REM%MIT-MC@sri-unix.UUCP (11/15/83)
From: Robert Elton Maas <REM @ MIT-MC> Whereas a normal "point" satellite sweeps out a ringlet, thus can collide only with something whose orbit intersects that ringlet and happens to be in correct phase once, a tower/elevator sweeps out a plane, and thus collides with anything that crosses that plane when it happens to be in the same phase as the tower/elevator. If you think about it a little, you'll see that every other orbit is either in that plane or intersects it, thus every object in orbit whatsoever is a candidate for colliding with the tower/elevator. If it's in the plane, and has exactly the same orbital period, there's no problem, thus geosynchronous satellites and geosynchronous tower/elevator can co-exist. If it's in the plane, and has any different orbit, there's a certainty they'll collide within time 1/(1/T-1/t) where T and t are the orbital periods (times of revolution) of the two objects (tower/elevator and satellite). If it's outside the plane, but with exactly the same period as the tower/elevator, it'll cross the plane twice each orbit at the same point, so if it misses the first two times it'll continue to miss. But if it's outside th plane and with a different period, it'll cross at a new point each time, eventually crossing where the tower/elevator happens to be at that moment and colliding with it. Active space missions can calculate the location of the tower/elevator throughout the mission and carefully avoid getting too close to it, but passive (non-motive) satellites and debris will eventually collide. The only place it'll be safe for a passive object, besides on Earth or in geosynchronous orbit or attached to the tower/elevator, will be far enough out that it's beyond the highest point of the tower/elevator, i.e. far beyond geosynchronous orbit, whereas virtually all existing debris and satellites are in low orbit. Thus it appears we need a space tug to clear out the debris and be on hand for occasionally shoving random passive satellites out of harm's way, before the tower/elevator will be practical.