We consider a simplified model for the line pinning of a contact line on a single (physical) spherical heterogeneity, and we show that this problem is related to the capillary problem of pushing a small spherical object through a liquid/gas interface. The model predicts that the contact line pins, distorts, and finally slides across the defect and is in agreement with experimental results. Furthermore, it gives an explicit criterion for the onset of sliding. The associated sphere/interface problem shows similar characteristics. We suggest that further modeling of line pinning phenomena should concentrate on modeling the capillary aspects as accurately as possible, a numerical approach being unavoidable if the essentially three-dimensional problem is to be modeled properly.