On October 6, 1962, the members of New York City Ballet boarded a plane in Vienna, bound for Moscow, the first stop on an eight-week tour that had been arranged by the State Department. The party numbered around ninety, including the dancers, the conductor Robert Irving, two mothers (escorting underage dancers), several translators, the company doctor, and the company’s co-founder and artistic director, George Balanchine. Balanchine had not wanted to go. Born in St. Petersburg in 1904, during the reign of the last tsar, he had experienced cold and starvation in revolutionary Russia, before fleeing the country, in 1924, going first to Europe and then, in 1933, to America. The U.S.S.R. filled him with dread, and his return brought to light one of the great themes of his life: he…