Does anyone know of a good method for calculating the visibility of the international space station from an arbitrary point on earth's surface? I've always been curious how NASA makes all those predictions about fly-overs and such. Any links to web sites explaining the procedure in as much detail as possible would be greatly appreciated. And no, this isn't homework. It's just a project I'm working on by myself to strengthen my skills and satisfy my curiosity. I have thought about this some already. The orbital path of the ISS does not appear to be exactly circular, but instead slightly elliptical (since its elevation supposedly varies between 278 km and 460 km). The eccentricity is so slight though, I think I'm safe in supposing that the orbit is circular. Assuming an altitude of 369 km, I also think I know how to calculate the speed of the ISS, and given the speed of the ISS with a presumed ideal circular orbit, I am pretty sure I can figure out its altitude. Of course, I am neglecting atmospheric drag here, and other such details. My question is this: is the ISS in a constant orbit? By that, I mean is its orbit wobbling all over the place or does it trace a fairly immobile ring around the earth? If the orbit is constant, I can envision calculating fly-overs for certain points on the earth’s surface by comparing the ISS orbital period to the earth’s rotation. It’s basically a really complex horse-race problem: if horse A passes point 1 every t seconds, and horse B passes point 1 every r seconds, find the period of their instantaneous synchronization at point 1. Thus, I plan to proceed by calculating the great circle of the ISS orbit, rotating the earth until Austin (where I live) is immediately below it, then drawing a vertical line upward from the surface. The point where this line intersects the ISS orbit is what I’m interested in. I can obtain the frequency which Austin passes immediately below this point (using the earth’s rotation), compare it to the frequency which the ISS passes through this point, and calculate an equation to predict alignments. Although the concept seems easy to me, I can see that in practice this will probably take awhile. But given the angle of the ISS orbit to the north pole, it shouldn’t be too terribly bad. Unfortunately, I do not have this angle. The part I see major difficulties with involves the calculation of visibility of the ISS from the earth’s surface. In my head, I can imagine drawing a line up to the ISS from a point on the earth’s surface. I see the line moving to follow the space station, almost like a radar dial, until the line bumps into the curved surface of the earth and the satellite is no longer visible. However, I do not have the slightest idea how to model this mathematically. I would assume the problem is similar to predicting when and where ships come over the horizon, but again I have no knowledge of how to approach that issue either.