FU Orionis objects are low-mass pre-main sequence stars characterized by dramatic outbursts of several magnitudes in brightness. These outbursts are linked to episodic accretion events in which stars gain a significant portion of their mass. The physical processes behind these accretion events are not yet well understood. The archetypical FU Ori system, FU Orionis, is composed of two young stars with detected gas and dust emission. The continuum emitting regions have not been resolved until now. Here, we present 1.3 mm observations of the FU Ori binary system with ALMA. The disks are resolved at 40 mas resolution. Radiative transfer modeling shows that the emission from FU Ori north (primary) is consistent with a dust disk with a characteristic radius of $sim$11 au. The ratio between major and minor axes shows that the inclination of the disk is $sim$37 deg. FU Ori south is consistent with a dust disk of similar inclination and size. Assuming the binary orbit shares the same inclination angle as the disks, the deprojected distance between north and south components is 0.6, i.e. $sim$250 au. Maps of $^{12}$CO emission show a complex kinematic environment with signatures disk rotation at the location of the northern component, and also (to a lesser extent) for FU Ori south. The revised disk geometry allows us to update FU Ori accretion models (Zhu et al.), yielding a stellar mass and mass accretion rate of FU Ori north of 0.6 M$_{odot}$ and 3.8$times10^{-5}$ M$_{odot}$ yr$^{-1}$, respectively.
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