INTRODUCTION
In October 1957 when the Soviets launched their first satellite, Sputnik I into space, many people would go outside looking for the satellite to cross the evening sky. Newspapers would print times at which the satellite would be visible in the sky in various cities.
What most people did not realise is that the satellite itself, at just under 60 cm in diameter was quite a dim object, and that what they were seeing was in fact the much larger rocket body that was the last stage to put the satellite into orbit.
Rocket bodies are still some to the brightest objects that we can see in the evening sky. It is only satellites and such debris in low Earth orbit (LEO) that are in general bright enough for us to see. And we can only see these objects in the early evening when the sky is dark enough but the satellite is still illuminated by the Sun.
ILLUMINATION
The image below shows the conditions under which a satellite may be visible to observers on the ground.
The observer, designated by "O" must be in the "Dark" area, but the satellite must be in the "Light" area. This means that the satellite must be at the height h or greater (when overhead).
The diagram is a little misleading because there is no abrupt transition on the ground from light to dark as the Sun sets. There is a twilight period, when the sky brightness slowly decreases over a one to two hour or more period (depending upon your latitude) from day to night.
The table below shows a typical evening at mid-latitudes where the solar elevation (or depression) angle is given for times after sunset, together with the minimum overhead height at which a satellite is still in sunlight and thus may be potentially visible to a ground observer.
SATELLITE OVERHEAD VISIBILITY HEIGHTS
Sun elev Sunset+ MinHeight
(deg) (hrs) (km)
-10 0.7 98
-12 0.8 142 [End Nautical Twilight]
-14 0.9 195
-16 1.1 257
-18 1.2 328 [End Astronomical Twilight]
-20 1.3 409
-22 1.5 500
-24 1.6 603
-26 1.7 717
-28 1.9 845
-30 2.0 986
-32 2.1 1142
-34 2.3 1314
-36 2.4 1504
-38 2.5 1714
-40 2.7 1946
BRIGHTNESS
We must still consider the brightness of the satellite to be able to determine whether or not it will be visible to the naked eye. This depends on a number of factors, the most important being its size, shape, its reflectivity and how it is illuminated by the Sun.
The graph below is a very rough estimate of the visual magnitude of a spherical satellite that has average reflectivity and is 50% illuminated by the Sun. If we consider that magnitude 5 is about the faintest we might expect to see a moving object among the stars in a dark sky, we see that the satellite has to be below 500 km altitude, and that a 2 m sphere is about the smallest object we can expect to see even when it only 300 km overhead.
Only when the satellite is over 10m in diameter might we expect to see it at altitudes a little greater than 1000 km when overhead.
MIRROR REFLECTIONS
There are some exceptions to the above graph, and these occur under special circumstances when the satellite has surfaces that give a mirror like or specular reflection of the Sun. These produce what are called glints which can be seen at specific places on the Earth for very short periods of time.
Am example of these glints occurs in the Motorola series of Iridium satellites. Some web sites specialise in giving satellite observers places and times to watch for these glints.
A similar phenomenon occurs around the equinoxes for geosynchronous satellites. Under normal conditions geosats are too faint for visual observations, with even the largest geosats being above (fainter) than magnitude 10. However, around the equinoxes (March-April and September-October), the satellites are in a position where near specular reflection occurs for a suitable placed ground observer and these satellites can reach below (brighter than) magnitude 5.
ATMOSPHERIC EFFECTS
The data presented above has considered only satellites that are overhead the observer. This is rarely the case, and it is more normal for the average satellite pass to be closer to the horizon.
This means that the light from the satellite has to pass through a lot more atmosphere, which will attenuate the light and cause scintillation as we observe with stars near to the horizon. Not only the atmospheric attenuation but also the inverse square law will reduce the intensity of the light we see due to the increased distance.
There are several web sites which provide satellite visibility information to those who would like to observe. These include:
REFERENCES
1 Desmond King-Hele, Observing Earth Satellites, MacMillan (1966)
2 Desmond King-Hele, Observing Earth Satellites, Van Nostrand Reinhold (1983)
3 Desmond King-Hele, Satellite Orbits in an Atmosphere - Theory and Applications, Blackie (1987)
Australian Space Academy