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Woltjer was the son of the classical scholar Jan Woltjer. On 13 December 1916 he married Hillegonda de Vries in Groningen. He worked and taught at Leiden University, where Gerard P. Kuiper was one of his students. He was the father of the astronomer Lodewijk Woltjer (1930-2019), who was the director general of the European Southern Observatory from 1975 to 1987.
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