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Recent statistical deconvolution methods have produced extended kinematicalmaps in a range of heliocentric distances that are a factor of two to threelarger than those analysed in the Gaia Collaboration based on the same data. Inthis paper, we use such maps to derive the rotation curve both in the Galacticplane and in off-plane regions and to analyse the density distribution. Byassuming stationary equilibrium and axisymmetry, we used the Jeans equation toderive the rotation curve. Then we fit it with density models that include bothdark matter and predictions of the MOND (Modified Newtonian dynamics) theory.Since the Milky Way exhibits deviations from axisymmetry and equilibrium, wealso considered corrections to the Jeans equation. To compute such corrections,we ran N-body experiments of mock disk galaxies where the departure fromequilibrium becomes larger as a function of the distance from the centre. Therotation curve in the outer disk of the Milky Way that is constructed with theJeans equation exhibits very low dependence on $R$ and $z$ and it iswell-fitted both by dark matter halo and MOND models. The application of theJeans equation for deriving the rotation curve, in the case of the systems thatdeviate from equilibrium and axisymmetry, introduces systematic errors thatgrow as a function of the amplitude of the average radial velocity. In the caseof the Milky Way, we can observe that the amplitude of the radial velocityreaches $\sim 10\%$ that of the azimuthal one at $R\approx 20$ kpc. Based onthis condition, using the rotation curve obtained from the Jeans equation tocalculate the mass may overestimate its measurement.

Gaia-DR2 extended kinematical maps. Part III: Rotation curves analysis, dark matter, and Modified Newtonian dynamics tests