  We fit an isothermal oscillatory density model of Neptune's protoplanetary
disk to the surviving regular satellites and its innermost ring and we
determine the radial scale length of the disk, the equation of state and the
central density of the primordial gas, and the rotational state of the
Neptunian nebula. Neptune's regular moons suffered from the retrograde capture
of Triton that disrupted the system. Some moons may have been ejected, while
others may have survived inside their potential minima. For this reason, the
Neptunian nebula does not look like any of the nebulae that we modeled
previously. In particular, there must be two density maxima deep inside the
core of the nebula where no moons or rings are found nowadays. Even with this
strong assumption, the recent discovery of the minor moon N XIV complicates
further the modeling effort. With some additional assumptions, the Neptunian
nebula still shares many similarities with the Uranian nebula, as was expected
from the relative proximity and similar physical conditions of the two systems.
For Neptune's primordial disk, we find a steep power-law index ($k=-3.0$),
needed to accommodate the arrangement of the outer moons Larissa, N XIV, and
Proteus. The rotation parameter that measures centrifugal support against
self-gravity is quite small ($\beta_0=0.00808$), as is its radial scale length
(13.6 km). The extent of the disk ($R_{\rm max}=0.12$ Gm) is a lot smaller than
that of Uranus ($R_{\rm max}=0.60$ Gm) and Triton appears to be responsible for
the truncation of the disk. The central density of the compact Neptunian core
and its angular velocity are higher than but comparable to those of Uranus'
core. In the end, we compare the models of the protoplanetary disks of the four
gaseous giants.
