I have been giving this a bit of thought and as usual have managed not to make myself at all clear. In fact I was about to post this reply in the wrong thread until I did a quick reread.

It is rocket science actually. If there is a second underlying geodesic then all the data from the telemetry and from others that did not alter should be able to determine if there is an underlying shape of space beneath what we know.

From the time of mission, start position, end position and velocity of each of the flybys then a basic size, curvature and shape could be determined. It is just a matter of plugging in the numbers.

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"Nature is obliged to let reality determine its laws, whereas mathematics is under no such constraint."