Is is possible to see a strong led mounted on a satellite at the
height of 800 Km from the ground? The on-ground spectator may use
binocular at the most. You can assume night and clear skies
conditions.

Thanks
Raz

This depends upon the luminosity of the LED, and the sensitivity of
the receiver. A candle two miles distant may be invisible to my
unaided eye, but my eye aided by a telescope of 10" aperture may see
it. What is the emission strength of the device you're thinking of?
What frequency of light? What is the maximum aperture you'll accept on
a binocular? (Some binos can get pretty big.)

You also need to consider the experience of the observer, how well
they're dark adapted and simply how good their eyesight is.  Are the
binoculars going to be mounted or hand held?  Is the satellite itself
visible?  On balance, even though many satellites are easily visible,
I think it's highly unlikely you could see a LED.

Ian G.

Doing some maths:

Assume the light emmitted from the LED subtendeds 30 degree (fairly
standard for an LED).  At 800km, the base of the light cone would be
around 414km in diameter with an area of around 1 million km^2. 
Assume the LED draws 30mA at 3V, this gives it a power of 0.9W.  It
therefore emits 0.9 Joules per second of energy (assuming 100%
efficiency).  The energy of a photon is given by E=hf where h is
plancks constant and f is the frequency of the light.  Assume a red
LED with a wavelength of 660nm, this gives an energy per photon of
3.01E-19 Joules.  We have 0.9 J of energy to play with, so this gives
3E18 photons per second.  However, assuming our pupils have an area of
1cm^2, this means that the number of photons entering our eyes would
be 300 photons per second.

Recent studies have shown that the human eye can respond to single
photons, so theoretically this would be possible.  However, this would
require an idealised situation and it is extremely unlikely that the
naked eye could percieve the LED in real life.

In reality, many photons will be absorbed by water vapour in the
atmosphere.  Also the night sky is not dark.  Even with no moon, the
background light coming from the stars and galaxy would drown out the
almost insignificant number of photons coming from the LED.  When we
see satellites in the night sky, we are really seeing the light from
the sun reflecting off them (just as we see the moon).  This is far,
far brighter than the light given off by an LED.

With a pair of binoculars with 5cm diameter aperture, the photon count
per second increases to 12000.  This is still difficult for a human to
detect, but may just be possible with some training and a truly dark
environment.