One of the triumphs of Newton's Mechanics was that he was able, using only his LAWS OF MOTION and a postulated UNIVERSAL LAW OF GRAVITATION, to explain the empirical LAWS OF PLANETARY MOTION discovered by Johannes Kepler. [Clearly there was a great deal more respect for Law in those days than there is now!] Although the phenomenology of orbits (circular, elliptical and hyperbolic) would appear to be rather esoteric and applicable only to astronomy [and, today, astrogation], in fact the paradigm of uniform circular motion (i.e. motion in a circle at constant speed) is one of the most versatile in Physics. Let us begin, therefore, by deriving its essential and characteristic features.