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KT Eridani was a very fast nova in 2009 peaking at V=5.42 mag. We marshallarge data sets of photometry to finally work out the nature of KT Eri. Fromthe TESS light curve, as confirmed with our radial velocity curve, we find anorbital period of 2.61595 days. With our 272 spectral energy distributions fromsimultaneous BVRIJHK measures, the companion star has a temperature of6200$\pm$500 K. Our century-long average in quiescence has V=14.5. With theGaia distance (5110$^{+920}_{-430}$ parsecs), the absolute magnitude is+0.7$\pm$0.3. We converted this absolute magnitude (corrected to the disc lightalone) to accretion rates, with a full integration of the alpha-disc model.This accretion rate is very high at 3.5x10$^{-7}$ solar masses per year. Oursearch and analysis of archival photographs shows that no eruption occurredfrom 1928--1954 or after 1969. With our analysis of the optical light curve,the X-ray light curve, and the radial velocity curve, we derive a white dwarfmass of 1.25$\pm$0.03 solar masses. With the high white dwarf mass andvery-high accretion rate, KT Eri must require a short time to accumulate therequired mass to trigger the next nova event. Our detailed calculations give arecurrence time-scale of 12 years with a total range of 5--50 years. Whencombined with the archival constraints, we conclude that the recurrencetime-scale must be between 40--50 years. So, KT Eri is certainly a recurrentnova, with the prior eruption remaining undiscovered in a solar gap of coveragefrom 1959 to 1969.

The Nova KT Eri Is a Recurrent Nova With a Recurrence Time-Scale of 40-50 Years