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We investigate the effect of a density gradient on Chandrasekhar's dynamicalfriction formula based on the method of 2-body encounters in the localapproximation. We apply these generalizations to the orbit evolution ofsatellite galaxies in Dark Matter haloes. We find from the analysis that themain influence occurs through a position-dependent maximum impact parameter inthe Coulomb logarithm, which is determined by the local scale-length of thedensity distribution. We also show that for eccentric orbits the explicitdependence of the Coulomb logarithm on position yields significant differencesfor the standard homogeneous force. Including the velocity dependence of theCoulomb logarithm yields ambigous results. The orbital fits in the first fewperiods are further improved, but the deviations at later times are muchlarger. The additional force induced by the density gradient, the inhomogeneousforce, is not antiparallel to the satellite motion and can exceed 10% of thehomogeneous friction force in magnitude. However, due to the symmetryproperties of the inhomogeneous force, there is a deformation and no seculareffect on the orbit at the first order. Therefore the inhomogeneous force canbe safely neglected for the orbital evolution of satellite galaxies. For thehomogeneous force we compare numerical N-body calculations with semi-analyticalorbits to determine quantitatively the accuracy of the generalized formulae ofthe Coulomb logarithm in the Chandresekhar approach. With the localscale-length as the maximum impact parameter we find a significant improvementof the orbital fits and a better interpretation of the quantitative value ofthe Coulomb logarithm.Comment: 17 pages, 16 figures, accepted for publication by Astronomy and  Astrophysics 19.10.200

Large scale inhomogeneity and local dynamical friction