What factors determine the brightness of a satellite flare?

From: Robert Clark (bobbygc2001@yahoo.com)
Date: Sun Jun 28 2009 - 09:17:26 UTC

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     I copied below a post to sci.astro about the possibility of sending naked-eye-visible light communications from a Google Lunar X Prize entrant. It's based on the brightness seen with some satellite flares. 
     What I need to know is what are the factors that contribute to the brightest satellite flares since then we could incorporate these facts into the design of the reflective surfaces at the Moon to produce the brightest images.
       Bob Clark
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