We calculate orbits for the Milky Way dwarf galaxies with proper motions, and compare these to subhalo orbits in a high-resolution cosmological simulation. We use the simulation data to assess how well orbits may be recovered in the face of measurement errors, a time-varying triaxial gravitational potential and satellite-satellite interactions. For present measurement uncertainties, we recover the apocentre ra and pericentre rp to ~40 per cent. With improved data from the Gaia satellite we should be able to recover ra and rp to ~14 per cent, respectively. However, recovering the 3D positions and orbital phase of satellites over several orbits is more challenging. This owes primarily to the non-sphericity of the potential and satellite interactions during group infall. Dynamical friction, satellite mass-loss and the mass evolution of the main halo play a more minor role in the uncertainties.
We apply our technique to nine Milky Way dwarfs with observed proper motions. We show that their mean apocentre is lower than the mean of the most massive subhaloes in our cosmological simulation, but consistent with the most massive subhaloes that form before z = 10. This lends further support to the idea that the Milky Way's dwarfs formed before reionization.