The onboard space navigation system "Alpha" for the USSR Project "L-1" of the manned fly by the Moon is described in the Paper. The system was developed by the Institute of Applied Mathematics of USSR Academy of Sciences and by the Central Design Bureau for Experimental Machine-Building in the years 1966-1968. A sextant was used to obtain the onboard measuring information; it allowed cosmonauts manual receiving the optical measurements of the angular elevations of the known stars above the horizons of Earth and Moon. The principal properties of the ballistic navigation algorithm are presented. This algorithm provided determination of the spacecraft orbit and correction velocity impulses for all the flight stages to ensure the safe spacecraft re-entry into Earth's atmosphere. The problems that were connected with implementing the algorithm in the onboard computer are shown. This autonomous navigation system was successfully tested for the fly-bys Moon with the unmanned variant of flight (spacecrafts "Zond 5 - Zond 8") from 1968 till 1970. The tests have shown that this onboard navigation system has met all the time and accuracy conditions in determination of the orbit parameters and correction velocity impulses.
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