## Limiting Magnitude Calculations

Use this form to calculate the faintest star you can see for a given place, time and observer.
Fill in the "Observer's Info" and click Calculate. To reset to the current time, click Current Time.

### Observer's Info

Longitude (dd mm) West East
Latitude (dd mm) North South
Elevation (meters) above sea-level
Time (hh:mm:ss)
 Daylight Savings ON OFF
 Year Month Day
 Temperature (F) Humidity (%)
 SnellenRatio Experience(0-10) Age(years) Where is the observer looking in the sky? Altitude Azimuth

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Hacked together by Ben Sugerman, Jan 2000.
Click for the Bibliography

### Estimated Physical Conditions

 Sun Moon Alt Az Elong-ation % Illum-inated V Magobserved
Limiting visual magnitude +/-

 Extinction coefficient [V mag per airmass] Extinction [V magnitudes]
 Total SkyBrightnessat pointing Lunar SkyBrightnessat pointing NanoLamberts V Mag per arcsec2

 Julian Date MLST

Altitude: Altitude is the number of degrees measured from the horizon toward the zenith (the point straight overhead). An object on the horizon has Altitude=0, and the zenith Altitude=90.

Azimuth: Azimuth is the number of degrees measured clockwise along the horizon from north. North=0, East=90, South=180 and West=270. To find the azimuth, draw an imaginary arc from the zenith through the point you are looking. You measure azimuth from due north to the point where this arc intersects the horizon.

Elongation: Elongation is simply the number of degrees on the sky between two points, in this case, from the sun (or moon) to the point where you are looking.

Snellen Ratio: This is the numerical value of dividing the numbers in your vision quality given by your optometrist. Normal vision is "20/20" so the snellen ratio = 1. Poor vision might be "20/100" = 0.2 while very good vision is "20/10" = 2. This ratio accounts for the fact that people with better seeing...see better!

Observer's Experience: This is a self-rating you must give yourself on a scale of 0-10. It doesn't test how well you see (that is the snellen ratio) but how sensitive your eyes are to faint light or how well you see in the dark. This is a very subjective question but here are my interpretive guidelines, in terms of observing experience, some sky objects, or daily experience.

• 0 You have never looked at the sky at night. You bump into everything in your bedroom at night (in the dark, assuming your room is lit by normal city lights or moonlight).
• 3 You have some experience with looking at faint objects. When your eyes are adapted to the dark you can see details in your room. You can find the visual double star (Alcor and Mizar, second in from the end of the handle) in the big dipper. If in doubt, use this one.
• 5 You are an average observer in an astronomy club. You can find messier objects in a telescope viewfinder. You can see most stars in constellations from big cities.
• 6 Set experience=6 if you want to evaluate the limiting magnitude without an "observer's experience" correction.
• 7 You are very experienced at observing. You can see many of the Messier objects with your naked eye (in a very dark area of course) and can distinuish that they are extended sources rather than point-like stars.
• 10 You are exceedingly experienced at observing, you have a very high sensitivity to faint objects, and you know it. You can read the newspaper by starlight only. You can count 14 stars in the Pleiades. You can see Jupiter's moons without a telescope.

Age: The observer's pupil will react differently from the standard adopted in this model depending on the observer's age. This correction term is added for completeness. Set age=25 to evaluate the limiting magnitude without an age correction.

Observed Moon/Sun Magnitude is the estimated visual magnitude of the moon given its phase and position on the sky. If the moon is below the horizon, then it is "down."

Limiting Visual Magnitude is the estimate of the faintest star you (the observer) can see for the conditions you input. This does not include city lights, cloud cover or weather conditions, or myriad other factors such as high dust levels (due to a recent volcanic eruption), the jet stream, etc. The quoted formal error assumes a 20% uncertainty in the sky brightness, unit error in observer experience and reasonable values for internal parameters. The "central value" assumes no error.

Total Sky Brightness includes the night sky (airglow, zodiacal light, etc.), brightness from the moon, the sun, sunset gradients and glare if the moon is less than 5 degree elongation. Brightnesses have roughly 20% uncertainty. These factors are calculated for average weather and air quality, and do not include human sources of light pollution (i.e. city lights). Lunar Sky Brightness is an estimate of the contribution of the moon only.

## Model Testing Results

As I make more tests of this model, I will post them here.

• Jan 15, 2000 at MDM Observatory in Arizona. Long=-111 37 E, Lat=31 57, Elev=1925m, Temp=58 F, Humid=8%, Snellen=1.0, Exp=6, Age=25
• 6:00 observed Bootes and saw star 46 (Alt=65 Az=96) at V=5.56
Model range 6.07 +/- 0.4 [full dark time]
• 17:30 observed Capella (Alt=37 Az=53) at V=0.08
Model range 0.07 +/- 0.34 [sunset + quarter moon]
• 19:20 observed Pleiades and saw star 19 (Alt=72 Az=111) at V=4.29
Model range 4.78 +/- 0.42 [dark sky + quarter moon]
• 19:40 observed Orion and saw star 52 (Alt=40, Az=110) at V=5.28
Model range 4.97 +/- 0.42 [dark sky + quarter moon]

## Bibliography

• Garstang R., 1986, P.A.S.P., Vol. 98, pp 364-375
• Garstang R., 1989, P.A.S.P., Vol. 101, pp 306-329
• Krisciunas K., Schaefer B., 1991, P.A.S.P., Vol. 102, pp 1022-1039
• Schaefer B., 1998, Sky & Telescope, Vol. 95, No. 5, p 57
• Schaefer B., 1990, P.A.S.P., Vol. 102, pp 212-229
• Schaefer B., 1991, P.A.S.P., Vol. 102, pp 645-660
• Shaefer B., 1993, Vistas in Astronomy, Vol. 36, pp 311-361
• Schaefer B., Bulder H., Bourgeois J., 1992, Icarus, Vol. 100, pp 60-72
• Brad Schaefer (schaefer@grb2.physics.yale.edu)
• John Thorstensen's Skycalc code (John.Thorstensen@Dartmouth.edu)
• Larry Bogan's javascript recoding of Schaefer's vislimit code (larry@go.ednet.ns.ca)