󔼢.73. The Hubble Space Telescope has located stars with magnitudes of 30 at visible wavelengths and the Keck telescopes have located similarly faint stars in the infrared.

Apparent magnitudes of known celestial objects
App. Mag. Celestial object
󔼢.73 Sun
󔼔.6 Full Moon
𕒸.7 Maximum brightness of Venus
𕒷.9 Faintest objects observable during the day with naked eye
𕒶.9 Maximum brightness of Mars
𕒶.8 Maximum brightness of Jupiter
𕒵.9 Maximum brightness of Mercury
𕒵.47 Brightest star (except for the sun) at visible wavelengths: Sirius
𕒴.7 Second brightest star: Canopus
0 The zero point by definition: This used to be Vega
(see references for modern zero point)
0.7 Maximum brightness of Saturn
3 Faintest stars visible in an urban neighborhood with naked eye
4.6 Maximum brightness of Ganymede
5.5 Maximum brightness of Uranus
6 Faintest stars observable with naked eye
6.7 Maximum brightness of Ceres
7.7 Maximum brightness of Neptune
9.1 Maximum brightness of 10 Hygiea
9.5 Faintest objects visible with binoculars
10.2 Maximum brightness of Iapetus
12.6 Brightest quasar
13 Maximum brightness of Pluto
27 Faintest objects observable in visible light with 8 m ground-based telescopes
30 Faintest objects observable in visible light with Hubble Space Telescope
38 Faintest objects observable in visible light with planned OWL (2020)

These are only approximate values at visible wavelengths (in reality the values depend on the precise bandpass used) — see airglow for more details of telescope sensitivity.

As the amount of light received actually depends on the thickness of the atmosphere in the line of sight to the object, the apparent magnitudes are normalized to the value it would have outside the atmosphere. The dimmer an object appears, the higher its apparent magnitude. Note that apparent brightness is not equal to actual brightness — an extremely bright object may appear quite dim, if it is far away. The rate at which apparent brightness changes, as the distance from an object increases, is calculated by the inverse-square law (at cosmological distance scales, this is no longer quite true because of the curvature of spacetime). The absolute magnitude, M, of a star or galaxy is the apparent magnitude it would have if it were 10 parsecs (

32 light years) away that of a planet (or other solar system body) is the apparent magnitude it would have if it were 1 astronomical unit away from both the Sun and Earth. The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).

The apparent magnitude in the band x can be defined as (noting that )

where is the observed flux in the band x, and is a constant that depends on the units of the flux and the band. The constant is defined in Aller et al 1982 for the most commonly used system.

The variation in brightness between two luminous objects can be calculated another way by subtracting the magnitude number of the brighter object from the magnitude number of the fainter object, then using the difference as an exponent for the base number 2.512 that is to say ( mfmb = x and 2.512 x = variation in brightness).

###  Example 1

What is the difference in brightness between the Sun and the full moon?

2.512 x = variation in brightness

The apparent magnitude of the Sun is -26.73, and the apparent magnitude of the full moon is -12.6. The full moon is the fainter of the two objects, while the Sun is the brighter.

Difference in brightness

Variation in Brightness

variation in brightness = 449,032.16

In terms of apparent magnitude, the Sun is more than 449,032 times brighter than the full moon. This is a good reason to avoid looking directly at the Sun, even during the non-total phases of a solar eclipse. (Viewing the completely eclipsed Sun is safe, but it only stays completely eclipsed for a very short period of time.)

###  Example 2

What is the difference in brightness between Sirius and Polaris?

variation in brightness

The apparent magnitude of Sirius is -1.44, and the apparent magnitude of Polaris is 1.97. Polaris is the fainter of the two stars, while Sirius is the brighter.

Difference in brightness

Variation in brightness

In terms of apparent magnitude, Sirius is 23.124 times brighter than Polaris the North Star.

The second thing to notice is that the scale is logarithmic: the relative brightness of two objects is determined by the difference of their magnitudes. For example, a difference of 3.2 means that one object is about 19 times as bright as the other, because Pogson's ratio raised to the power 3.2 is 19.054607. A common misconception is that the logarithmic nature of the scale is due to the fact that the human eye itself has a logarithmic response. In Pogson's time this was thought to be true (see Weber-Fechner law), but it is now believed that the response is a power law (see Stevens' power law) [3] .

Magnitude is complicated by the fact that light is not monochromatic. The sensitivity of a light detector varies according to the wavelength of the light, and the way in which it varies depends on the type of light detector. For this reason, it is necessary to specify how the magnitude is measured in order for the value to be meaningful. For this purpose the UBV system is widely used, in which the magnitude is measured in three different wavelength bands: U (centred at about 350 nm, in the near ultraviolet), B (about 435 nm, in the blue region) and V (about 555 nm, in the middle of the human visual range in daylight). The V band was chosen for spectral purposes and gives magnitudes closely corresponding to those seen by the light-adapted human eye, and when an apparent magnitude is given without any further qualification, it is usually the V magnitude that is meant, more or less the same as visual magnitude.

Since cooler stars, such as red giants and red dwarfs, emit little energy in the blue and UV regions of the spectrum their power is often under-represented by the UBV scale. Indeed, some L and T class stars have an estimated magnitude of well over 100, since they emit extremely little visible light, but are strongest in infrared.

Measures of magnitude need cautious treatment and it is extremely important to measure like with like. On early 20th century and older orthochromatic (blue-sensitive) photographic film, the relative brightnesses of the blue supergiant Rigel and the red supergiant Betelgeuse irregular variable star (at maximum) are reversed compared to what our eyes see since this archaic film is more sensitive to blue light than it is to red light. Magnitudes obtained from this method are known as photographic magnitudes, and are now considered obsolete.

For objects within our Galaxy with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. This relationship does not apply for objects at very great distances (far beyond our galaxy), since a correction for General Relativity must then be taken into account due to the non-Euclidean nature of space.