  We consider the behavior of macroscopic bodies within the framework of
relative locality, which is a recent proposal for Planck scale modifications of
the relativistic dynamics of particles which are described as arising from
deformations in the geometry of momentum space. These lead to the addition of
non-linear terms to the energy-momentum relations and conservation laws, which
are suppressed by powers of ratio between the energy E of the particles
involved and the Planck mass M_P. We consider and resolve a common objection
against such proposals, which is that, even if the corrections are small for
elementary particles in current experiments, they are huge when applied to
composite systems such as soccer balls, planets and stars, with energies
E_{macro} much larger than M_P. We show that this "soccer-ball problem" does
not arise within the framework of relative locality, because the non-linear
effects for the dynamics of a composite system with N elementary particles
appear at most of order E_{macro}/ N M_{P}.
