Part 1 of Section 1 (SATELLITE COMMUNICATIONS - A SHORT COURSE) of SATELLITE COMMUNICATIONS, prepared by Dr. Regis Leonard for NASA Lewis Research Center
For 10,000 years (or 20,000 or 50,000 or since he was first able to lift his eyes upward) man has wondered about questions such as "What holds the sun up in the sky?", "Why doesn't the moon fall on us?", and "How do they (the sun and the moon) return from the far west back to the far east to rise again each day?" Most of the answers which men put forth in those 10,000 or 20,000 or 50,000 years we now classify as superstition, mythology, or pagan religion. It is only in the last 300 years that we have developed a scientific description of how those bodies travel. Our description of course is based on fundamental laws put forth by the English genius Sir Isaac Newton in the late 17th century.
Please note, we say we have a "description" of how the sun and moon travel - not an "explanation." Even Sir Isaac, after publishing his theory of gravitation, made that distinction. Although his theory was an accurate description of how gravity works and was consistent with every bit of experimental evidence available at that time, he was careful to disavow any knowledge of why gravity worked that way. |
The first of Newton's laws, which was a logical extension of earlier work by Johannes Kepler, proposed that every bit of matter in the universe attracts every other bit of matter with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between the two bits. That is, larger masses attract more strongly and the attraction gets weaker as the bodies are moved farther apart.
OPTIONAL FOR THE MATHEMATICALLY INCLINED Stated mathematically, Newton's law of gravity
says that the magnitude of the attractive force (between the earth and the sun for
example) is given by: where: |
Newton's law of gravity means that the sun pulls on the earth (and every other planet for that matter) and the earth pulls on the sun. Furthermore, since both are quite large (by our standards at least) the force must also be quite large. The question which every student asks (well, most students anyway) is, "If the sun and the planets are pulling on each other with such a large force, why don't the planets fall into the sun?" The answer is simply (are you ready for this?)
THEY ARE! The Earth, Mars, Venus, Jupiter and Saturn are continuously falling into the Sun. The Moon is continuously falling into the Earth.
Our salvation is that they are also moving
"sideways" with a sufficiently large velocity that by the time the earth has
fallen the 93,000,000 miles to the sun it has also moved "sideways" about
93,000,000 miles - far enough to miss the sun. By the time the moon has fallen the
240,000 miles to the earth, it has moved sideways about 240,000 miles - far enough to miss
the earth. This process is repeated continuously as the earth (and all the other planets)
make their apparently unending trips around the sun and the moon makes its trips around
the earth. A planet, or any other body, which finds itself at any distance from the
sun with no "sideways" velocity will quickly fall without
missing the sun, will be drawn into the sun's interior and will be cooked to
well-done. Only our sideways motion (physicists call it our "angular velocity"
) saves us. The same of course is true for the moon, which would fall to earth but for its
angular velocity. This is illustrated in the drawing below.
The Earth Orbits the Sun With Angular Velocity
People sometimes (erroneously) speak of orbiting
objects as having "escaped" the effects of gravity, since passengers experience
an apparent weightlessness. Be assured, however, that the force of gravity is at
work. Were it suddenly to be turned off, the object in question would instantly leave its
circular orbit, take up a straight line trajectory, which, in the case of the
earth, would leave it about 50 billion miles from the sun after just one century. Hence
the gravitational force between the sun and the earth holds the earth in its
orbit. This is shown in the drawing below, where the earth was happily orbiting the sun
until it reached point A, where the force of gravity was suddenly turned off.
The Earth No Longer Orbits the Sun if Gravity is Switched Off
The apparent weightlessness experienced by the orbiting passenger is the same weightlessness which he would feel in a falling elevator or an amusement park ride. The earth orbiting the sun or the moon orbiting the earth might be compared to a rock on the end of a string which you swing in a circle around your head. The string holds the rock in place and is continuously pulling it toward your head. Because the rock is moving sideways however, it always misses your head. Were the string to be suddenly broken, the rock would be released from its orbit and fly off in a straight line, just as earth did in the drawing above.
One question which one might ask is " Does the time required to complete an orbit depend on the distance at which the object is orbiting?" In fact, Kepler answered this question several hundred years ago, using the data of an earlier astronomer, Tycho Brahe.
Except for Kepler's analysis of his data, it is possible that Tycho Brahe would be best remembered today as a drinker and womanizer. However, without Brahe's unbelievably careful measurements of the planetary positions over many years, Kepler's revolutionary proposals would have been impossible. |
After years of trial and error analysis (by hand - no computers, no calculators) , Kepler discovered that the quantity R3 / T2 was the same for every planet in our solar system. (R is the distance at which a planet orbits the sun, T is the time required for one complete trip around the sun.)Hence, an object which orbits at a larger distance will require longer to complete one orbit than one which is orbiting at a smaller distance. One can understand this at least qualitatively in terms of our "falling and missing" model. The planet which is at a larger distance requires longer to fall to where it would strike the sun. As a result, it takes a longer time to complete the � trip around the sun which is necessary to make a circular orbit.
OPTIONAL FOR THE MATHEMATICALLY INCLINED Kepler's laws and the dependence of period on
radius are simple consequences of Newton's second law of motion and Newton's law of
gravitation. We know that the second law (which every physics student should recognize)
says: |
Very soon after Newton's laws were published, people realized that in principle it should be possible to launch an artificial satellite which would orbit the earth just as the moon does. A simple calculation, however, using the equations which we developed above, will show that an artificial satellite, orbiting near the surface of the earth (R = 4000 miles) will have a period of approximately 90 minutes. This corresponds to a sideways velocity (needed in order to "miss" the earth as it falls), of approximately 17,000 miles/hour (that's about 5 miles/second) . To visualize the "missing the earth" feature, let's imagine a cannon firing a cannonball.
Launching an Artificial Satellite
In the first frame of the cartoon, we see it firing fairly weakly. The cannonball describes a parabolic arc as we expect and lands perhaps a few hundred yards away. In the second frame, we bring up a little larger cannon, load a little more powder and shoot a little farther. The ball lands perhaps a few hundred miles away. We can see just a little of the earth's curvature, but it doesn't really affect anything. In the third frame, we use our super-shooter and the cannonball is shot hard enough that it travels several thousand miles. Clearly the curvature of the earth has had an effect. The ball travels much farther than it would have had the earth been flat. Finally, our mega-super-big cannon fires the cannonball at the unbelievable velocity of 5 miles/second or nearly 17,000 miles/hour. (Remember - the fastest race cars can make 250 miles/hour. The fastest jet planes can do a 2 or 3 thousand miles/hour.) The result of this prodigious shot is that the ball misses the earth as it falls. Nevertheless, the earth's gravitational pull causes it to continuously change direction and continuously fall. The result is a "cannonball" which is orbiting the earth. In the absence of gravity, however, the original throw (even the shortest, slow one) would have continued in a straight line, leaving the earth far behind.
For many years, such a velocity was unthinkable and the artificial satellite remained a dream. Eventually, however, the technology (rocket engines, guidance systems, etc.) caught up with the concept, largely as a result of weapons research started by the Germans during the second World War. Finally, in 1957, the first artificial satellite, called Sputnik, was launched by the Soviets. Consisting of little more than a spherical case with a radio transmitter, it caused quite a stir. Americans were fascinated listening to the "beep. beep, beep" of Sputnik appear and then fade out as it came overhead every 90 minutes. It was also quite frightening to think of the Soviets circling overhead inasmuch as they were our mortal enemies.
Let's think about what would have happened to a "bomb" which would have been dropped from an orbiting Soviet satellite (America's worst nightmare in 1957). Simply "dropping" the bomb would do nothing. The bomb had a sideways velocity of 17,000 miles/hour when it was part of the spacecraft. Simply separating it from the spacecraft will not cause it to drop to earth. It still has its sideways velocity and will continue to miss the earth as it falls. In order to make it hit the earth, we must get rid of its sideways velocity - a task almost as challenging as imparting that sideways velocity in the first place. |
After Sputnik, it was only a few years before the U.S. launched its own satellite; the Soviets launched Yuri Gagarin, the first man to orbit the earth; and the U.S. launched John Glenn, the first American in orbit. All of these flights were at essentially the same altitude (a few hundred miles) and completed one trip around the earth approximately every 90 minutes.
People were well aware, however, that the period would be longer if they were able to reach higher altitudes. In particular Arthur Clarke pointed out in the mid-1940s that a satellite orbiting at an altitude of 22,300 miles would require exactly 24 hours to orbit the earth. Hence such an orbit is called "geosynchronous" or "geostationary." If in addition it were orbiting over the equator, it would appear, to an observer on the earth, to stand still in the sky. Raising a satellite to such an altitude, however, required still more rocket boost, so that the achievement of a geosynchronous orbit did not take place until 1963.
You may have heard of Arthur Clarke. He is the same gentleman who wrote "2001: A Space Odyssey" and lends his name to "Arthur Clarke's Mysterious World" - the television series. |
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