  We study the scattering of two Skyrmions at low energy and large separation.
We use the method proposed by Manton for truncating the degrees of freedom of
the system from infinite to a manageable finite number. This corresponds to
identifying the manifold consisting of the union of the low energy critical
points of the potential along with the gradient flow curves joining these
together and by positing that the dynamics is restricted here. The kinetic
energy provides an induced metric on this manifold while restricting the full
potential energy to the manifold defines a potential. The low energy dynamics
is now constrained to these finite number of degrees of freedom. For large
separation of the two Skyrmions the manifold is parametrised by the variables
of the product ansatz. We find the interaction between two Skyrmions coming
from the induced metric, which was independently found by Schroers. We find
that the static potential is actually negligible in comparison to this
interaction. Thus to lowest order, at large separation, the dynamics reduces to
geodesic motion on the manifold. We consider the scattering to first order in
the interaction using the perturbative method of Lagrange and find that the
dynamics in the no spin or charge exchange sector reduces to the Kepler
problem.
