_In the case of the Echo I satellite (see page 16), we engaged in the first and third of these activities. We had many chances to follow the satellite with our radars, and we could speculate how its orbit was changing through the months. In the case of the Telstar I satellite, we engaged in all three kinds of activity. We shall take a look at these problems in the sequence in which we came across them, for both the Echo and Telstar satellites._ How We Track Satellites We collect on the ground most of the information to calculate a satellite’s orbit, using optical instruments or radar equipment. Following a satellite through the sky is called _tracking_; in the early days after the first Sputniks, some of this tracking was done with the naked eye or with very simple telescopes by the Moonwatch teams. Many of you may have observed Echo I on a clear night without any kind of instrument. [Illustration: _Figure 1_] satellite horizon elevation azimuth North East If we use a telescope, we note the time of the observation and we usually take a photograph of the satellite. We locate the satellite in terms of the two angles shown in _Figure 1_. One of these is the _elevation_ angle—the number of degrees a telescope must be tilted above the horizon to see the satellite. The second is the _azimuth_ angle—the number of degrees between the plane in which we measure the elevation angle and the north direction. Of course, we can also point a radar antenna at the satellite in the same manner. The radar can receive a signal transmitted by the satellite, or else it can send a signal to the satellite and watch for the reflected waves that eventually return. In the latter case, the satellite must have sufficient surface area to produce an adequate reflected signal. These two kinds of precision tracking were both possible with Echo I. Radar can also do something that optical equipment usually can’t do: measure the distance out to the satellite. The Basic Physics of Satellite Motion [Illustration: _Figure 2_] earth north pole satellite θ = _n_ · _t_ The Echo I satellite was launched into a circular orbit inclined at an angle to the plane of the earth’s equator. In _Figure 2_ this equatorial plane intersects the plane of the satellite orbit along the line OPM. The point O represents the center of the earth, the point M is on the satellite orbit, and the Point P is on the equator. At any instant, the satellite may be located in its orbit by the angle θ, which is measured between the line OM and the line OQ, where the point Q is the satellite’s location. If the satellite moves in a circular orbit, as in this case, the angle θ is proportional to time. That is, we can write θ = _nt_. We call _n_ the _angular speed_ of the satellite; one way of measuring this is in degrees per second.