Hagihara graduated from Tokyo Imperial University with a degree in astronomy in 1921 and became an assistant professor of astronomy there two years later. In 1923 the Japanese government sent him abroad as a traveling scholar. Hagihara went to Cambridge University in England to study under the mathematician H.F. Baker and also visited the University of Göttingen and the Sorbonne.
Hagihara finished his studies at Harvard in 1929 and returned again to the University of Tokyo where, in 1930, he completed a D.Sc. dissertation on the stability of satellite systems. He was promoted to full professor at the University of Tokyo five years later. From 1945 to 1957 he was the director of the Tokyo Astronomical Observatory and subsequently was a professor at Tohoku University (1957–1960) and president of Utsunomiya University (1961–1967). In 1961 he was elected vice-president of the International Astronomical Union and president of the IAU's commission on celestial mechanics.
He retired from all of his official duties, except for the Japan Academy, in 1967 and devoted himself to writing his comprehensive five volume work, Celestial Mechanics, which was based on his lecture notes.
- The main-belt asteroid 1971 Hagihara was named in his honor.
- Fellow of the Royal Astronomical Society
- Chairman of the National Committee of Astronomy (Japan)
- Member Japan Academy
- Member Science Council of Japan
- Order of Cultural Merit (Japan)
- Recipient of the James Craig Watson Medal from the U.S. National Academy of Science (1960)
- Hagihara, Yusuke (1970). Celestial mechanics : Dynamical principles and transformation theory (vol. 1). Cambridge: MIT Press. ISBN 0-262-08037-0.
- Hagihara, Yusuke (1972). Celestial mechanics: Perturbation theory (vol. 2, parts 1 and 2). Cambridge: MIT Press.
- Hagihara, Yusuke (1975). Celestial mechanics: Differential equations in celestial mechanics (vol. 3, parts 1 and 2). Tokyo: Japan Society For the Promotion of Science.
- Hagihara, Yusuke (1976). Celestial mechanics: Periodic and quasi-periodic solutions (vol. 4, parts 1 and 2). Tokyo: Japan Society For the Promotion of Science.
- Hagihara, Yusuke (1977). Celestial mechanics: Topology of the three-body problem (vol. 5, parts 1 and 2). Tokyo: Japan Society For the Promotion of Science.
- Hagihara, Yusuke (1971). Theories of equilibrium figures of a rotating homogeneous fluid mass. Washington, D.C.: U. S. Government Printing Office. NAS 1.21:186.
- Kozai, Yoshihide (1979). "Yusuke Hagihara". Quart. Jour. Royal Astron. Soc. 20 (3): 325–8.
- Kozai, Yoshihide (1998). "Development of Celestial Mechanics in Japan". Planet. Space Sci. 46 (8): 1031–36. Bibcode:1998P&SS...46.1031K. doi:10.1016/s0032-0633(98)00033-6.
- Herget, Paul (1979). "Yusuke Hagihara". Physics Today. 32 (6): 71. doi:10.1063/1.2995600.
- Schmadel, Lutz D. (2007). Dictionary of Minor Planet Names – (1971) Hagihara. Springer Berlin Heidelberg. p. 159. ISBN 978-3-540-00238-3. Retrieved 29 August 2016.
- Greene, Jay E., ed. (1980). McGraw-Hill Modern Scientists and Engineers. 3 vols. New York: McGraw-Hill.