Artificial satellites can provide the basis for all-weather, long-term navigation systems to determine with accuracy geodetic position, speed, and direction of a surface vehicle or aircraft, north reference, and vertical reference. Other methods, such as dead reckoning, Sun and star sighting during clear weather, and use of inertial guidance devices can provide such information with adequate precision in many applications for limited periods of time. It is, however, necessary in many cases to check, independently and periodically, the navigation data indicated by these systems.

In checking and correcting navigational data, two distinct techniques employing a satellite are of interest: (1) Sphereographical navigation, which is very similar to celestial navigation, and (2) a method which makes use of the doppler-shift phenomenon. ^1-4

Celestial guidance involves measurement of the angle between the vertical and the line of sight to a celestial body. The position of the observer on the Earth's surface can be determined from a pair of such observations of two celestial bodies. The same kind of procedure can be used to determine position from two successive observations of a satellite. There are, of course, differences in detail between navigation by stars and by satellite, since star positions change very slowly while a satellite fairly close to the Earth moves at great speed. In both applications, the observer must also determine the local direction of the vertical by pendulum or some other device.

For all-weather navigation, the satellite would radiate a continuous radio signal. The observer, equipped with an electronic sextant and an indicator of the vertical, would then be able to determine his position from radio observations of the satellite.

An all-weather navigation system can also be based on a satellite broadcasting a continuous radio signal, by using the "doppler-shift" principle. The basic phenomenon is the following: The radio signal received from a moving vehicle will appear higher in frequency as the vehicle approaches the observer and lower as the vehicle recedes from the observer. The difference between the observed signal frequency

¹ Lawrence, L., Jr., Navigation by Satellites, Missiles and Rockets, vol. 1, No. 1, October 1956, p. 48.

² Siry, L. W. The Vanguard IGY Earth Satellite Program Naval Research Laboratory, presented to the Fifth General Assembly of CSAGI. Held in Moscow July 30 to August 10, 1958.

³ Leighton, R. B., Tracking an Artificial Satellite Using the Doppler Effect, California Institute of Technology, October 28, 1957.

⁴ Quier, W. H., and G. C. Weiffenbach, Theoretical Analysis of Doppler Radio Signals From Earth Satellites, Johns Hopkins Applied Physics Laboratory, Bumblebee Series Rept. No, 276, April 1958.

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and the known transmitter frequency is a measure of relative position and motion of the vehicle and observer; and, therefore, proper use of such frequency shift information can provide navigational data. This type of system does not require determination of the local vertical by the observer.

For either of the above methods, the observer must know the true position of the satellite at the time of observation. Thus, he must be provided with a table of satellite positions covering the duration of his trip. These tables must be prepared in advance as mathematical predictions, as is now done by the Naval Observatory in the case of tables of positions of celestial bodies for navigation purposes.

Navigation accuracy is dependent upon the precision with which satellite position can be predicted into the future. This precision is, in turn, dependent largely upon the accuracy of observations, the computational procedure used, the accuracy with which the relevant physical constants are known, and the magnitudes of unpredictable disturbing effects acting on the satellite. The most important of these disturbances is the uncertain air drag at lower altitudes. Since it is at fairly high altitudes, the orbit of Vanguard I can be predicted into the future for about a month with reasonable accuracy, whereas predictions of the lower Explorer IV orbit are useful for only about 1 day in the future. Current predictions of Vanguard I position tend to be in error by some tens of miles after a month, but are in error by less that 5 miles over a few days. Prediction a few hours in advance would be off by less than a mile.

In addition to errors in satellite observations, there are two sources of difficulty in accurate orbit predictions. First, the classical methods used for many years by astronomers to determine orbits have not proven to be adequate when used in connection with artificial satellite orbits. New techniques or modifications of existing techniques appear to be necessary in order to improve the accuracy of orbital predictions. Second, further study must be made of the disturbing forces influencing orbital motion.

The basic measurements required in sphereographical navigation are the azimuth and elevation angles of the satellite and the time of observation. The equipment of the navigator consists of a highly directional antenna and receiver, a clock, and equipment for defining the vertical. The accuracy of navigation is determined by various equipment characteristics. The factor with greatest implications for vehicle design is the antenna size.

As an indication of this size, an antenna about 12 feet in diameter will allow position determination within an error of about a mile when directed toward a satellite 1,000 miles away under representative conditions. A smaller antenna would lead to larger errors. The other equipments involved are generally comparatively small and light. The satellite would carry a transmitter.

For using the doppler technique of navigation the physical extent of the equipment needed on the navigated vehicle is less. The navigation equipment consists of a sensitive radio receiver, an accurate frequency reference, and an accurate clock. The equipment carried by the satellite would again be a transmitter, but one specifically designed to emit a very stable frequency.