Pings, SAR and probability
Per the recent discussion on what additional satellite ping data (about which we have not been given info) could provide...
It is unlikely that the additional pings would tell us exactly where the aircraft was. But... it would change the probabilities regarding possible flight paths and thus possible end points. In other words, it almost certainly would allow additional refinement of probabilities along the final ping path.
Expert SAR techniques (such as by the US Civil Air Patrol) use probability to allocate assets to search areas. Higher probability sectors get more assets, sooner. As a sector is searched, the probability of not seeing the target if it is really there is used to assign a new probability to that sector, ultimately altering overall probabilities and subsequent assignments. Certainly some agencies are using these techniques in this search. *Any* information may be used to adjust probabilities.
Finally, I have yet to see a definitive source for the accuracy of the ping arcs. If timing is used, one mile of slant range (from satellite to aircraft) corresponds to about 10 microseconds of round trip latency. Uncertainties in this are introduced by any variation in the latency within the aircraft's satellite system, the precision of measurement at the satellite, and the resolution of the logged time. If signal strength is used, uncertainties are likely higher.
That the estimated last ping is located exactly on the 40 degree antenna tilt angle (a circle of constant range from the bird) suggests that the accuracy is not high. Otherwise, we'd more likely see something like 38.52 degrees, or whatever.
Hopefully, someone will find a definitive answer to this question, to satisfy the curiosity of some of us, if nothing else.