  Extending the analysis of hep-th/0504128, we obtain a formal expression for
the coupling between brane matter and the radion in a Randall-Sundrum
braneworld. This effective theory is correct to all orders in derivatives of
the radion in the limit of small brane separation, and, in particular, contains
no higher than second derivatives. In the case of cosmological symmetry the
theory can be obtained in closed form and reproduces the five-dimensional
behaviour. Perturbations in the tensor and scalar sectors are then studied.
When the branes are moving, the effective Newtonian constant on the brane is
shown to depend both on the distance between the branes and on their velocity.
In the small distance limit, we compute the exact dependence between the
four-dimensional and the five-dimensional Newtonian constants.
