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Can an artificial satellite reflect "moonlight" and be seen by an observer on earth?
Just curious, if the angles are ever right, and the satellites have enough reflectivity, can they be seen in our night sky by reflecting moonlight (which is already reflected sunlight), or must the satellite be illuminated only directly by the sun to be visible to an observer on earth.
I'll accept naked eye answers as well as binocular/telescope answers, if you do indeed know.
Let me see if I can get technical about it. My first guess is that the Moon does not provide enough reflected light to be visible by reflecting on an artificial satellite.
First point of order: Moon and Sun are about the same apparent size, and light from them reaches the satellite in roughly parallel rays, meaning the reflection takes place roughly the same way and only the brightness of either Sun or Moon are important comparatively. Agreed?
2) By now, you already know what apparent magnitude is: http://en.wikipedia.org/wiki/Apparent_magnitude . My argument would then follow into the statement that magnitude is a logarithmic scale, meaning one point less in magnitude means 2.512 times more brightness. Wiki already did the math for me, and in the table lists Sun's apparent magnitude - 26.73; Moon's app magn - 12.6; Sun's brighter than Moon 449 000 times.
QED) Satellite would need to be 449 000 times larger to reflect as much moonlight, as with its regular size reflects sunlight.
Let's see if an expert from this section finds any grounds to fine tune this rough guess of mine. Actually, taking a bold dash into the unknown, I'd say that if the satellite looks like a magnitude -1 star under sunlight, it should look like a magnitude +12 under moonlight. Remember, with the naked eye we only see up to +6, and +9.5 with binoculars.
Is this right? Any mathematician in the house?...
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For a complete review of the answer I would like to state how I estimated the magnitudes for a reflecting satellite.
A detailed calculation would include angles, albedo, shape/reflecting area, and brightness of the light source. Assuming optimal viewing conditions, and all things being equal, most practical factors appear as multiplying factors, thus, as I said under optimal conditions reflection of sunshine would be 449 000 times brighter than reflection of moonshine. Some of the answerers discussed in detail the probability of observing the reflecting satellite in a practical way. I am interesting in establishing an upper bound for brightness in the best case scenario.
Now, if in this best case 449 000 times less light is reflected from the Moon, the magnitude difference between Sun reflection and Moon reflection would be roughly the difference in apparent magnitude of the sources, or 13, maybe 14 points. Notice that factors like albedo of reflecting surface area would multiply a detailed calculation and affect the reflected light intensity in the same way. Additionally, the brightness of the source also multiplies which in a logarithmic scale corresponds to a difference equal to the one between Sun and Moon.
Finally, I had my share of watching cruising artificial satellites back in the day, and I agree that a few hours after sunset, what we see are seemingly average stars except that they move in a straight line. These correspond to reasonably high orbits, because in the satellite you'd still be in line of sight with the Sun. Their brightness, yes, could correspond to a star with a +2 or +3, or even higher, apparent magnitude. However, I once had the opportunity of watching a satellite in a North to South run, at dusk, with the Sun still partially in the horizon. It was very bright, perhaps brighter than Sirius (this was way before the ISS). Conservatively lets assign it a brightness in terms of apparent magnitude of -1. Then, all things being equal, the same satellite making a run when a full Moon has just risen in the horizon, would look like a star of apparent magnitude of say +12, as my argument goes.
The +12 magnitude I suggested is then a best case scenario and practical observation would certainly put its brightness deeper down in the magnitude scale. No hope of ever watching one with binoculars.
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