Started in 1998 and continuously occupied since November 2000, the ISS is currently the largest space station ever constructed, at 120yds by 80yds - larger than a soccer pitch - and weighing around 415 tons. For further facts about the ISS, click here.
The orbit of the ISS has a height of about 250 miles and an inclination of 51.6 degrees to the equator. As a consequence of this inclination, locations with a latitude greater than this (i.e. most of the UK) can never see it pass directly overhead as it will always cross the sky somewhat to the south. As it orbits in the same direction as the Earth rotates, it tends to rise in the west, attain maximum height in the south and then set in the east.
The ISS's large flat solar-cell arrays are excellent reflectors of sunlight, with the result that it can appear as a very bright object in the sky. The brightness depends on the angle at which it is "flying" relative to the observer and to the sun (as this determines how reflective it is) and on the distance from the observer. The angles vary quite a lot because its attitude is actively controlled by on-board systems to, amongst other things, maximise power generation by ensuring the solar cells are pointing towards the sun. Also, because each orbit passes over an observer on a slightly different track, even if the ISS itself didn't move it would be presented to the observer (and the sun) at a different angle each time. The straight-line distance at the point of closest approach varies from about 250 to over 800 miles but when just rising or setting it can be as much as 1350 miles away. All this means that its maximum brightness on a pass over my location (Eastern England) ranges from about magnitude -0.2 to -3.8: a variation by a factor of over twenty-seven times! Passes which are easily visible (i.e. quite high in the sky) are very much towards the top end of the range, however. The other thing which is affected by distance is the speed at which the ISS appears to move. When it is low down (and thus far away) it moves really slowly but as it gets nearer and nearer its speed across the sky increases considerably so that at maximum elevation it can be quite difficult to track with a camera or through binoculars.
The ISS does of course need to be illuminated by the sun to be visible at all though, and this clearly can't be during daylight hours as the sun will be too bright to permit an observation, so in practice what is required is for the sun to have set (or not yet risen) as seen by the observer but still be visible from the ISS. This constraint means that there will tend be two distinct "windows of opportunity" for observation, one just after sunset and one before sunrise, though these can merge together in summer as the sun is then never far below the horizon. The Station will not necessarily be visible for the entire length of its track across the sky though, because it may be in sunlight for only a portion of its pass and so may move into the Earth's shadow before it goes out of view below the horizon. As with the same phenomenon when it involves the Earth's natural satellite the Moon, this is called "going into eclipse".
There's more to be said about when the ISS is visible to an observer on the Earth, so I've placed that discussion, together with more information on Iridium flares, in an article within the Astronomical Theory section of this website. There's a link to this section at the bottom of the previous page.
