You see them everywhere you go in the civilized world; on rooftops, jutting out of walls, and pointing at the sky, those little 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 and take for granted every single day.

Take a look at your satellite dish. Have you ever wondered why it is pointing at a specific point in the sky and why you don't have to move it? The answers form the basic principles of why your satellite dish is capable of delivering your satellite services reliably.

Our world constantly requires faster and broader communications. From Morse (telegraph) to Marconi (radio), communications became faster, more reliable and most importantly profitable.

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". Before "2001" (actually In October 1945) he published an article in "Wireless World" entitled "Extra-terrestrial Relays" in which he proposed that three satellites, placed 120 degrees apart, orbiting at a specific orbit altitude over the Earth's equator would be able to provide reliable worldwide radio communications. He argued that there was a specific orbit altitude such that the satellite will orbit the Earth with exactly the same period as the Earth's axial rotation, 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!
 

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

     One way to explain his unique orbit proposal is to use Kepler's Third Law of orbital mechanics:

"The square of the period of orbit is proportional to the cube of the average distance of the object from the parent body"

If you compared the ratios of the square of the period vs. the cube of the average distance of all the objects orbiting the Sun, you should get nearly the same number! 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
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
T_sat       = period of the Earth's axial rotation = 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 to solve for a_sat, you will find that the hypothetical 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 quickly. The "Clarke Belt" would have to be very thin!

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 continuously move your satellite dish to receive the satellite's 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 axial rotation. Today, the Clarke Belt is better known as the Geostationary Belt.

All the working satellite dishes you see in your neighbourhood are oriented at a satellite orbiting within the Geostationary Belt. Not only does the geostationary orbit make your life easier, it also simplifies the tracking and control of the satellite.

Most of us were taught that the Earth's day is exactly 24 hours long. This refers to the amount of time for the Sun to appear in the same spot in the sky as it was yesterday. However, most forget that the Earth is not only rotating on an axis, but also orbiting the Sun! The Earth moves enough in its orbit in 24 hours such that the Sun will appear in a slightly different position amongst the stellar background. 24 hours refers to the "Solar Day", and is not exactly the real Earth's rotation time. If we used the orbit radius calculated earlier, the satellite would slowly fall behind and eventually be inaccessible as the satellite slowly drifts 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.

This "day" depends on what you are measuring the Earth's rotation against. 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. 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) 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 green and red observers take a note of the Sun's position and the distant star's position, respectively. At t=24 hours, 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, but 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.
 

The ideal geostationary orbit period must be 23 hours, 56 minutes and 4 seconds 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; 125km less than the 36,000km calculated for the solar day period.
 
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. What I saw was astounding. In just two hours of walking, I saw approximately 50 satellite dishes. The two biggest (Canadian) names were Bell ExpressVu and Star Choice, both of which are receiving their signals from a handful of Canadian-owned geostationary satellites.
 

Figure 3: Typical Bell ExpressVu and Star Choice satellite dishes in Ottawa, Ontario Canada.

How do you prove that the satellite dishes from a specific provider are all pointing at the same satellite? I was very fortunate that the Sun was shining. 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 nearly 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.
 

   
Figure 6: Can you spot the seven satellite dishes in the image? This image is of a single block of houses on Orleans Boulevard in Ottawa. This single image illustrates our dependence on the geostationary satellite population.
 

If you take a look at satellite dishes anywhere in North America, you might have noticed that none of them are pointing to a high angle above the horizon. All the geostationary satellites are orbiting the Earth's equator at an altitude of 35,875km. As you travel northward away from the equator, your satellite dish will be pointing at a lower angle above the horizon. There is a limit to how far north you can travel and still access a geostationary satellite. North of the Arctic Circle, the angle of the satellite is too low to be useful because of atmospheric disturbances.
 

Figure 7: A satellite dish on Earth (green dot) has a local horizon (green line). The geostationary satellite (red dot) is orbiting the Earth's equator (thin red line on Earth). The satellite dish "sees" the geostationary satellite along its line of sight (purple line). The angle is measured from the horizon to the dish's line of sight. If you imagine the dish traveling north away from the equator, the angle will decrease until the satellite will appear on the dish's horizon. At that point, the dish cannot receive signals from the satellite.
 

Figure 8: This is what your satellite dish sees every day. The streaks are stars. The dots are the geostationary satellites Anik F1 and Anik F1-R.
 

Figure 9 depicts the current geostationary satellite population as viewed from the Earth's north pole. Note that the satellites are roughly clustered in three main areas: one cluster over North and South America, another cluster over Europe and Africa, and another cluster over Asia and Australia. The positions of these clusters roughly match the initially proposed locations of the first Clarke Belt satellites!
 

Figure 9: The current geostationary satellite population. There are approximately 250 individual satellites in this image, all serving specific regions of the world. Sir Arthur C. Clarke's proposed positions for the geostationary satellites are indicated by the yellow lines. With the exception of the Asian region, the satellites cluster over the initially proposed positions nicely. Note the large gap over the Pacific Ocean, and the thinner population over the Atlantic Ocean. It appears there is little purpose to place many geostationary satellites over such vast oceans.