For the Echo satellite this time, T, turns out to be just about two hours.
Figure 3
Calculating the Orbit of Echo I
These basic physical principles of satellite motion can give us many useful answers. They tell us how fast we must move a precision tracker to follow the satellite through the sky, how much time a satellite will spend above the horizon, and how long will be the time from one chance of seeing it to the next. However, in the Echo project we were not merely concerned with planning our experiments from hour to hour; we also needed to know how the satellite would move for weeks and perhaps months in advance. When you study the motion of a satellite over such a length of time, you discover that its circular orbit will not remain the same as it was at launch. This fact had been observed on other satellites and was to be expected also with Echo.
In everything we have said so far it was assumed that the earth was a perfect sphere, which is the way a geographer’s globe presents it to us. In reality, the earth is somewhat flattened, with its diameter from the north pole to the south pole being somewhat shorter than its diameter at the equator. One way of looking at this is to visualize the earth as a sphere with some material added in the equatorial zone, which we may call equatorial bulge. This bulge causes Echo’s orbit to have a slow “wobble” about the earth’s polar axis, somewhat like that of a spinning top.
Another force that makes the satellite’s orbit shift slightly is the faint pressure caused by the light from the sun. Although this pressure is much too small for us to perceive without the help of very delicate instruments, it is enough to affect a satellite, which has nothing to support it in space and is exposed to solar pressure for a very long time. Since the Echo balloon is a plastic sphere, 100 feet in diameter, that weighs only a little more than 100 pounds, the light rays striking its surface are enough to cause a second “wobble” effect. This wobble centers about the line from the earth to the sun. Light pressure also forces the orbit to go slightly out of round from a perfect circle, and other gradual effects on the satellite’s orbit are caused by the gravitational attraction of the moon and the sun.
All these disturbances are ever-present and act simultaneously, and a satellite’s total response to them is very complicated. Fortunately, however, most of the changes take place at a very slow and uniform rate, and we can predict them fairly accurately.
Calculating the Orbit of Telstar I
