  We study the motion of a heavy impurity immersed in a weakly interacting BEC
using the Gross-Pitaevskii equation (GPe). We construct a perturbative solution
to the GPe in powers of impurity velocity in the case when the boson-impurity
potential is tuned to unitarity and calculate the effective mass of the
polaron. In addition, we calculate the interaction energy of two unitary
polarons which are sufficiently far apart. Our formalism also reproduces the
results for both the mass and interaction energy obtained at weak
boson-impurity coupling.
