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<TITLE>Artificial Satellite Tracking - (Part I)</TITLE>
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<center><H1>Artificial Satellite Tracking</H1>
<h2>(Part I)</h2>
<h3>Greg Roberts</h3>
<i>South African Astronomical Observatory<br>
PO Box 9, Observatory, 7935, South Africa<br>
<a href="mailto:grr@saao.ac.za">grr@saao.ac.za</a></i>
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<h2><A NAME="SECTION00010000000000000000">1. Introduction</A></h2>
<P>
Go outside on a clear moonless summer night, approximately fifty minutes after
sunset, and scan the sky with your naked eye. As the sky gets darker and more
and more stars appear you cannot fail to see one or more stars that are 
moving with respect to their surrounding stars.  What you are seeing is 
 probably one the the thousands of man-made
satellites that are orbiting our small world.
<P>
On the 4th of October 1957 a new era started in mankind's history -- that of the 
Space Age.  On that date, over forty years ago,  the USSR launched SPUTNIK 1, 
the first man-made object to orbit the earth.  Most of the world had expected 
the United States to be the first to achieve this milestone and little notice 
had been taken of the intentions of the USSR.  To say that this caused major 
consternation in the western world is somewhat of an understatement. It was
compounded a short time later when the female dog Laika was orbited in
SPUTNIK 2.  Some disbelievers stated it was a hoax but all one had to do was 
to go outside at a predicted time and sure enough there was a moving `star,'
which was
the orbiting rocket casing.  Those of us young enough at the time will recall
the excitement as each new space achievement took place.  The first relay of 
television across the Atlantic, photographs of the far side of the moon,  unmanned
crash landings on the moon followed eventually by man actually landing on the 
moon, briefly exploring its surface and then returning to earth, and probes
that were
sent to the planets and returned photographs of strange worlds -- these are just 
a few of the dramatic events that took place.
<P>

<center><img src="mir.jpg" alt="MIR space station" width=354 height=314 border=0><br>
<STRONG>Figure 1:</STRONG> <small>The MIR space station, the largest man-made object in orbit, is visible from all inhabited regions of the Earth.</small></center>

<P>
Sadly, the exploration of space has lost its early impact on the general
public and we all take for granted the television we receive via satellites, 
our international satellite telecommunications links,  weather satellite
pictures, navigation and numerous other benefits to mankind.  It is only when
something spectacular happens that one is reminded of what is going on about
us.
<P>
It is not surprising therefore to find that most people know very little about
space and even less about artificial satellites.  Relatively few people have even
seen an artificial satellite for the simple reason that not many people look 
skywards (except when they have seen a TV feature or film on UFOs and then 
suddenly become sky conscious).  If you live in a city it is not surprising if 
you do not look skywards, since what is there to see other than a few paltry 
stars dimmed almost into insignificance by the light pollution of man? 
However,
go out into the country,  away from all bright lights, and see the stars as they
should be seen.  If you watch for several minutes,  under suitable conditions 
which will be described shortly, you cannot fail to see several satellites and 
perhaps you might feel some of the wonder and excitement of the space age if 
you think a bit about what you are seeing, how it got there and its meaning.
<P>
In this article I will try to convey some of the excitement and thrills
of satellite spotting.  Perhaps this article may encourage you to explore further 
on your own and become one of the amateur satellite tracking fraternity. 
Amateurs played a major role in the early days of the space
age, but today,  with the advances in tracking technology,  the amateur is no
longer in demand.  That is not to say there is no place for the amateur -- far
from that, the sky is your limit in what you can do or hope to achieve. 
In a later article I will describe some of the things that amateur satellite 
trackers can do, but before you can run you have to learn to crawl and this 
article is aimed at helping you to crawl.
<P>
<h2><A NAME="SECTION00020000000000000000">2. Fundamentals of Satellite Spotting</A></h2>
<P>
Many people think that satellite spotting or tracking requires expensive
equipment.  Depending on what you want to do you can start with nothing more than
your naked eye.  If you want to pursue tracking more seriously then a stop-watch
and a pair of binoculars will be a big asset and will enable you to make valuable
contributions.  If you want to progress further, then a personal computer will
be of great value since you can then make your own predictions.
This is satellite tracking as opposed to satellite spotting.
<P>
Before going into the more advanced aspects of satellite spotting, some basic
fundamentals have to be defined.  For a satellite to be seen with the naked eye
it must meet certain criteria, the most important of which are:
<OL><LI> The geometry of the orbit must be such that the satellite can make
    suitable passes over your location;<LI> The satellite must be large enough to be visible to the naked eye;<LI> The satellite must be suitably illuminated,  <EM>i.e.</EM>  the satellite 
must be in sunlight whilst the observer is in darkness;<LI> The satellite must be relatively close to the earth,  preferably closer
    than about 1000 kilometres;<LI> The satellite must be suitably placed in the sky to be readily seen;<LI> One should have an idea of what to look for. 
</OL>
<P>
Satellites come in a wide variety of orbits.  The type of orbit is chosen
depending on the mission requirements of that particular spacecraft.  Some
satellites may be in circular orbits where the altitude above the earth is
more or less constant over the entire orbit.  In other cases one might have
an elliptical orbit where the satellite might approach the earth to within a
few hundred kilometres and then travel far out into space before returning
earthwards.  The point closest to earth is known as PERIGEE, whilst the
furthest point is APOGEE.  Most of the satellites described in this article
have fairly circular orbits with the apogee height mostly under 1000
kilometres.  Obviously the shape or size of the orbit determines the time
the satellite takes to complete one orbit -- this is known as the orbital
PERIOD and can be as low as 88 minutes (anything lower than that means the
satellite is very close to falling out of orbit), or as high as several days
in some cases. However, most satellites will have a period of about 100
minutes, or slightly less.
<P>

<center><img src="shadow.gif" alt="Earth's shadow drawing" width=600 height=478 border=0><br>
<STRONG>Figure 2:</STRONG> <small>To be visible, a satellite must be illuminated by the Sun against a dark sky.<br>(Source: <EM>Observing Earth Satellites,</EM> by D.
King-Hele, MacMillan 1966)</small></center>

<P>
Another important parameter is the INCLINATION, the angle that the orbital 
plane makes with the earth's equator.  
 Whilst a satellite orbits, the earth is spinning on its own axis so it
should be easy to see that sometimes an observer on the earth's surface will
see the satellite moving in a particular direction, but half an orbit later
the satellite will be moving the opposite way.  If the plane of the
satellite's orbit does not pass near to your location then you cannot see
the satellite since it will be below your horizon.  If the inclination is
equal to or greater than your latitude then you will see the satellite at
some time or other, depending on where you are with respect to the plane of
the orbit.
<P>
Whilst the satellite is whizzing around the earth, you are spinning along
with the earth inside the orbital plane, so sometimes the satellite might be
passing over in daylight, other times in the middle of the night.  Earlier
it was stated that one's latitude must be less than or equal to the
satellite's inclination -- there is some leeway as the satellite is above
the earth's surface and can be seen some distance away when at low
elevations - (elevation is the angle above the horizon with 0 degrees being
on the horizon and 90 degrees directly overhead).  If the inclination is,
say 28 degrees, and your latitude is also 28 degrees then the satellite can,
under optimum conditions, pass straight overhead.  If however you are at 35
degrees latitude south and the inclination is 28 degrees then it should be
clear that the satellite, at its closest to you, will always pass north of
you and that overhead passes are not possible.  Roughly speaking, one must
be at a latitude within about 15 degrees of the orbital inclination for
visibility to be possible.  When the inclination is greater than one's
latitude, the orbital plane will intersect your location at some time or
other.  When the inclination is around 70 degrees or higher, then you will
see the satellite travelling south to north or, if on the other side of the
orbital track, moving north to south.  It should also be apparent that for
inclinations close to one's latitude you can only have the satellite
travelling from west to east since all satellites (except for a few cases
which we can ignore) follow a west-to-east path in the sky.  This is because
most launches make use of the earth's rotational velocity to reduce the
launch energy requirements and launch with an eastward component.
<P>
<h2><A NAME="SECTION00030000000000000000">3. Visibility of Artificial Satellites</A></h2>
<P>
To see an artificial satellite with the naked eye requires the satellite
to be physically quite large or possess some other attribute that will draw
the observer's attention.  Besides the actual physical size one has to
bear in mind the distance of the satellite from the observer since satellites
orbit the earth at widely different heights.  The brightness of a satellite is
measured in the astronomical `magnitude' scale.
An exceptionally bright satellite has a magnitude of +1,  whilst a satellite
that is barely visible to the naked eye will be about magnitude +5 or +6. 
A pair of good binoculars will enable 
one to see satellites down to about magnitude +8 under good conditions.
<P>
In order to spot a satellite with casual random looking it is necessary for 
the satellite to have an appreciable apparent speed at 
which it travels across the sky.  This speed is a function of the satellite's 
distance from the observer,  referred to as `range.'  When the satellite is
directly overhead it will usually be at its closest to the observer and
have its greatest apparent speed.
As the satellite's elevation decreases, it draws further
away from the observer and appears to move slower.  It also decreases in 
brightness on account of the increased range.  By the time the satellite is
near the horizon it will be moving much slower and may be so faint that one 
may not pick it up easily, so the best place to look is above an elevation
of about 45 degrees.  A satellite at an
altitude of 300 kilometres has an angular velocity overhead which is twenty 
times faster than at the horizon.
<P>
Satellites higher than about 3000 kilometres move very slowly,  even when
directly overhead, and are not easily picked up at random unless the observer
happens to be looking directly at the satellite when it passes close to a
star.
A phenomenon that will be noticed while looking for
satellites is that eventually all the stars appear to be moving - this is
a result of looking too long and straining the eyes.  It is better to relax and
not concentrate on a particular area for too long.  Another phenomenon that
will be noticed is that the observed satellite may appear to move across the
sky in a jerky or slightly zig-zag motion -- this is caused by the eye not moving
smoothly when changing the point of view.
<P>
Even if a satellite meets all the other visibility requirements it could
still be difficult to observe.  Like the moon, artificial satellites  also
go through phases. This produces
a `phase angle,' which is the angle between the sun and satellite as seen by
the observer on the earth's surface. Satellites are not normally observable at
a phase angle near zero degrees (corresponding to new moon), and depending
on the height of the satellite,  the phase angle remains in the range 50 to 
130 degrees with a mean value of around 90 degrees.  At a phase angle of
50 degrees the satellite is almost 2 magnitudes fainter than its maximum
possible brightness,  whilst at 130 degrees phase angle it is only about
0.25 magnitudes fainter than its maximum brightness which occurs at a phase
angle of 180 degrees.  Clearly, a satellite
cannot be seen at a phase angle of 180 degrees since it would then be on
the opposite site of the earth to the sun and would consequently not be 
illuminated, but in eclipse.
<P>

<center><img src="hi_i-ps1.gif" alt="Satellite visibility diagram" width=462 height=441 border=0><br>
<STRONG>Figure 3:</STRONG> <small>The circle of visibility of a satellite from the ground depends on its altitude. The area of visibility is the area of the circle in the dark hemisphere. In the example above the satellite is visible from a small
area in the south Atlantic.</small></center>

<P>
As the satellite crosses the sky its phase angle changes and the brightness
will be seen to vary quite noticeably.  In addition to this change there are
other factors which may cause the brightness to change rapidly. It has been
found that most satellites have uncontrolled rotation about an off-centre
(with respect to the body of the satellite) axis. The spin axis usually
varies little during the course of an orbit, but it undergoes a slow
precession over a length of time. The rate of spin or tumble decreases
slowly under the action of magnetic and aerodynamic damping.
<P>
Satellites and spent rockets observed in the eastern part of the sky after 
sunset may appear steady,  yet when in the western part of the sky they may 
start flashing, sometimes with invisible minima. This is 
due to specular reflection causing brightening when the angle of
incidence from the sun to the satellite is equal to the angle of reflection
from the satellite to the observer and the sun catches a shiny satellite 
surface as it spins or tumbles. In addition, external fixtures such as aerials and
de-spin weights, 
solar panels, <EM>etc.</EM>, can also cause bright flashes.
<P>
Some 
satellites exhibit very complex flash patterns which  change
quite  noticeably over a
period of time.  Spherically-shaped satellites appear either steady or 
scintillate rather rapidly, which indicates the rotation of a sphere that 
has external protuberances.  A remarkable similarity exists between 
the flash patterns of rocket 
casings in low orbits with similar rocket casings in higher 
orbits having a much more rapid tumble -- this is probably due to the damping 
effect of the earth's magnetic field.  Rocket casings have a distinctive and 
more prominent appearance than satellites,  usually flashing 
or tumbling very rapidly with flashes separated by between 0.5 and 2 
seconds,  while satellites exhibit a smaller range of brightnesses and are 
usually steady. 
Most satellites spotted casually are in fact rocket casings.
<P>
It frequently happens that a satellite is confused with aircraft
navigation lights and even the most experienced observer occasionally gets
caught. What must be remembered is that satellites appear whitish in colour
with perhaps a tinge of yellow or orange, especially at low elevations,
and that satellites do not change direction.  Obviously, green and red
lights are `out'!  However, from time to time satellites may
look a little different to what we are accustomed to.  The following are
some examples: 
<UL><LI> A whitish cloud-like object may be seen close to the space
shuttle. This is most probably due to either a minor orbital change or the
dumping of water into space from the shuttle itself. If one sees a slow moving
cloud it is probably due to a rocket burn taking place to change the orbit
of a satellite, for example when a geostationary satellite is launched it
undergoes several `transfer' burns to reach its final orbit.<LI> Another rather unusual sight that many people saw recently was a `stick'
travelling through space. This was the tether attached to a satellite that
had broken free of the space shuttle during a test. (There is another tethered
satellite where two satellites are joined together by a thin cable but it is too faint to be seen without optical aid).<LI> A frequent naked-eye sighting
is that of three objects flying in formation. This is a classified
US military object and the three satellites fly in formation as they monitor
naval activity. There are several such formations of satellites but only
this one is bright enough to be seen without optical aid. 
</UL><h2><A NAME="SECTION00040000000000000000">4. Observing Hints</A></h2>
<P>
In order to observe a satellite visually the observing conditions must be suitable. 
Since one needs a relatively high contrast between the sky and the satellite it
is rather pointless looking for the fainter satellites with a bright moon in
the sky. As a rule, one looses about 4 to 5 magnitudes when trying to 
observe with a full moon in the sky.  Generally, if the sky is covered in thin
cirrus or smoke, one's chances are somewhat reduced and one can only expect to
see the really bright satellites,  so ideally one needs a dark sky away from city
lights and pollution and little or no moonlight.
<P>
With all the above restrictions one might think it is pointless looking for
satellites, but this is not the case.  Most of us are not fortunate enough to have
dark skies unless we take a long drive out into the country, so we have to
cope with less than ideal conditions.  This does not mean that one has to forget
about seeing a satellite and I will now indicate to the potential
observer how to optimize the chances of seeing a satellite.
<P>
Well over 20,000 objects have been placed in orbit about the earth, of which
about half are still orbiting,  the rest having re-entered the earth's atmosphere
and burnt up.  This still leaves more than 10,000 objects of which a good 
percentage are large enough to be seen with the naked eye. The slightest
optical aid will increase this number considerably,  so one stands a
reasonable chance of being able to see several hundred satellites. In fact,
under reasonably good conditions, the
casual observer  can expect to see several
satellites per hour. On one occasion I was able to observe seven unpredicted
satellites in the space of five minutes in different parts of 
the sky.
<P>
The requirement of the satellite having to be above the earth's shadow and also
being solar illuminated should indicate to the potential observer that the
best time to look is during the first two hours after twilight and the last two
hours before dawn.  As a rough guide the sun should be about 12 degrees below
the horizon at start/end of the observing period.
<P>
Recalling the effects of phase on the brightness,  if observing in the
evening, the best direction is to face towards the east, <EM>i.e.</EM> with
your back to where the sun has set, and looking from about halfway up from
the eastern horizon to overhead.  As the evening progresses the earth's
shadow will creep up the sky from the eastern horizon and increase its
elevation until at about local midnight, where it will be at its highest;
thereafter the shadow starts lifting in the east as the sun approaches dawn.
In the case of early morning observing the best place to look is high up in
a westerly direction.
<P>
The height of the earth's shadow above the earth is a function of the
position of the sun and the observer and it should be apparent that the
earth's shadow will reach its lowest level when the sun appears highest in
the sky -- that is, in mid-summer.  In winter the earth's shadow extends
further and in view of this, and the cold winter nights, the
winter months are not the ideal time to look for satellites.  In summer it
is possible for most satellites to be visible at any time during the night
in some part of the sky and in the southern hemisphere, for example, the sun
will be in the south so the satellites will generally be clear of shadows
towards a southern direction, whilst in winter the shadow will be least
towards the northern part of the sky.
<P>
Having established the best time to look, the next question is in which 
direction to look.  Satellites have been launched into virtually every
conceivable type of orbit and on this basis one would expect satellites in
any direction.  However,
the majority of satellites are in polar orbits, so they appear to be either 
travelling in a southerly to northerly direction or going the other way.  There
are also a few large satellites in low-inclination orbits and they
have a westerly to easterly movement.  There are a few that travel from
east to west but they are probably too faint for the novice to worry about,
 although it is amusing to see a satellite `going the wrong way.'
<P>
If you want to observe the low-inclination satellites, then the best direction
to look is towards the equator. As
the inclination of the orbit approaches one's latitude the orbital plane will
appear higher in the sky so that when the inclination is equal to the latitude
the satellite passes directly overhead.
<P>
As the inclination increases, the satellite's motion assumes a greater
north-south component. A satellite with an inclination near 90 degrees is
called a polar orbiter since it passes over the earth's poles.
It is quite possible to see the same polar orbiting satellite moving 
in opposite directions by viewing two passes about 
about half a day apart.  On
one pass it will move from (say) south to north,  and then approximately ten
hours later it will appear to move from north to south.
<P>
Unless the satellite is fairly high above the earth's surface, say about
800-1000 kilometres, it may be possible to observe only one pass in an
observing spell of several hours.  If, for example, the satellite was
observed to be moving in a polar orbit and was spotted in the western sky it
is unlikely that one will see the next pass, which will occur even more due
west of the observer and probably thus below the horizon.  If, however, a
pass is observed low in the east in the early evening it is quite possible
to see a second pass about 90 minutes later with the satellite now appearing
in the western sky.  Since the minimum orbital period is about 87 minutes
this fixes the minimum time spacing between successive passes.
<P>
The length of time that a satellite may be observed on a pass or `transit'
depends on whether the satellite is clear of the earth's shadow during the entire pass
and on its orbiting altitude.  If the satellite is only 200 kilometres above
the earth it will traverse the sky from horizon to horizon in about seven
minutes, whilst for a height of 500 kilometres this time increases to about
eleven minutes.  If the orbiting altitude is about 2000 kilometres then the
satellite will take about 29 minutes to cross the sky,  so if one assumes
that the orbit is circular one can make a good guess as to the satellite's
altitude by noting how long it takes to cross the sky.
<P>
The next  article will deal with satellite tracking and what the amateur can
do.  It will also deal with predicting passes so one does not have to waste
time looking for a `casual' satellite. A list of useful Internet WWW sites,
 where more information may be obtained, will also be supplied.  Good spotting
in the meantime!

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