In 1921, while still a student, Nielsen established his private observatory "Spica" in Glostrup. The observatory was located on the premises of a local enterprise, where Nielsen's father was employed as a manager. Axel V. Nielsen graduated in 1926 from the University of Copenhagen. In 1927 Nielsen was employed as an assistant with the Ole Rømer Observatory in Aarhus, later as head of section. The Ole Rømer Observatory had been established in 1911; in 1956 it was handed over to the University of Aarhus.
The crater Nielsen on the Moon is named after Axel V. Nielsen and the American physicist Harald Herborg Nielsen (1903-1973).
Nielsen published several books and articles on astronomy and the history of astronomy in Denmark. In 1944 he published a major work on the Danish astronomer Ole Rømer (1644-1710). Nielsen's publication record includes:
Ole Rømers ”Dimensionstavle”, Nordisk Astronomisk Tidsskrift 1928, 30
Ildkugler og Stjerneskud: Tidsskrift for Skole og Hjem. 2. Aarg. 8. Hft., Hellerup 1929
The normal light curve, Astronomische Nachrichten, vol. 262, May 1937
Hvornaar forelagde Ole Rømer sin Afhandling om Lysets Hastighed for Akademiet i Paris, NAT 1944, 60
Ole Rømer. En Skildring af hans Liv og Gerning, København 1944
Ole Rømers Triduum i det 18. århundredes astronomi, s. 205-223 i Vagn......