REM%IMSSS@SU-AI.ARPA (Robert Elton Maas) (11/16/86)
CAW> Date: Thu, 30 Oct 86 11:24:54 EST CAW> From: weltyc%cieunix@rpics.arpa (Christopher A. Welty) CAW> Subject: Mirrors is [SIC] space >...The drawback to the scheme is that the finite angular size of the >sun makes the reflected footprint on the Earth rather large. CAW> Couldn't you just make the mirrors slightly concave? Nope, you misunderstand how mirrors work. The angle of incidence equals the (negative of the) angle of reflection. So, considering the incoming rays converging on a infinitesimal piece of mirror, they come in over a range of angles determined by the Sun's angular diameter, which is half a degree from anywhere near Earth, and go out over an equal range of angles, i.e. half a degree again. With a flat mirror, the outgoing beams produced by reflection from all the parts of the mirror are mis-registered by the separation between mirror elements, so in worse case they mis-register by the diameter of the mirror. Over long distances, the mis-registering is a constant but the basic diameter of the images is linear with the distance, and from orbit the mis-registering is only a tiny fraction of the overall "footprint" (image). If you make the mirror concave just enough that all the images exactly match when they hit Earth, you have eliminated that little mis-registration (diameter of mirror, say a hundred feet), but have done nothing about the basic angular diameter of Sun causing half-degree fanout of the beam, which is SIN(half degree)*distance = 0.0087*distance. For satellite (mirror) 100 miles up that's 0.87 miles in diameter, while for satellite at geosynchronous position that's 20,000 miles up which gives a footprint diameter of 170 miles, and from L-4 or L-5 or Moon that's 200,000 miles which gives footprnt 1,700 miles across. (Hope you don't mind single significant digit, actually moon is 205,000 miles away or somesuch. But that doesn't affect my point.) With a mirror even a few miles across, making it concave to eliminate that few miles of footprint width while retaining the half-degree fanout doesn't help any significat amount at geosynchronous or beyond. To reduce fanout below half a degree, thus decrease footprint significantly, you need to actually absorb the sunlight, and re-radiate over a more narrow beam by microwave or laser etc. A simple mirror (of reasonable size; flat or concave), from anything other than Low Earth Orbit, can't possibly be used as a weapon against Earth targets except perhaps to slightly warm the tropical ocean to enhance a hurricane or some such subtle effect. (In case you next argue that you can put a mask between the Sun and the mirror to cut out all but a tiny portion of the Sun and thus reduce the angular diameter: Yes, but you merely decrease the total energy reflected, you don't change the density of energy at all. You still end up with a little bit of energy spread over a large area, or a teensy bit of energy over a small area. Only by an extremely large mirror could you reflect enough energy to burn something on Earth. It's cheaper to re-transmit using microwave or laser.)