The postulated very large angular deflections of the earth's axis due to gravitational encounters, say with Venus or Mars, as espoused by many rationalistic catastrophism, most eminently by Velikovsky, are analyzed and found wanting. Useful analytic expressions are derived and are also applied against the alleged accuracy of astronomical dating and Copernicanism. Large Angular deflections seem to be possible only if a large body were to be captured for a considerable period of time. It will be understood that this article is concerned only with possible changes in the direction of the earth's axis. Possible changes in the orbit, as some catastrophists have proposed for the earth or for other bodies, are not investigated here.