Neuro, what if it wasn't a massive object, but a large asteroid field? It would then be distributed in space, and as we get closer to it, the center of gravity appears to shift towards the center of the field rather than staying with the leading objects, and also increasing in magnitude.

I agree the constant 188 day cycle doesn't make much sense for an elliptical obit of a large object. And if it wasn't elliptical, then the object wouldn't just appear there.