Limiting visual magnitude, extinction angle and shadow casting

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Binocular naked eye observations with no clouds/city light model/etc. obstructing the view can be determined using the below form. Schaefer predicts in the below form a 90% probability of seeing the contrast difference between the sky and the celestial object by an experienced observer with natural fixation and using long observing times.

Angular positions []
Topocentric altitude
Lower left corner
of sky window
Some defaults for moon and sun locations:
2001-05-12, 01:42 BST
2001-07-05, 22:18 BST
2003-07-14, 23:12 BST
Venus on 2001-12-19, 08:19 BST
Dark sky at winter solstice
Dark sky at summer solstice

Relative humidity [%]
Air temperature [C]
Visibility Range (Vr)

[km] or NA
(if not NA; Variation of ka will be zero)
Variation of kW and/or ka [sk], will have effect on ka if Vr is NA
(if 0.0001; Calculate cycles through to 0.9999 and -0.9999)
Latitude [] (+:N, -:S)
Height [m]
Snellen ratio 20/20=1: 20/10=2; Average SN is ~1.4
Person's age [year]
Moon's distance [km]
Bcity [nL], Garstang [1986]
Date -- (yyyy-mm-dd)
all values on 22:18 BST, July 5th, 2001 at Newgrange, Ireland with the moon at the same position as the winter solstice sun

Limiting visual magnitude of point source

the naked eye limiting visual magnitude of point source at lower left corner of sky window: 
Extinction angle: [] (equal to lower left corner of sky window) and sk[sk]

Maximum sky brightness to have visibility of the Moon (uniform extended source)

Illumination: [%]
Moon's size observed: []
Start sky brightness for iterations at: [nL]

the maximum background sky brightness at which the Moon (at [], be aware: angle determined by Moon's position and time added) is still visible: [nL] and sk[sk]
Visibility range: [km]
Moon's brightness: [nL]
Contrast threshold: 
Actual contrast between Moon light and background: 
Moon is visible by naked eye: 

Shadow casting of Moon in an enclosure (uniform extended source)

The size of the sky window in this enclosure is:
Angular size []
Size of sky window

The Moon's shadow will be cast on a screen with the following parameters:
Screen angle [] (measured in same plane as the altitude of Lower left corner)
Screen albedo [-]
Object size []
Add to time [min]

if Moon's shadow is visible by naked eye: and sk[sk]

Average background sky brightness outside Moon disk within the defined sky window:  [nL] (number of samples: )
Screen brightness due to background light visible through sky window: [nL]
Contrast threshold: 

Phase of Moon: [] (0=full, 180=new), illumination: [%] (be aware: the illumination is the calculated value from Sun and Moon position) at []
Screen brightness due to Moon shining through sky window: [nL]
Actual contrast between Moon light and background on screen: 


I would like to thank the following people for their help and constructive feedback: Larry Bogan, Dennis Duke, Tim Lamb, Brad Schaefer, Thomas Schmidt, Louis Strous, Ben Sugerman and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.

ktot[km-1], Bnight, Bmoon, Btwi, Bday[nL]

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Last major content related changes: April 30, 2003