  The highly organised distribution of satellite galaxies surrounding the Milky
Way is a serious challenge to the concordance cosmological model. Perhaps the
only remaining solution, in this framework, is that the dwarf satellite
galaxies fall into the Milky Way's potential along one or two filaments, which
may or may not plausibly reproduce the observed distribution. Here we test this
scenario by making use of the proper motions of the Fornax, Sculptor, Ursa
Minor and Carina dwarf spheroidals, and trace their orbits back through several
variations of the Milky Way's potential and account for dynamical friction. The
key parameters are the proper motions and total masses of the dwarf galaxies.
Using a simple model we find no tenable set of parameters that can allow Fornax
to be consistent with filamentary infall, mainly because the 1 sigma error on
its proper motion is relatively small. The other three must walk a tightrope
between requiring a small pericentre (less than 20 kpc) to lose enough orbital
energy to dynamical friction and avoiding being tidally disrupted. We then
employed a more realistic model with host halo mass accretion, and found that
the four dwarf galaxies must have fallen in at least 5 Gyrs ago. This time
interval is longer than organised distribution is expected to last before being
erased by the randomisation of the satellite orbits.
