Lunar Brightness at Opposition

When the moon is directly opposite the sun from the earth, it is in eclipse. The angular size of the sun is 0.53° and the angular size of the Earth from the moon is 1.9°. If the moon is within 0.95-0.53 = ±0.42° it is in the dark umbral shadow, and if it is between that and 0.95+0.53 = ±1.48° it is in partial penumbral shadow. If we were in a spaceship directly between the sun and the moon, without the earth in the way, the moon would appear very bright. This is due to heiligenshein (also known as "opposition effect"), shown below in this Apollo 11 photograph (just past Buzz Aldrin's head), alongside data for the angular geometry of the Moon, Earth, and Sun:

According to Whitaker, the heilingenshein is 50% greater at 1 degree than at 5%. The reason for this specular reflection is that meteoroid impacts throw up melted debris, which forms into tiny glass beads that cool and harden before they fall back down. These beads act like retroreflectors, much like the glass spheres in Scotchlite. At two degrees off exact opposition (syzygy ) which occurs near lunar eclipse times, the moon is 35% brighter than we would expect from direct reflection.

This occurs when either the moon's ascending or descending node points away from the sun, every 7.8 lunar months or so (slightly longer than half a year because of the 18.6 year nodal precession). The perigee also precesses, making a circuit every 8.9 years, bringing the moon closer by 5% and increasing total lunar reflection light by 11% due to a larger angular size. When these add together, every few years, the full moon is at its brightest, perhaps 50% brighter than average.

Note that the earth's orbit is very nearly circular, with an eccentricity of less than 1.5% (± 3% illumination change), and the 11 year sunspot cycle causes an illumination change of less than 0.1%.

Atmospheric attenuation plays a role, of course; clouds block moonlight, and even clear air scatters it. The air column is thinner in the mountains, and thinner near the equator since the moonlight is coming closer to straight down.

Conclusion: The largest illumination/variation effect is caused by nodal syzygy (35%), then perigee precession (11%) with sun distance and brightness effects coming in as a distant third.

NASA SP-201 : Analysis of Apollo 8 photography and visual observations. January 1, 1969. Page 38: Photometry, An Investigation of Lunar Heiligenshein by E. A. Whitaker

. Krisciunas & Schaefer, "A Model of the Brightness of Moonlight", Publications of the Astronautical Society of the Pacific, 103: 1033-1039, September 1991.

http://home.earthlink.net/~kitathome/LunarLight/moonlight_gallery/technique/moonbright.htm

P.S. Why is this relevant to Server Sky? Because an out-of-control server sky constellation could cause night pollution in the night sky. While normal operation should be constrained to produce near-zero light pollution, the debris from a derelict constellation should never be ecologically damaging even in the extreme worst case. Nature evolved to the full moon cycle; we must not approach even a noticable fraction of that amount of illumination.