  Close binary systems present challenges to planet formation. As binary
separations decrease, so too do the occurrence rates of protoplanetary disks in
young systems and planets in mature systems. For systems that do retain disks,
their disk masses and sizes are altered by the presence of the binary
companion. Through the study of protoplanetary disks in binary systems with
known orbital parameters, we seek to determine the properties that promote disk
retention and, therefore, planet formation. In this work, we characterize the
young binary-disk system, FO Tau. We determine the first full orbital solution
for the system, finding masses of $0.35^{+0.06}_{-0.05}\ M_\odot$ and
$0.34\pm0.05\ M_\odot$ for the stellar components, a semi-major axis of
$22(^{+2}_{-1})$ AU, and an eccentricity of $0.21(^{+0.04}_{-0.03})$. With
long-baseline ALMA interferometry, we detect 1.3mm continuum and
$^{12}{\mathrm{CO}} \ (J=2-1)$ line emission toward each of the binary
components; no circumbinary emission is detected. The protoplanetary disks are
compact, consistent with being truncated by the binary orbit. The dust disks
are unresolved in the image plane and the more extended gas disks are only
marginally resolved. Fitting the continuum and CO visibilities, we determine
the inclination of each disk, finding evidence for alignment of the disk and
binary orbital planes. This study is the first of its kind linking the
properties of circumstellar protoplanetary disks to a precisely known binary
orbit. In the case of FO Tau, we find a dynamically placid environment
(coplanar, low eccentricity), which may foster its potential for planet
formation.
