I was doing some thinking (I know, some might feel that is perhaps not such a good idea ) about classical, i.e. non quantum based, clocks and was confronted by the question if in general relativity there is such thing as a frame independent notion of a full orbit. Let's get a bit more specific to avoid misunderstandings or irrelevant matters. Suppose we have two point masses that are in orbit with each other. The masses are significant, they are not so-called "test particles" and their masses are not identical. We also assume that this system is not influenced by far away gravitational fields. Now, can we construct a frame invariant definition of a full orbit? Any orbit is ok and with or without rotation of the point masses. I am trying to think of one I fail to see how.