Heston: guilty as charged! However, I must be being dense because if the particle is moving along the plane of rotation (along a parallel of latitude) I can't see how gravity would cause it to appear to change direction.
The wikipedia page is interesting (especially the Eötvös effect, which I hadn't heard of) but sadly the days when I could intuitively understand matrix determinants are long gone.
BillieBob: that's pretty good but I think the average bod would struggle with the idea that the locus of any point on the surface has a degree of circularity - in fact I'm struggling a little. Do you have a convincing explanation, or just one based on the limits?
HFD