Thus, the satellite is whirling at a constant speed about the earth like a stone tied to a string. Let us examine the physics of this situation a little more closely with the help of _Figure 3_. If the satellite is moving with the velocity _v_, then we know that the centrifugal force acting on it is (_mv_²)/(_r_), where _m_ is the mass of the satellite and _r_ is its distance from the center of the earth. Obviously, no string ties the satellite to the earth, but the force of gravitational attraction between the earth and the satellite has the same effect. Newton’s law of mutual attraction tells us that this force is proportional to the product of the two masses divided by the square of the distance between their centers, or (_km_)/(_r_²), where _k_ is a constant that essentially represents the mass of the earth.[1] Newton’s law also tells us that this force will be pointing toward the center of the earth if the earth is spherical. When the satellite is in circular motion, the centrifugal force and the gravitational force must balance each other. Hence we have (_km_)/(_r_²) = (_mv_²)/(_r_) and from this we can solve to find that the velocity of the satellite must be equal to _v_ = √((_k_)/(_r_)). In the case of the Echo I satellite, which was designed to have a radial distance of _r_ = 5000 miles, this velocity amounts to about 4.4 miles per second. The time for one revolution in orbit is obtained with the formula _T_ = (2_πr_)/(_v_). For the Echo satellite this time, _T_, turns out to be just about two hours. [Illustration: _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.