We study the scattering of two Skyrmions at low energy and large separ
ation. 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 grad
ient flow curves joining these together and by positing that the dynam
ics is restricted here. The kinetic energy provides an induced metric
on this manifold while restricting the full potential energy to the ma
nifold defines a potential. The low energy dynamics is now constrained
to these finite number of degrees of freedom. For a large separation
of the two Skyrmions the manifold is parametrized by the variables of
the product ansatz. We find the interaction between two Skyrmions comi
ng from the induced metric, which was independently found by Schroers.
We find that the static potential is actually negligible in compariso
n to this interaction. Thus to lowest order, at large separation, the
dynamics reduces to geodesic motion on the manifold. We consider the s
cattering to first order in the interaction using the perturbative met
hod of Lagrange and find that the dynamics in the no spin or charge ex
change sector reduces to the Kepler problem.