Using analytic calculations and N-body simulations we show that in constant density ( harmonic ) cores , sinking satellites undergo an initial phase of very rapid ( super-Chandrasekhar ) dynamical friction , after which they experience no dynamical friction at all .
For density profiles with a central power law profile , \rho \propto r ^ { - \alpha } , the infalling satellite heats the background and causes \alpha to decrease .
For \alpha < 0.5 initially , the satellite generates a small central constant density core and stalls as in the \alpha = 0 case .

We discuss some astrophysical applications of our results to decaying satellite orbits , galactic bars and mergers of supermassive black hole binaries .
In a companion paper we show that a central constant density core can provide a natural solution to the timing problem for Fornax ’ s globular clusters .