While engaged in the observation and prediction of the position of Sputnik I, it was realized that, if a reliable orbit were available, and an observation of the satellite against the background of stars were made to a precision of about 0°·1 and timed to about 0·2 of a second, then the position of the observer could be determined to a precision sufficient for most navigational purposes. The following account demonstrates how this has actually been done from a single visual observation of the American Balloon Satellite Echo I (designated 1960ι1).

Principle of method. The direction in which an observer on the Earth's surface sees an artificial satellite at any instant differs from that in which it is seen by any other observer and from that in which it would be observed from the centre of the Earth. The amount and direction of the parallactic shift can be determined from the comparison of the direction of observation with that calculated from the geocentric ephemeris of the satellite; and the position of the observer on the Earth's surface can be uniquely calculated from this parallactic shift. Only a single observation is required, without reference to the vertical.