A method and apparatus for processing and transmitting precise orbit predictions of satellites in a Global Navigation Satellite System such as Navstar-GPS which employs curve fitting techniques and a polynomial and sinusoidal model to encode ephemerides, and particularly ephemerides of durations 6 hours or longer, in order to minimize bandwidth requirements over-the-air and NVRAM storage requirements. The methods also apply to GNSS constellations such as Galileo or GLONASS. Also, methods are disclosed for recovering the ephemeris on a GNSS receiver device in the constellation's native format.