Satellite conjunctions involving `near misses' of two space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but although regularly calculated by space engineers this has some counter-intuitive properties and its interpretation has been debated. Here we formulate an approach to satellite conjunction based on a simple statistical model and discuss inference on the miss distance between the objects. The usual collision probability estimate can be badly biased, but highly accurate inference on the miss distance is possible. The ideas are illustrated with case studies and Monte Carlo results that show excellent performance. The work is joint with Soumaya El-Kantassi.