by Michael A. Earl

 INTRODUCTION
 

     Everywhere you go in the civilized world, you see them. On rooftops, jutting out of walls, and pointing at the sky, those little grey satellite dishes are everywhere. They seem to vigorously reproduce themselves, multiplying more and more every passing year. They represent the ever-expanding satellite communications universe in which we depend on every single day without knowing it. In fact, we take a specific type of satellite orbit for granted every single day without knowing how it came to be, how it works, or what its future might be (or not be). Have you ever wondered why your satellite dish is pointing at a specific azimuth and altitude? Have you wondered why you rarely have to adjust your dish's position? Have you wondered what this has to do with astronomy (like, maybe right now)? The answers are simpler than you think and form the basic principles of why your satellite dish is capable of delivering your satellite services reliably.
 

A SEA OF TELEVISION AERIALS

     Back in the 1940s and 50s, television was being introduced into homes all over North America. In order to receive the television stations' signals, you required a television antenna. So, up they went, all over the country, normally on the roofs of the houses. They were big metal structures that had to be placed high up to pick up the television (VHF and UHF) signals that had a very limited range. A problem with the aerials is that they had to be oriented in a specific way, depending on the originating TV transmitter location, the signal direction and the strength. There was also that very disturbing picture of the father struggling (sometimes violently) with the "rabbit ears" desperately trying to get the picture to stop wrinkling up and snowing over.
     Then along came cable TV in the 1960's. Suddenly, households no longer required those straggly, intrusive metal aerials. Many were taken down in favor of the better reception cable TV provided. However, the problem with cable was that it required, well, cable! It had to be strung for miles along telephone poles, and later underground, and amplified every few miles to counteract the inevitable line losses. With all these problems, cable TV has endured extremely well for the past 40 years or so. Cable TV is still a problem for those living in very remote areas. The cost of all that cable is not very economical, nor practical. So, until the mid 1980's many remote dwellings had to rely on the good old aerial on the roof.
 

THE FIRST PROPOSAL OF WORLDWIDE SATELLITE BROADCASTING

     One constant that has prevailed in history is the requirement for faster communications. The so-called "need to know" is one driving force behind any communication empire, oh yes, the money too! From Morse to Marconi, communications became more reliable, faster, and most importantly, timely (and of course profitable). So, it was only a matter of time until a theory of using orbiting communication relays was put forth.
     There is some controversy over who was the first to propose a satellite communications infrastructure, but the credit is normally given to Sir Arthur C. Clarke, author of "2001, a Space Odyssey". In October 1945, he published an article entitled "Extra-terrestrial Relays" in which he proposed that three satellites, placed 120 degrees apart, within a specific orbit radius over the Earth's equator would be able to provide reliable worldwide radio communications. He argued that there was a specific orbit radius such that the satellite will orbit the Earth in exactly the same time as the Earth rotates on its axis, thus keeping the three satellites over the same locations on Earth at all times. It is worth noting that his article was published 12 years before Sputnik, the first artificial satellite, was launched. What a pioneer indeed!
 

Figure 1: Sir Arthur C. Clarke's original drawing, illustrating the proposal of placing three
satellites in orbit to relay radio transmissions to potential customers all over the world.
 

     One way to explain his unique orbit proposal is to use Kepler's Third Law of orbital mechanics. It basically states that the square of the period of orbit is proportional to the cube of the average distance of the object from the parent body. Check it out! If you compare the ratio of the square of the period vs. the cube of the average distance of the planets from the Sun, you should get nearly the same number for all the nine (or ten) planets! We can use the Earth's only natural satellite, the Moon, to determine the approximate orbit radius the hypothetical satellite would need to orbit in synch with the Earth's rotation period (about 24 hours).

a_moon = average distance from the Moon to the center of the Earth = 384,400 km (Observer's Handbook)
a_sat = average distance from the satellite to the center of the Earth = ??????
T_moon = period of the Moon's orbit about Earth = 27.322 days (Observer's Handbook)
T_sat = period of the satellite's orbit about Earth = 1 day

Using Kepler's Third Law, the following is true:

a³_sat / T²_sat = a³_moon / T²_moon
OR
a_sat = (a³_moon / T²_moon x T²_sat)^1/3

     If you use the values above in the equation derived, you will find that the approximate ideal orbit radius of the Clarke satellite is about 42,330km. If you subtract the Earth's equatorial radius (6378km), you will find that the satellites would be about 36,000km above the Earth's surface. If the satellite was placed outside this orbit radius, it would orbit too slowly, and lag behind the Earth's rotation. Conversely, if it was closer than that, it would be orbiting too fast. Thus began the "Clarke Belt".
 

THE CLARKE BELT AND YOU

     So, what exactly does the Clarke Belt have to do with your satellite dish? By now you might have deduced that if the satellite appears stationary with respect to the Earth's surface, you will not have to move your satellite dish to receive signals. You would be right! If you could see a Clarke Belt satellite with your naked eye, you would see that the satellite would seem to hang in the same location in the sky at all times. Remember that the satellite orbits with the same period as the Earth's rotation, so it would appear to be stationary in the sky. Today, the Clarke Belt is called the Geostationary Belt, which is a much more descriptive name.
     Every single satellite dish you see in your neighbourhood is oriented at a satellite orbiting in the Geostationary (Clarke) Belt. Despite the modern claims of "high-tech", the original proposal for our modern satellite communications infrastructure was published at the end of World War II. Not only does the geostationary satellite orbit make your life easier, but it also simplifies the satellite controller's life by knowing just where the satellite is at all times in order to communicate with it reliably. In other words, it does not appear to be a moving target, at least not in the short term anyway.
    

THE 23.934 HOUR DAY

     We were taught in school that one day is exactly 24 hours, and we still believe that today. For most, that will do just fine, however, there is a problem with geostationary satellites orbiting at a period of exactly 24 hours. They would fall behind, and therefore the satellite would drift slowly westward from day to day. This would cause customers to require to change the positions of their satellite dishes constantly throughout the year, and endure massive blind spots as the satellite passes below their local horizon for over half the year.
     Why, do you ask, is this true? Earth rotates on its axis in 24 hours, does it not? This depends on what you are measuring the rotation against. The 24-hour day is based on the Sun's apparent position in the sky. As the Earth rotates on its axis, it is also orbiting the Sun. In other words, the Sun's apparent position with respect to the sky background is dependent on the Earth's rotation AND its motion in its orbit. Therefore, we cannot rely on the Sun's apparent position as a reference point for its true rotation period. So, what can we use as an ideal Earth rotation period, and therefore geostationary satellite orbit period?
     Astronomers have observed for centuries that the stars rise (and therefore set) about 4 minutes earlier every passing day. What clock are we basing this on? We use timepieces that are set to solar time, in which exactly 24 hours per day is used as the standard. What if we had used the stellar background as the benchmark for our standard day? The great thing about using the stellar background is that the Earth's orbital motion is a negligible component. Why? Because the stars are too far away for this motion to affect their observed positions. In other words, the parallax is much to small to matter. What time span is necessary for the stars to be in exactly the same positions in the sky from night to night? The answer is exactly 23 hours, 56 minutes and 4 seconds if measured in solar time (about 4 minutes less!). So 24 hours of this specific time standard (called sidereal time, by the way) is 23 hours, 56 minutes and 4 seconds of solar time.
 

Figure 2: The Solar Day vs. the the Sidereal Day. Two observers, denoted by the green and red dots are on the opposite sides of the world and viewing the Sun and a distant star, respectively. At t=0, the observers take a note of the Sun's position and the distant star's position, respectively. In 24 hours, in which the Earth has both rotated and moved in its orbit, Observer Green will see the Sun at the same location in the sky as he/she saw it 24 hours earlier. Observer Red, however, will not see the distant star in the same position. He/she will see the star shifted slightly westward from the day before. Observer Red will actually observe the distant star reaching the same position 4 minutes before Observer Green sees the Sun reach its last observed position. This is because the Earth has to spin a little more to compensate for its new position in its orbit. Observer Green will have seen the Solar Day, while Observer Red will have seen the Sidereal Day.
 

     So, the ideal geostationary orbit period must be close to 23 hours, 56 minutes and 4 seconds long (with respect to the solar clock) in order for the satellites to remain in their positions with respect to the fixed satellite dishes on Earth. How does this affect the geostationary orbit altitude calculated above? It should have to be slightly closer for it to orbit in a sidereal day, and indeed it is; 35,875km to be exact, which is about 125km less than the 36,000km calculated above.
 

A SEA OF SATELLITE DISHES - THE "GREAT" DISH HUNTING EXPEDITION

     In order to truly appreciate just how much we depend on satellites in our daily lives, I took a 2-hour stroll around my neighbourhood and had a look at the various households to see which ones had satellite dishes installed. I brought my camera along to get a few images of them, while trying to avoid getting unwanted attention from the police. What I saw was astounding. In just two hours of walking, I saw approximately 50 satellite dishes. The two biggest names were Bell ExpressVu and Star Choice, both of which are receiving their signals from several Canadian-owned satellites.
 

Figure 3: A typical Bell ExpressVu and Star Choice satellite dish in Ottawa. Most of the satellite dishes that were observed were from one of these two companies. Notice the different shapes of the dishes.
 

     I know what you're thinking. Walking around taking images of satellite dishes is a very strange thing for someone to do with his/her time. My excuse is that the persistent clouds made me do it. What else can an astronomer do? However, the Sun did come out for a few hours, and I am very glad it did, as it gave me an idea for a unique experiment involving satellite dishes.
     How do you prove that specific satellite dishes from a specific satellite dish provider is pointing at the same satellite? I was very fortunate to see that the Sun was in the right position such that the shadow of the dish amplifier (that little arm in front of the dish) was cast onto the dish itself. How is this important? If specific dishes were pointing at a specific satellite located at a specific azimuth and altitude, then wouldn't all the shadows be cast on the same area of the dishes at one specific time? Take a look at Figures 4 and 5.
 

Figure 4: Take a look at these three different Bell ExpressVu satellite dishes. Each are located in a different area of Orleans (Ottawa). Take a look at the shadow cast by their signal amplifiers. In each case, the shadow lies in the lower right-hand corner of the dish. This indicates that these three dishes are pointing at the same azimuth and altitude, and therefore the same satellite.
 

Figure 5: Take a look at these two different Star Choice satellite dishes. They are located in two different area of Orleans (Ottawa). Take a look at the shadow cast by their signal amplifiers. In each case, the shadow lies near the bottom of the dish. This indicates that these dishes are pointing at the same azimuth and altitude, and therefore the same satellite, but at a different satellite than the Bell ExpressVu dishes.
 

   
Figure 6: Can you spot the seven satellite dishes in the image? This image is a composite of two images of a single block of houses near the northern end of Orleans Boulevard in Ottawa (near the Ottawa River). This single image illustrates our dependence on the geostationary satellite population, more specifically, on five of them: Nimiq 1, Nimiq 2, Nimiq 3, Anik F1-R and Anik F2. All the satellite dishes shown are pointing at one of these five satellites, as are most of those in the Ottawa area, and all of southern Canada.
 

DISH-ORIENTED?

      If you look at satellite dishes in the Ottawa area, you might have noticed that they are all pointing to a rather low altitude above the horizon. You will also notice that none of them are pointing at the zenith (those that are working anyway). What exactly is going on? Remember that all the geostationary satellites are orbiting about the Earth's equator at about 35,875km from the surface, and this is a clue as to why you have to point your dish to a low altitude. The dish's orientation is also dependent on your latitude on Earth. In the northern hemisphere, the further North you are, the lower your dish will need to be pointed to access a specific geostationary satellite. There is a point at which you are so far North that the altitude of the satellite is too low to be useful because of atmospheric disturbances as well as natural and man-made obstructions. In this case, a different orbit strategy is utilized (see the Satellite Radio section).
 

Figure 7: Why satellite dishes in the Ottawa area are pointed at such a  low altitude. An observer on Earth (depicted by the green dot) has a local horizon (the green line). The geostationary satellite (the red dot) is orbiting the Earth's equator (the red line). The satellite dish sees the geostationary satellite along the purple line of sight. The altitude is measured from the horizon to that line of sight. If the dish had been oriented to the observer's zenith, there would be no way the dish could pick up the satellite's signal. Only those living in the equatorial region would need to point their satellite dishes at their local zenith, and this is only if the satellite is positioned over their specific longitude. If you imagine this observer going further and further North, you will find that there is a point at which the satellite lies near or on that observer's horizon. At that point, the dish cannot see or access the satellite.
 

WHAT DOES YOUR DISH SEE?

     As you enjoy the services that your satellite TV provides, do you ever wonder what your satellite dish is seeing? Both Bell ExpressVu and Star Choice satellite services are relayed by satellites owned and operated by Telesat Canada. If you use Bell ExpressVu, your satellite dish is pointing at either the Nimiq 1 (and Nimiq 3, which is co-located) satellite, or the Nimiq 2 satellite. If you are using Star Choice, you are pointing your dish at either the new Anik F1-R (English-Canadian service) or Anik F2 (mainly French-Canadian service). See the reference table at the end of this article for specific angular location data for these particular geostationary satellites.
 

Figure 8: This is what your satellite dish sees. The stars streak by, while the two geostationary satellites (the two dots) appear motionless because of their orbit period is the same as the Earth's sidereal rotation period (23h 56m 4s). The two geostationary satellites shown are Anik F1 (bottom) and Anik F1-R (top). Anik F1 mainly services South America, while Anik F1-R services Canada for the Star Choice direct-to-home satellite service. Since these two satellites are positioned over the Earth's equator, each can service a different continent.
 

TODAY'S GEOSTATIONARY SATELLITE POPULATION

     At the present time, in 2006, there are approximately 250 active geostationary satellites orbiting the Earth. This is a far cry from the 3 satellites that Clarke had originally envisioned. Competition, innovation and engineering can greatly diversify a pioneering idea. They serve the entire world, from ABC TV to Zookeepers. Notice in Figure 9 that the satellites are clustered in three main areas: one over North and South America, another over Europe and Africa, and the third over Asia. If you check the suggested positions of the three geostationary satellites in Sir Arthur C. Clarke's proposal, they roughly correspond to these three areas.
 

Figure 9: Today's geostationary satellite population. There are approximately 250 individual satellites in this image, all serving specific regions of the world. Nimiq 1, 2 and 3, and Anik F1-R and F2 are located near the 90 degrees W portion of the belt, which gives them access to Canada. Sir Arthur C. Clarke's proposed positions for the geostationary satellites is labeled on this image. With the exception of the Asian region, the satellites cluster over the postulated zones very nicely. Note the large gap over the Pacific Ocean, and the thinner population over the Atlantic Ocean. It appears there is no purpose to have many geostationary satellites over such vast oceans.

SATELLITE RADIO

     Here's something you thought you would never read in an astronomy article. Howard Stern. Yes, Howard Stern. Why? Recently, Mr. Stern has announced that he will be broadcasting exclusively over Sirius Satellite Radio. Now, remember Sir Arthur C. Clarke's proposal. We have come full circle in the sense that the proposal to broadcast radio from geostationary satellites is now a reality. Mr. Stern's views about commercial radio aside, satellite radio services offer CD quality music anywhere in North America. This is different from commercial radio in the sense that you can listen to the same station wherever you are in the continent (even in your car!), as long as you have a satellite radio receiver (aha, there's the catch!).
     Sirius Satellite Radio uses (wait for it!) 3 satellites, just as Clarke had proposed, except that instead of orbiting directly above the Earth's equator, they orbit at an inclination of 63.5 degrees from the Earth's equator. This introduces a new concept called the "geosynchronous" orbit. What is the difference between a geostationary and a geosynchronous orbit? They both orbit in the same time as the Earth's rotation: 23h 56m 4s. The geostationary orbit is exclusively over the Earth's equator. The geosynchronous satellite can orbit within any plane (including equatorial). The geostationary orbit is circular, or a zero eccentricity. The geosynchronous orbit can have any eccentricity. In effect, all geostationary satellites are also geosynchronous, but not vice-versa.
     You can count on the geosynchronous orbiting satellite to appear in the same point in its orbit every 23 hours, 56 minutes and 4 seconds, but you cannot count on it being in the same point in the sky at all times, like geostationary satellites.
     Sirius' only major competitor, XM Satellite Radio, utilizes two co-located genuine geostationary satellites. Since it only services North America, there is no need for three or more, which might keep this particular service's costs low. Figure 10 and 11 illustrates the orbits of these two competing satellite radio providers.
     Disconcerting as it is to see Sir Arthur C. Clarke and Howard Stern mentioned in the same paragraph, they now have something in common. What interesting times we live in! Satellite radio has only increased our dependence on artificial satellites for our communications and entertainment.
 

Figure 10: The Sirius and XM satellite radio constellation orbits. The two co-located XM satellites are geostationary (equatorial, circular), while Sirius satellites are geosynchronous (63.5 degree plane, eccentricity of 0.27. The Sirius satellite constellation is better placed for northern region reception (such as the Arctic). This figure was generated by AGI's Satellite Tool Kit version 6.0.
 

Figure 11: The ground tracks of the XM and Sirius satellite radio constellations. The XM constellation consists of geostationary satellites, and as a consequence, they appear as small dots on the surface of the Earth. The arrow points to their location on the equator. The Sirius constellation consists of geosynchronous satellites favoring the North American continent. Their orbit eccentricity places them over North America for longer periods of time than they are over South America. This figure was generated by AGI's Satellite Tool Kit version 6.0.
 

     In short, just by looking at the sea of satellite dishes in your neighborhood, you can appreciate just how dependent everyday people are on geostationary satellites. Satellite radio will only deepen this dependence, if it catches on. The geostationary orbit was specifically designed for the convenience of both the satellite controller and customer.
     By the way, you might be wondering if I have a satellite dish or subscribe to satellite radio. My answer is no and no. Although I greatly appreciate the satellite community that makes direct-to-home satellite television broadcasting possible, I have already seen Gilligan's Island, although the reception was not as good at the time! As for music, I get that from somewhere else.
     So, when you are taking a stroll around your neighborhood and see a satellite dish, just remember how dependent it is on concepts in astronomy, such as the solar and sidereal days and all of Keplerian orbital mechanics. Hopefully, it will deepen your appreciation for our vast sea of dishes.

DISCLAIMERS

     This article is in no way meant as an advertisement for any of the following: Bell ExpressVu, Star Choice, Telesat, the satellite industry in general, AGI, the cable industry in general, Sirius, XM, Arthur C. Clarke, Howard Stern, or Gilligan's Island (sitcom or reality TV show). These were all merely used as examples and descriptive tools. There, I think that covers everything!
 

REFERENCE TABLE FOR MENTIONED GEOSTATIONARY SATELLITES
(AS OF JANUARY 9, 2006)

This page last modified: January 9, 2006