  An analytical model is presented for calculating the surface density as a
function of radius $\Sigma(r)$ in protoplanetary disks in which a planet has
opened a gap. This model is also applicable to circumbinary disks with extreme
binary mass ratios. The gap profile can be solved for algebraically, without
performing any numerical integrals. In contrast with previous one-dimensional
gap models, this model correctly predicts that low-mass (sub-Jupiter) planets
can open gaps in sufficiently low-viscosity disks, and it correctly recovers
the power-law dependence of gap depth on planet-to-star mass ratio $q$, disk
aspect ratio $h/r$, and dimensionless viscosity $\alpha$ found in previous
numerical studies. Analytical gap profiles are compared with numerical
calculations over a range of parameter space in $q$, $h/r$, and $\alpha$,
demonstrating accurate reproduction of the "partial gap" regime, and general
agreement over a wide range of parameter space.
