  Turbulence in protoplanetary disks affects planet formation in many ways.
While small dust particles are mainly affected by the aerodynamical coupling
with turbulent gas velocity fields, planetesimals and larger bodies are more
affected by gravitational interaction with gas density fluctuations. For the
latter process, a number of numerical simulations have been performed in recent
years, but a fully parameter-independent understanding has not been yet
established. In this study, we present simple scaling relations for the
planetesimal stirring rate in turbulence driven by magnetorotational
instability (MRI), taking into account the stabilization of MRI due to Ohmic
resistivity. We begin with order-of-magnitude estimates of the
turbulence-induced gravitational force acting on solid bodies and associated
diffusion coefficients for their orbital elements. We then test the predicted
scaling relations using the results of recent Ohmic-resistive MHD simulations
by Gressel et al. We find that these relations successfully explain the
simulation results if we properly fix order-of-unity uncertainties within the
estimates. We also update the saturation predictor for the density fluctuation
amplitude in MRI-driven turbulence originally proposed by Okuzumi & Hirose.
Combination of the scaling relations and saturation predictor allows to know
how the turbulent stirring rate of planetesimals depends on disk parameters
such as the gas column density, distance from the central star, vertical
resistivity distribution, and net vertical magnetic flux. In Paper II, we apply
our recipe to planetesimal accretion to discuss its viability in turbulent
disks.
