by Paul D. Maley

Satellite monitoring can be enabled by plotting their light variations in graphic form, either manually or using a computer-aided graphics package. Either way, the revelation of light curves makes the experience much more invigorating. Building a light curve is one of the more interesting aspects of satellite watching. It is also a more permanent way to log optical characteristics in addition to low light level video that I also employ. Development of optical light curves is preferable to video records because the latter do not capture certain types of variation. The human eye is much more sensitive than intensified video equipment.

A single satellite, if stable, should exhibit the same or similar brightness over time. An example of my earlier observations was the Space Shuttle payload called LDEF( Long Duration Exposure Facility). The graph below shows my 1989 observations of various passes of this satellite over a series of phase angles (x-axis) with the brightness corrected to a standard slant range (absolute magnitude, y-axis). You can see that the overall profile  is quite similar.

Another example  in the next graphic is my observations of Vanguard 2, the 11th object placed into orbit. It is a 1.7 foot diameter sphere launched into a 32.9 degree inclination orbit.   The following graph shows a series of observations made between 1964 and 1967.  The yellow line was created with the average of these observations indicating a brightness trend with respect to satellite phase angle.

As an example, here is a video image of flashes from the Japanese EGP spacecraft taken August 15, 1986. You can see a line of closely spaced dots indicated the instantaneous reflections of the sun off surfaces of the satellite as it moves through the sky. EGP is covered with mirrors and corner cube reflectors. These flashes appear quickly as perceived in binoculars. The video equipment can capture them well, yet the resolution is not as good as the human eye.

I first record spoken data on a portable battery-powered cassette tape recorder that is hung about the neck or otherwise secured so that both hands are free. This record consists of a continuous stream of verbal information on the brightness of the rocket as it moves through the sky and varies in brightness with respect to time.

Let’s define some terms the way I use them. These are not absolute definitions and others may choose to use the terms differently:

  • light curve – the time history of variation of a satellite or rocket brightness
  • maximum – maximum brightness in a variably changing light pattern
  • minimum – minimum brightness in a variably changing light pattern
  • flash – peak brightness usually occurring over a short time such that it looks like a flash; the length of time might be a fraction of a second or longer
  • pulse – a rise in brightness lasting longer than a flash; e.g. 1 second duration
  • glint – a brief reflection lasting a short fraction of a second and normally not repeating
  • flare – a rise in brightness lasting a brief amount of time, usually much longer than a flash or a pulse; e.g. several seconds duration.
  • flash rate – time between flashes. Often an object will exhibit regular flashes of different amplitude. I interpret the flash rate as being the time between flashes of equal time spacing but not necessarily identical amplitude.
  • flash period – time between maxima. Here the satellite light variation has maxima and minima and sometimes secondary maxima. The flash period as I interpret it is the time between consecutive maxima.
  • sparkle – generally a rapid flashing at low amplitude like a rotating chandelier
  • tumble period – complete 360-degree rotation of an object. Often this can be difficult to determine. A ‘tumble period’ might be referred to if the satellite is not really seen to flash. This is the case for satellites that vary in brightness with gentle regularity.
  • magnitude – brightness of the satellite with respect to reference stars
  • amplitude – height of brightness level above a certain level; e.g. if a satellite’s background magnitude is +7, it may exhibit brief flashes to +6.5 magnitude. Hence the amplitude is 0.5.

A light curve can be simple or quite complex.  More than 40 years ago I hand drew light curves from visually obtained data. The drawings are not intended to be super accurate but merely representative of different optical signatures.  The next graphic shows a simple light curve  of an SL11 rocket body taken March 16, 1971. I visually used a 5-inch apogee refractor f/5 to make the observation.  The flash period was timed at 1.38 seconds between flashes and the maximum brightness +5 magnitude, minimum brightness +7.

The next light curve is a little more complex. It shows Cosmos 312 rocket on March 18, 1971. Every fourth flash had a double maximum and each maximum actually had a flash at the peak of the light curve.

The final example is a complex light curve that I made using a 16-inch Schmidt-Cassegrain telescope on the Russian communications satellite Molniya 16. It was taken February 27, 1971.  The average duration of each minimum was 4 seconds and spacing of maximums, while generally + 10 magnitude in this long track ranged from 66 to 51 to 14 to 25 to 34 to 43 seconds as the spacecraft was followed for 16 minutes.

Stop right here. If you are unfamiliar with astronomical magnitudes it helps to do several things to cure this problem. First, become familiar with star charts and how different stars of differing brightness are depicted. Then go out and learn the constellations. This is an iterative process and could take several months depending on the amount of time you have and your skies. You will have to do this anyway in order to find positions unless you are using a ‘GO TO’ type telescope. Develop a series of star references that proceed from magnitude 0 to +1 to +2, etc. so you can regularly make such measurements with the unaided eye. Then use the same method to develop a binocular magnitude scale starting with +4 and going down in brightness to +9. The limitation depends on how powerful your binoculars are and how good your sky is. You can also use variable star charts, which have very precise references.

The next step is to decide on an instrument to use when observing satellites and stick to that one device. I have used the same pair of 7×35 Tasco binoculars for 35 years, for example. The use of the same instrument leads to consistency in brightness estimation.

Finally, locate star magnitude references. This can be taken even from a star atlas that shows stars to the nearest magnitude. That will give you a reference frame from which to begin understanding the subtle differences in brightness estimation. Becoming interested in variable stars will make you even more experienced, as exacting magnitude estimation is a formal requirement.

With satellites that are moving targets, unlike variable stars, you have to follow and estimate brightness as they move through different patterns of stars. Hence it is not really necessary to estimate to the nearest 0.1 magnitude; in fact, this is impractical to achieve. I estimate to the nearest 0.5 magnitude. This is more than sufficient. As you gain proficiency, it will be possible to estimate to the nearest 0.25 magnitude. The idea is to be able to determine maxima and/or minima depending upon which is easier to fathom. For some satellites the maxima may be rather broad and indeterminate as to the exact moment of maximum brilliance. The same might also occur for the minimum. If the brightness range between max and min is high (e.g. 3 or 4 magnitudes), you might want to estimate the moment when fading from maximum begins as the key point for the light curve estimate.

Timing the number of flash cycles is done quite simply by counting the first maximum as ‘0’ (here is where you start your stopwatch) and each successive maximum as ‘1’, ‘2’, etc. until 10 or 20 is reached. The resulting value on the stopwatch can be divided out by the number of cycles and you can get the flash rate. That is the simple idea. But if you look at the light curves presented here, it may not be so simple. The real flash rate may not reveal itself until after you have graphed the data. Even then there may be some strangeness in the curve. Note the leftmost part of graph A. If we just had that first bit of data, we might have made an erroneous assumption about the flash period.

One other note about using a stopwatch. Some stopwatches give the users the capability to time multiple laps. Not just for racing, the satellite observer can start the watch on the first maximum, then stop it on the second one, thus capturing an interval between two consecutive maxima. The multi-lap function can be activated so that the second lap can start on another maximum and stopped at the one thereafter and so on depending how many separate laps you wish to time. This function at first may not seem necessary, yet there are some satellites that will actually vary irregularly. This apparent irregular flashing may not be noted unless one is careful about it. Hence the observer should be aware to watch each cycle and see if there is anything odd about it while the watch is running. As an example, a satellite could be flashing regularly, say at 5.2 seconds between flashes for 10 cycles; then at the 11th cycle, the maximum is not observed—it just seems to have vanished. This phenomenon is notable as the satellite viewing geometry may change during a given pass. This is only one of a number of possible different variation scenarios. The message here is to watch what you time in order to be certain that all of your data is valid. Accuracy is the most important component in collecting data. If your data is to be used for anything more than just for fun (e.g. for contribution to a research project), your credibility is at stake.

Some satellite light curves appear as garbage and nothing can be determined from them. I mean by this that if variation is observed, the originating features may be so irregular that it is impossible to determine any periodicity. Also, the rotation period may be so long that it is not possible to evaluate it. Other objects may have very slight amplitudes in variation such that it may fool the observer into believing that the vehicle is actually steady (nonvariant). Remember that observation as we describe it is an indirect technique. Unless you can visually discern the shape of a vehicle, you have to work with a reflected blob of light. Hence many conclusions derived from this low-resolution method have a certain amount of ambiguity in them.

Many satellites and some rockets exhibit ‘steady’ or nonvarying brightness; or if there is variation it is due principally to changes in the geometry between sun, observer and spacecraft (phase variation).

A sparkle effect can be observed from some spacecraft that have multi-layer insulation (MLI) such that they reflect light specularly in brief patterns. Usually the peak-to-peak brightness is too short to measure because the rate is not sustained long enough and occurs at unexpected interval(s).


I use a recorder containing a fresh set of batteries to collect pass data. You need to practice to ensure that you minimize your personal equation (defined as delay in starting/stopping the stopwatch caused by your own reaction time); experience will improve this. Later, I transfer the raw information to my observation log and reduce the tumble period by means of a stopwatch. If you do not have logbook it is wise to record the date/time/elevation/azimuth/height/range/phase angle for future reference. In addition add to this the maximum/ minimum brightness of the satellite and any rotational information you have been able to gather.

An alternate mechanism that I can use is to simply record the tumble rate in real-time with a stopwatch while watching the satellite provided the tumble period is obvious and regular. I start the watch at a maximum and call it ‘0’, then proceed to count as many maxima as I choose, taking care to stop the watch as close as possible to the top of the final maximum.

I can then utilize a computer program called STATISTICA to process the data and output it into the form of a least squares curve fit. If you do not have a computer program, it is almost as easy to plot the data by hand on ordinary graph paper. Unless I am concerned with very exact differences in the flash rate from week to week, I can normally be content with a flash period accurate to the nearest 0.1 second. But for developing histories of accelerations, it may require many more flash cycles to be timed in order to get a more accurate flash period.

One thing that might impact flash period measurements is the ‘diurnal effect’, which shows up as a satellite, moves from one part of the sky to another. The geometry change can lead to an apparent change in the actual flash period.

One study I conducted a few years ago was on Ariane IV rocket bodies. I chose this family because from my latitude (30 degrees North) the rockets are approaching perigees (located in the southern hemisphere) in the southern part of my sky. Their distances from earth are smaller and thus easier to observe in my binoculars. Also, trees and other structures to the west and north block my horizon so this was an ideal group to monitor. Such an effort took many months and resulted in observing at all times of night under varying weather conditions. I used 25×150 Fujinon binoculars that are elevation-azimuth mounted. The binoculars have a 2.7 degree field of view, and I can typically observe satellites down to +10 magnitude from my site in Clear Lake City, Texas. They are very difficult to use at elevations above 70 degrees.

The Ariane IV rocket stages are cylindrical spent tanks that ply the earth in geostationary transfer type orbits. Their elongated paths have perigees below 500 km and apogees over 30,000 km. They are all built the same way, and you might think the appearances would be very similar. In fact, what distinguishes this ‘space family’ is their rate of rotation and also the signature in the light curves. In the four panels below, curves A, B, C, and D, peak-to-peak variation of the primary maximum increase from 23 to 55 to 125 to 242 seconds. Now these panels show the appearance of four different rocket bodies in the same Ariane IV family. The flash periods reveal that not all rockets tumble at the same rate. There is typically a damping function that causes them to slow down over time. The intriguing shapes of the curves are quite similar in respect because they show periodicity, and yet they are also distinctly different. They resemble the light curves of some variable stars. The reason for the difference between one rocket’s signature and another is in the presentation of features on the surfaces of the vehicles as they reflect sunlight down to the observer. In fact, the same rocket might have a different signature depending upon what part of the sky it is viewed in and whether the rocket is oriented between you and the sun or where the rocket is located behind you with respect to the sun (e.g. sun low in the west, rocket high in the east).

Light curves can be sometimes misleading, and observers are warned that it takes multiple observations over time to understand sometimes whether the information you have is correct. There have been many instances where I have observed a satellite appearing to be steady in brightness, and then seen it exhibit variable light curve characteristics on another date. In general this has been due solely to the geometry changes that have occurred between the observation dates. Also, the orientation of the spin axis can play a significant role in which features are presented to an observer at a particular point in time.

Accelerations or decelerations in rotation are commonly observed. The former can be due to venting of residual fuel on board. The latter take place as a result of hysteresis effects as the metallic construction of the rocket is influenced by the earth’s magnetic field.

Light curves can have all kinds of features including spikes created by instantaneous flashes or maybe prolonged dips caused by the satellite fading from view so that its minimum brightness is indeterminate. The four graphs above show patterns in the light curves of four identical rocket bodies. The rate of rotation depends upon how the rocket was left after it was inserted into its orbit. Though the rockets are generally cylinders, they also have surfaces, which are the results of asymmetries of equipment and other components. The shapes of the curves offer additional insight into the complex business of interpreting the variation patterns and linking them to their physical appearance.


In order to match a specific satellite to a group, observations need to be made over a number of phase angles and then corrected to a standard slant range. The following examples show my early attempts to match up class members.

The next figure shows plots of optical behavior of a group of Russian geodetic satellites launched into 73.6 deg inclination orbits (those with X and .) and a single one in an 82.6 degree inclined orbit. Mean motion for all was 12.40 revs/day.

The above graph was made from raw notes but shows that most members tend to have brightness values clustering around a common area as depicted between phase angles of 70 to 110 degrees.

The above graphic depicts my observations of a group of Russian minor military satellites as observed during 1988 and 1989. The Y-axis shows the absolute magnitude, while the x-axis the phase angle.   As in the previous graph there is a clustering of common brightness values between 50 and 110 degrees phase angle.  The graphs above correlate to spacecraft as follows:

1= Cosmos 1960

2=Cosmos 1601

3= Cosmos 1985

4 and 4A= Cosmos 1601

5 = Cosmos 1662

6 and 7 = Cosmos 2002

8 and 9 = Cosmos 1615


The following graphic shows absolute magnitude versus phase angle for more than 30 Russian ELINT satellites observed during 1987.   All were in 81.2 degree inclination orbits.