The amateur observer can contribute to the observation of satellites through flash period measurements. The Belgian Working Group for Satellites (BWGS) co-ordinate such observations and collate the data. More information on the activties and publications of the BWGS can be found on their Home Page. The PPAS is their computerized database of Photometric Periods of Artificial Satellites, maintained by Mike McCants.
Measuring the period between two flashes or maxima/minima in the light curve can give a good approximation for the satellite's rotation period (or half of it).
Fig. 1: Light curve of the orbital stage of the Russian Zenit rocket that orbited Cosmos 1844. The smooth variation due to diffuse reflection is regularly interrupted by bright spikes due to specular reflection. Data courtesy of Dr. Graham Appleby of the Satellite Laser Ranging Team, Royal Greenwich Observatory, England.
In some cases payloads will turn around an axis (e.g. for stabilization purposes, or when they are out of control after their useful life) and show specular reflections. Polished extensions, such as antennas or solar panels behave periodically as mirrors, and cause bright flashes, which can reach negative magnitudes.
Rocket bodies can receive a little kick during insertion of the payload into orbit and can start to tumble around one or more axes. Depending on the reflectivity of the surfaces, rockets can give off specular or diffuse flashes.
Fragments are brought into orbit in an uncontrolled way and usually show some rotation.
We define a flash period as the time interval between two flashes. Measuring the time interval during which the rocket has flashed some tens of times can, after dividing this total time by the number of flash periods, give a good approximation for the true rotation period. Counting at least hundred flashes, an accuracy of up to 0.001 seconds can be obtained. Immediately after the launch, most flash periods of rocket stages are of the order of a few seconds. However, the rotation period changes with time. Several forces act upon the satellite and (generally) slow down the rotation until the flash period has grown so large that after months or years the satellite no longer shows brightness variations. It has become "steady".
Fig. 2: The orbital stage of the Russian Zenit rocket that brought Cosmos 2263 into orbit (93- 59 B) photographed tumbling on July 10, 1994. Flash period was 2.18 seconds.
Rocket stages, usually hollow metal cylinders, tumble through the Earth's magnetic field. This generates eddy currents in the skin of the structure. The Earth's magnetic field acts on these currents which creates a torque on the rocket. Due to this torque the rotation will slowly decrease. It will also change the rotation from spinning (rotation about the long axis) to tumbling (rotation about the short axis). This is comparable to a toy top which spins slower due to the friction, and lays flatter.
Fig. 3: The American COBE satellite (Cosmic Background Explorer, 89- 89 A) photographed flashing on November 1992. The flash period was 7 seconds.
Another factor is the air resistance which the satellite experiences in its orbit. Although the atmosphere is very thin at those heights (a few molecules per cubic meter at some hundred kilometers height), it does brake the rotation of the satellite around its own axis.
Often there is still some leftover fuel in the tanks which can slowly escape through the nozzle or through a puncture caused by a micrometeorite or space debris. The rotation period of the rocket can suddenly change strongly due to such an event. Depending on the geometry both an acceleration and a deceleration can take place.
Regular observations of the flash period can shed light on the rotational behavior of satellites. Very little research has been done on the rotational behavior of satellites, and especially the accelerations prove to be very puzzling.
Fig. 4: The flash period as a function of time for the rocket that brought Cosmos 1559 to 1566 into orbit (84- 52 J). The first part shows a steadily increasing flash period (i.e. a deceleration), followed by an acceleration (rapid decrease of the flash period), which is again followed by a steadily increasing flash period. The deceleration is due to magnetic friction. The acceleration is probably due to a fuel leak.
About forty enthusiastic observers worldwide make regular measurements of flash periods. The Belgian Working Group for Satellites (WGS) of the VVS (Vereniging voor Sterrenkunde, the Belgian Astronomical Society) has specialized in collecting and analyzing flash periods.
The practical side to these observations can be followed here, whilst the theory itself is covered here.