  Nitric oxide is an open-shell molecule abundantly detected in the
interstellar medium. A precise modeling of its radiative and collisional
processes opens the path to a precise estimate of its abundance. We present
here the first rate coefficients for fine and hyperfine (de-)excitation of NO
by collisions with the most ubiquitous collision partner in the interstellar
medium, $para$-H$_2$ hydrogen molecules, using a recently developed accurate
interaction potential. We report quantum scattering calculations for
transitions involving the first 74 fine levels and the corresponding 442
hyperfine levels belonging to both $F_1$ and $F_2$ spin-orbit manifolds. To do
so, we have calculated cross sections by means of the quantum mechanical
close-coupling approach up to 1000 cm$^{-1}$ of total energy and rate
coefficients from 5 to 100 K. Propensity rules are discussed and the new
NO-H$_2$ rates are compared to those available in the literature, based on
scaled NO-He rates. Large differences are observed between the two sets of rate
coefficients, and this comparison shows that the new collision rates must be
used in interpreting NO emission lines. We also examined the effect of these
new rates on the NO excitation in cold clouds by performing radiative transfer
calculations of the excitation and brightness temperatures for the two NO lines
at 150.176 and 250.4368 GHz. This shows that the local thermodynamic
equilibrium is not fulfilled for this species for typical conditions. We expect
the use of the rates presented in this study to improve the constraints on the
abundance of NO.
