Among his chief achievements is the foundation of the Skalnaté Pleso Observatory and the discovery of the comet C/1947 F2 (Bečvář) (also known by the designations 1947 III and 1947c).
His lifelong illness led him to the High Tatras where he founded the observatory.
[2] Bečvář is particularly important for his star charts: he led the compilation of the Atlas Coeli Skalnate Pleso (1951), published by Sky Publishing Corporation as the Skalnate Pleso Atlas of the Heavens, which was the state-of-the-art atlas of its kind until Wil Tirion's "Sky Atlas 2000.0" in 1981.
A dozen star names in the atlas are of unknown origin, no connection to any language or previous source has been discovered despite an extensive search.
American Avant-garde composer John Cage used Bečvář's star charts as the basis of several works: Atlas Eclipticalis (1961–1962), Etudes Australes (1974–1975), Etudes Boreales (1978) and Freeman Etudes (1977–1980, 1989–1990).