I think the easiest and simplest answer is:
a neutron star or a black hole.
Original from: http://imagine.gsfc.nasa.gov/docs/teachers/blackholes/bhm/images/st_diagram.gif
Imagine both orbits inside the funnel, the first slightly "above" the neutron star and the second 150.000km further up the funnel, but still with almost the same orbit length.
A strong point of gravitation will curve space-time.
Imagine a very heavy weight on an elastic plane, it will create a deep funnel.
If the enterprise is close to the object, it will orbit around it inside of the funnel. If it moves away from the object, the enterprise will "climb up" the inside of the funnel for 250.000 km, but will still be inside of the funnel.
From a top down view the enterprise will have almost the same distance to the black hole in both cases, since it moved along the curved surface "upwards" away from the anomaly, but the funnel will have almost the same radius, so the orbit has almost the same size (it will be a bit bigger, but the numbers are ~about the same)
From their personal viewpoint they will measure their distance along the wall of the funnel "down" to the black hole and by that measurement will have a distance of 250.000 km in the second case and keep this distance while moving in orbit. - Only once they are out of the extremely curved space-time around the black hole the relation of radius and orbit length will get back to expected values.
So, is this physically possible? It seems that it is.
Suppose our anomaly has a mass of about 30,000 solar masses. Its Schwarzschild radius will then be about 100,000km. Let the object be just barely too big to collapse into a black hole; then for a large range of radial distances from its surface, the circumference of a circle concentric with the object hardly changes.
(In the limit where the size of the object equals the Schwarzschild radius, it becomes a black hole; its surface is the event horizon; and the event horizon is infinitely distant from any point outside, as viewed by a stationary external observer.)
So now we begin 100,000km away (radially) from the surface of the anomaly; the fact that our orbit's circumference is about $2\pi$ times this distance is a mere coincidence; what's physically significant is that it's about $2\pi$ times the Schwarzschild radius of the object. We move to 250,000km away, but provided we put the anomaly surface close enough to the Schwarzschild radius this is still close enough that the orbit circumference is approximately $2\pi r_s$.
The term "orbit" is a bit misleading here, because
there are no actual stable orbits this close to a very massive object. (There are none closer than $3r_s$.) So the Enterprise must actually be taking active measures to avoid being pulled in by the anomaly.