>So the rest is just the manipulation of vectors which is fairly ordinary >mathematics (OK, it's a little advanced). Two questions remain: Have you an explanation that a mathematically sophisticated person might understand? If so, could you make it available in .pdf or some other form that doesn't look like Fortran? I think you've been terribly clever to figure this out, and I would like to be able to appreciate the cleverness. My biggest question, however, is why are these Iridium flares so very much brighter than flares we all see occasionally on satellites with large solar panels? Are these antennae much larger than most solar panels? Are they much more highly reflective than most solar panels? Leigh