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Abstract. In Part 1 of this two-part series a brief introduction was given to spotting and observing the larger/brighter artificial satellites orbiting the earth. In this part we discuss simple predictive methods and Internet resources that can be used to predict satellite transits or to identify unknown satellites.
Sommaire. La première partie de cet article (cf. AS/CA 3) a décrit brièvement comment apercevoir et observer les plus grands et/ou les plus brillants des satellites artificiels qui orbitent autour de la terre. Dans cette dernière partie nous discutons les méthodes simples de prévision et les moyens Internet qui peuvent être utilisés pour prédire les passages satellitaires ou pour identifier les satellites inconnus.
One may decide that one wants to observe classified satellites - this is certainly possible as the orbital data are on the web (obtained by other amateur observers). There is usually a need for accurate positions of such satellites as the satellite may carry out orbital changes and, unless it is observed fairly regularly it could become ``lost'' until picked up again. For this type of work one needs nothing more than a stopwatch (to determine the time when a satellite was close to an identifiable star) and modest optical aid. You need to know your geographical coordinates quite accurately, have accurate time, and it helps to have some astronomical knowledge so that you can identify the star or starfields involved. This is known as ``positional'' work and there is some need for such work, especially in the southern hemisphere.
One could be interested in trying to observe satellites in geostationary orbit. Normally this does require optical aid but it is sometimes possible to see such satellites with the unaided eye. Such information may be found on the Internet, especially if you subscribe to SeeSat (more on this later).
One could try to observe a satellite in the last few days of it orbiting the earth before it plunges back into the denser layers of the earth's atmosphere and burns up, sometimes with really spectacular effects. Even before it finally re-enters it is fun to see a bright very fast-moving satellite cross the sky.
Artificial satellites follow the basic rules of celestial mechanics. If a satellite is in a stable orbit it will follow a pattern that you should soon begin to recognize. If a satellite is in a low orbit, and thus subject to atmospheric drag from the upper layers of the earth's atmosphere, the subject becomes a bit more complicated and falls outside the scope of this article.
At this stage we assume the potential observer has little or no knowledge of the situation, so some assumptions will be made to simplify the matter initially. The satellite's orbital plane remains fairly fixed in space during the course of a day, so in the first instance its movement, or ``precession,'' can be ignored and all we have to consider is the rotation of the earth which we know is 15 degrees per hour. If the satellite completes one orbit in 120 minutes the earth will rotate through 30 degrees EAST, which means the satellite's ground track will move 30 degrees to the WEST. Thus, having observed a satellite at some given time we know that another pass will occur about 120 minutes later with the satellite 30 degrees further west. A shift in longitude of 30 degrees can decrease the elevation of a satellite above the horizon from a near-overhead pass to one low on the horizon, so if the satellite is in the western sky when you first spot it, it is unlikely that you will be able to see the next pass that evening because the satellite will either be too low in the west or even below your horizon. However, if you spot the satellite in the east early in the evening, you stand a fair chance of seeing the next pass two hours later. If the satellite's inclination is fairly close to your latitude you may well see two passes or more during a night, but since the majority of naked-eye satellites are in near-polar orbits with an inclination of around 85 degrees or so, observers at low and middle latitudes will see the satellite travelling north to south, or south to north, and probably only get one pass a night bright enough to be seen without optical aid. So, whilst you may only get one pass an evening, there is a very good chance you will be able to predict the pass on the next evening.
In predicting from one night to the next we have to refine our first approximation, namely that the orbital plane is fixed in space. The initial assumption was that the earth rotates through 360 degrees in 24 hours. The rotation period is actually 23 hours 56 minutes - this means the earth actually rotates through 361 degrees in 24 hours 00 minutes (its actually 360.9856 degrees if you want to be more accurate!), so in a 24-hour period the satellite's orbital plane moves by 1 degree WEST in longitude.
The second refinement that has to be made is that the orbit precesses in space at a rate that depends on the inclination and the period (or height, since height is related to the period) of the satellite. The daily shift can be as much as 9 degrees and this can play havoc with our simple predicting, so it is necessary to take account of this, if not exactly, then at least by making a reasonable approximation. This is not as bad as it sounds - from the direction of travel you should be able to guess the inclination to within, say 15 - 20 degrees, and from the apparent speed of the satellite across the sky you can roughly guess the height of the satellite and hence its period.
Most of the naked-eye satellites are in polar orbits with an inclination of about 85 degrees and an orbital period of about 100 minutes, so for the polar satellites we can use a value of about 0.7 degrees per day. Should we observe the International Space Station (which is very bright and has an inclination of about 57 degrees and an orbital period of about 90 minutes) we can use a value of about 4.8 degrees per day, whilst for the Hubble Space Telescope and several other satellites in a similar orbit, we can use an inclination of about 30 degrees and an orbital period of about 95 min to get a daily change of about 6.5 degrees.
The following equation can be used to calcuate the daily shift for different inclinations and orbital periods:
where:
= rate of change of the orbital plane
n = number of orbits per day
a = semi major axis (which is related to n)
e = eccentricity of the orbit
i = inclination of the orbital plane
(for our initial estimate one can take the orbit as being circular (e = 0)
which simplifies the equation a little)
For illustrative purposes we assume a daily shift of (say) 1 degree westward to account for the orbit precession, so if the satellite passes overhead at the same time on two successive days, the orbit will be 1 degree further west because of precession and another 1 degree further west because of the earth's rotation in 23 hr 56 minutes, so in total the satellite ground track will have moved about 2 degrees further west. Call this quantity × degrees.
Now we have to add another complication! In most cases the satellite does not pass at the same time every day. It is however quite easy to take this into account. If the satellite does an integral number of orbits per day it will pass overhead the same time every day. The highest integral number of orbits a satellite can do in one day is 16, which is an orbital period of 90.0 minutes. For 15 integral orbits the period is 1440/15 = 96.00 minutes, 14 orbits gives 102.857 minutes, etc. However, suppose the orbital period is 100 minutes. If we divide this into one day we see the satellite completes 1440/100 = 14.4 orbits. How will this affect our calculations? Quite simply, the satellite will either come 40 minutes earlier or 60 minutes later (i.e. 0.4 × 100 minute orbital period = 40 minutes or 0.6 × 100 minutes = 60 minutes) than the previous day. Consider another example: a satellite has an orbital period of 95.4 minutes, and so completes 1440/95.4 = 15.09434 orbits per day. The satellite will either come 0.09434 × 95.4 = 9.00 minutes earlier than the previous day, or 0.90566 × 95.4 = 86.40 minutes later. Obviously the pass coming earlier by 9 minutes will be closer to the path followed the previous day than the pass that occurs 86 minutes later. Why? - because we have to take into account the rotation of the earth. During 9 minutes the earth will rotate through 2.25 degrees so the observer will be 2.25 degrees west of the satellite's ground track, whereas if the satellite came 86 minutes later the earth would have moved through 86/4 = 21.5 degrees, with the observer east of the ground track. So, to summarize, if the satellite comes n minutes earlier each day, its track will be 0.25 × n degrees to the east. If it comes n minutes later per day, its track will be 0.25 × n degrees to the west of its passage on the previous day.
Combining this with orbital plane precession we find that:
Figure 1:
Sample screen display of the space station MIR passing over Paris.
The program may be downloaded from Alphonse Poupliers' web site mentioned in
the article.
An excellent source of information on all aspects of the visual tracking of satellites is the Visual Satellite Observing FAQ (Frequently Asked Questions) that may be found at
http://www.satellite.eu.org/sat/vsohp/satintro.html
or
ftp://ftp.cc.utexas.edu/people/worden/vsohp/FAQ/
Here you will find the answer to virtually every conceivable question, as well as many sources of additional information. This site is a MUST for all visual observers.
Another good place to visit is the web site run by a colleague of mine, Willie Koorts. He has compiled a list of many sites dedicated to satellite tracking, astronomy and telescope-making and it is constantly updated. The address is http://canopus.saao.ac.za/~wpk/sat.html
If all you want to do is see some of the brighter satellites, including such objects as MIR, ISS (International Space Station), STARSHINE and the IRIDIUM satellites (which produce spectacular bright flashes sometimes visible in broad daylight), the one site that offers predictions for ANY location on the earth is situated at
http://www.gsoc.dlr.de/satvis .
This is not the only site that provides predictions for naked-eye satellites but it is one of the best.
As many readers are French-speaking one site that should be of interest is that run by Alphonse Pouplier. Besides giving predictions for the brighter satellites his webpage has satellite prediction software written in French (Fig.1), available for downloading. The address is
http://users.skynet.be/alphonse
Another site of interest to French users is
http://members.aol.com/marionjc/eurosat/telechar.htm
This site does not list predictions, but you can download the French prediction program EUROSAT.
Figure 2:
Sample screen output of the space shuttle passing over Cape Canaveral.
This was obtained from the popular STSPLUS satellite program by Dave
Ransom.
There are several other sites that offer predictions on the Internet. A few are:
http://www.chara.gsu.edu/sat.html
http://acsprod1.acs.ncsu.edu/scripts/HamRadio/sattrack
http://www2.satellite.eu.org/sat/vsohp/satpred.html
http://www.hq.nasa.gov/osf/mir/mirvis.html
One of the largest collections of on-line satellite prediction software for IBM PC compatibles may be found at
ftp://ftp.satellite.eu.org/pub/sat/programs/ibmpc/
It is no use having a satellite-predicting program if you have no orbital data. Moreover, you should use the freshest elements available. If you use an old element set (say older than about a month) there is a very good chance that you will see nothing at the predicted time. Even with new orbital data, a satellite may run early or late with respect to the predicted time, so it is advisable always to start looking two or three minutes ahead of the predicted time, and if not seen at the predicted time, to wait another two or three minutes in case it is running late. Some satellites, especially the space shuttle, Mir and the International Space Station, frequently carry out orbital manoeuvers which change their orbital periods, subsequently affecting the predicted times. The orbital data are normally referred to as ``two-line elements'' (TLEs) although there are actually three lines, the extra line usually conveying information on the object's brightness, size and, in the case of transmitting satellites, the frequency easiest to hear. There are numerous sites where one can get orbital elements and/or software. My favourites are:
ftp://ftp.fc.net/pub/users/mikem/
ftp://ftp.dransom.com/dransom.com/current.data/
http://www.dransom.com/
http://www.amsat.org/amsat/ftpsoft.html
http://www.portents.com/marek/satellite
http://celestrak.com/NORAD/elements/index.html
http://www.adelaide.net.au/ starman
http://oig1.gsfc.nasa.gov
(select OIG MAIN PAGE, then select DOWNLOADABLE FILES)
After you have been observing for a while you may become frustrated by the unidentified satellites that you have seen. Without access to the Internet and a computer, identifying these satellites can can be an almost impossible task. But should you have access to regular orbital data, there are several computer programs available at the sites mentioned above, which enable you to identify what you have seen. It may happen that you cannot find a suitable candidate, in which case you may have seen a classified satellite for which orbital data are not available in the public domain. There is software available to derive orbital data that might assist in seeing the satellite again.
It is theoretically impossible to derive an accurate orbit from a single pass of a satellite since we only see a very small portion of the orbit track and the assumption is usually made that the orbit is reasonably circular, which may not be the case. This is where joining a group such as SeeSat (to contact please refer to details overleaf) is very useful - you can compare observations with others and perhaps assist in ``tying down'' a classified satellite's orbit.
There are two books that are highly recommended. The first is Observing Earth Satellites by Desmond King-Hele. It came out in two editions and unfortunately appears to now be out of print, but can sometimes be found in libraries. More readily available is The Satellite Experimenters Handbook by Martin Davidoff. This is published by the American Radio Relay League, 225 Main Street, Newington, CT 06111, USA. Although primarily intended for radio amateurs (``hams'') it is full of useful information and is a useful reference book - I use my copy often.
Finally, if you are really interested in observing satellites and want the latest information on what is happening, as well as meeting other satellite observers, ranging from the raw beginner to the expert, then the thing to do is join the SeeSat group on the Internet. Membership is free (obviously you need access to the Internet) and every aspect of visual tracking is covered. To subscribe to SeeSat you need to do the following:
Send an e-mail message to
SeeSat-D-request@lists.satellite.eu.org
with the word ``subscribe'' in the SUBJECT field. Within a day or so you should start to get messages related to the visual tracking of satellites, new launches etc. If you are interested in their archives, earlier messages may be found at
http://www2.satellite.eu.org/sat/seesat/
Should you perhaps be interested in listening to the radio signals that come from some spacecraft then the group to join is HearSat. I have not dealt with this subject since it is a bit more demanding technically than visual observing (for which one is normally well equipped!). To subscribe to HearSat you do the following:
Go to http://www.qth.net/
Select ``hearsat-l'' from the many newsgroups offered and then select ``subscribe''. Shortly thereafter you will receive a message requesting confirmation of your actual subscription. Thereafter you will start receiving messages. The archives of past messages are also available at http://www.qth.net/
Good luck with whatever satellite spotting you do, and may you have clear and dark skies and not too stiff a neck from peering skywards!
WGSSA