  I report on the discovery of the orbital periods of three recurrent novae in
our galaxy. V745 Sco has an orbital period of 510+-20 days with ellipsoidal
modulations, based on SMARTS photometry from 2004-2008. V3890 Sgr has an
orbital period of 519.7+-0.3 days with ellipsoidal modulations and a shallow
eclipse, based primarily on SMARTS and AAVSO photometry from 1995-2008, but
also extending back to 1899 with archival plates. In addition, a sinusoidal
modulation of amplitude 0.2 mag and period 103.8+-0.4 days is seen mainly in
the red, with this attributed to ordinary pulsations in the giant companion
star. V394 CrA has an orbital period equal to twice its primary photometric
period (P_orb=1.515682+-0.000008 days), as based on photometry extending from
1989-2008. I use all available information (including the UBVRIJHK spectral
energy distributions) to get distances to the four RNe with red giant
companions as 800+-140 pc for T CrB, 4300+-700 pc for RS Oph, 7300+-1200 pc for
V745 Sco, and 6000+-1000 pc for V3890 Sgr. Further, the red giant in the RS Oph
system has a mass loss rate of close to 3.7x10^-8 M_sun/yr as based on many
confident measures, and this is too weak (by a factor of 100,000) to supply the
white dwarf with mass at the known rate of 3.9x10^-6 M_sun/yr. Thus, the only
way to get matter onto the white dwarf fast enough is through Roche lobe
overflow, and this confidently demonstrates that the distance to RS Oph is
>~3000 pc.
