Use of satellites for navigation

Any position on earth can be determined as the intersection of two circles, with their centers located at 0 and 0´ on the earth´s surface just beneath two satellites. Therefore any flying path can be described as a locus of many such positions. One synchronous satellite can cover 45 percent of the surface of the earth. When an aircraft flies outbound along the earth´s surface from the reference point 0, the traveling time of the wave pulses transmitted from the satellite to the aircraft becomes longer and longer, but it is not proportional to the flying distance, because the altitude angle (the intersection angle between the line from the satellite to the measured point and the tangent line to the earth´s surface at the point) changes from time to time. The increase of the transit time will be less when flying the same distance over the area near the reference point than it would be farther away. A correction factor cos(90-α-β) should be introduced to equalize the measured distance to the true flying distance.