| km |
| r² |
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 |
| r² |
| mv² |
| 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 =
| 2πr |
| v |