Bound systems in an expanding universe

The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess an extrinsic curvature miss-match. One consequence is that some trajectories are discontinuous functions of their initial conditions. An alternate metric is proposed which goes smoothly between the Schwarzchild exterior solution and the Friedmann-Lemaitre, expanding universe metric. It is further shown that the effects of the expansion on planetary motions in the solar system are too small to be currently observed for this alternate metric