Satellites orbiting the Earth have no light of their own, so are visible to an observer only if they reflect sunlight. This will usually just be a diffuse reflection which, as most satellites aren't that large, will mean they are not particularly bright. However, if there are any extensive flat surfaces on the satellite and the Sun reflects from these surfaces directly into the viewer's eyes it will be spectacularly bright - this is known as a "flare". A flare is not just a "flash" though - they build from nothing to maximum brightness and then fall away to nothing again as the alignment with the Sun becomes established and then breaks down. This gives photographs of flares much more interest than those of satellite trails, which are usually of constant brightness along their length.
The most famous flares were produced by the first generation of the Iridium constellation of communications satellites. They were particularly good at flares, having three large flat antennae which, as part of their operational procedures, were kept facing in a constant direction relative to their orbit track (see picture on right). This means that not only were the flares bright but they were also highly predictable, the one factor that is usually variable (the orientation of the satellite) being exactly known. They were also frequent, as there were sixty-six active satellites in the constellation (plus some "in-orbit spares"). The area on the Earth that can see any given flare was small though (as the Sun-satellite-observer geometry must be very precise) and they lasted no more than 30secs (for the same reason, given that the satellite is, of course, moving), so to find out where and when they would occur it was imperative to use a prediction program such as heavens-above.com.
The prediction program also told you the exact direction and altitude you had to look to see the flare as this varied considerably with time of day & season. The flare magnitudes were also highly variable, mainly depending on how far the observer is away from the line of perfect alignment - at their brightest, flares were 40 times brighter than Venus and could be seen in broad daylight! Even a "dim" one was brighter than almost every star in the sky so they were well worth looking out for.
Unfortunately, the first generation satellites have now been replaced with more capable versions which do not have the same type of antennae and so do not produce flares - the descriptions in this section thus refer only to the earlier generation. Flares are sometimes produced by other satellites though so if you keep your eyes to the sky you might just catch one of these dramatic events.
Iridium orbits were inclined at 86.4deg so the satellites could pass overhead at almost every point on the Earth's surface. This means that flares could potentially be seen in any compass direction. Interestingly though, the orbital inclination of 86.4deg results in a ground track which is almost exactly north-south for a good proportion of the orbit. This is because the west-to-east component of the velocity of the satellites is very close to the rotational velocity of the Earth (just over 1000mph at the equator) and so the two tend to cancel out. The ground track slants much more as the satellites get towards the poles though (as the rotational velocity decreases with increasing latitude) which restores the overall movement of 25deg to the west per orbit. For a satellite passing directly overhead the track will thus be almost exactly from north to south (or vice versa) but, because the geometry of a flare requires there to be an angle between the satellite and the observer, an overhead flare is not possible. Flares produced by an overhead pass will be seen almost directly north or south and ascending or descending vertically, as shown by the image of Iridium 55 on the previous page, descending at an azimuth of just 2deg N. Non-overhead orbit tracks will still begin and end at the north and south compass points but will arc to the west or east of the observer. The trail of a flare from a satellite on such an orbit will thus be "tilted over" to the west or east, by an amount determined by the direction at which it is seen. Flares seen to the south (or north) will still be nearly vertical, as the tilt has least effect there, but a flare seen directly to the west or east will be horizontal because the arc of the track is changing from "rising" to "falling" at that point. Flares at intermediate compass points will be slanted by different amounts depending on both the compass direction and the altitude they are at (as, if the satellite is to reach a higher altitude, its track must clearly climb more steeply which means it will then fall more steeply as well). Thus the double-flare on the previous page, at 160deg azimuth (i.e. SSE in compass terms), is approaching the vertical but the one of Iridium 53, at 84deg (E), is almost horizontal. [ Note that this situation is exactly the opposite from that for the ISS, which rises in the west and sets in the east and so will be going horizontally when in the south ].
While Iridium flares could be seen in any direction, there was some regularity about their appearance because the motion of the satellites themselves was regular. The 66 active satellites were organised in six planes of eleven satellites each, the planes being arranged at 31.6deg to each other around the equator (leaving just a 22deg separation between planes 1 and 6, whose satellites will be moving in opposite directions where the planes meet). Each satellite took just over 100mins to orbit the Earth once and so for each plane the eleven satellites were separated by a little over 9mins. Therefore, in principle at least, if one satellite in a plane produced a flare another one may do so about 9mins later, when it got to the same place as the first one. This requires the Sun-satellite-observer geometry to still be correct however, so in practice it only happened in a minority of cases and even when it did the interval varied from the inter-satellite gap time as the geometry takes some seconds to get aligned again. Also, because the Earth has turned a little in the 9mins, the observer's view of the two flares will be different and so they will not be seen in the same place in the sky. Satellites used as in-orbit spares are not restricted to a 9min gap however and so could produce flares separated by much shorter periods, as shown on the "pictures" page. This is the more so as spares were often in a lower orbit and thus went round the Earth faster than operational satellites, meaning they could catch up and overtake them and so increase the chance of two flares happening very close together. It also meant it was possible to have two flares in exactly the same position relative to the stars or in the same direction relative to the Earth. [ Click here for some calculations ].
A second sort of periodicity happened because of a remarkable coincidence. After 24hrs minus 6mins not only does the ground-track of a given plane of satellites repeat but also the satellite eight places forward in the plane from the one that was in position to produce a flare the first time round has moved into exactly the right place to produce one itself. [ Click here for the maths involved in this conclusion ]. This means that once a plane of satellites was in position to produce flares it would tend to do so at 24hrs minus 6mins intervals for a long time (as the coincidence is quite exact) and these flares were in very nearly the same position in the sky. Note however that the 9minute periodicity mentioned above could sometimes interpose, if the alignment isn't quite right, giving flares on successive nights 24hrs plus 3mins apart: the minus 6mins period will re-start after this.
While the observed position of "24hrs minus 6min" flares shifted by a few degrees per day, this was in "compass" terms i.e. relative to the Earth's surface (and thus trees, buildings etc.). Relative to the stars, the flares moved very much less because the stars also shift their position from day to day. The calculation is similar to that which showed that the ground track would repeat [ Click here if you didn't read it the first time ]. The smaller offset can be seen in the composite image of flares from Iridiums 64, 67 & 62 on the "pictures" page: when aligned on the stars the tracks are separated by only about 1/5deg despite having "compass" differences of 2deg or so.
The final periodicity was caused by the fact that the satellites orbit in distinct planes, not randomly. This means that once the Earth's rotation caused a plane of satellites to move out of the part of the sky where the geometry is correct to produce flares there will be no more flares until another plane moves into its place. This process can then repeat, possibly several times in one night. Each cycle would take at most 2hrs (the time it takes for the Earth to rotate through the plane separation angle) but tended to be quite a bit less than this due to the ever-changing Sun-satellite-observer geometry and because Iridium satellites had three antennae that could each produce flares, thus increasing the possibility of one occuring - I haven't done any work on the exact timings involved though.