Okay, I think I now follow what you are saying. This contention is not really about apparent angular velocity, though, but only of the radius of the apparent circle. How about an infinite radius. Angular velocity is the same for any radius.......... In terms of rectangular Cartesian coordinates, where we draw the x- and y-axes on a sheet of paper and the z-axis comes out of the paper towards you, am I right in saying that, if we consider an object at some distance along the x-axis, say, then we will perceive a particular apparent motion of that object as we rotate around the z-axis, and another if we simply travel along the y-axis? This point needs to be clarified before I continue. Yoir telling me.......Never did get the hang of those coordinates thingos, Give me straight geometry, and a we bit of trig is ok.....I like x's and y's though better'n apples. but this post did help a lot. thanks Mike and Neville for putting it all together. But if polaris makes a circle, then Polaris makes a circle, just as does the sun.....not us.....sorry for keeping me eccentric, er um geocentric....? Philip.