If that were all there was to it, then the story would end there. You would never be able to pinpoint your brother-in-law’s location, and Inmarsat would never be able to locate MH370. But there’s a wrinkle. Your brother-in-law thinks that you’re standing still in a certain position, but in fact you’re a short distance away from that spot, and you’re moving. As a result, what you hear isn’t exactly F sharp.
In the case of MH370, the satellite communication equipment was programmed to assume that the Inmarsat satellite in question was orbiting over a fixed position at the equator. But in fact its orbit has a slight wobble. During the hours the plane was missing, the satellite was above the equator, moving first north, and then south with increasing speed.
This error in calculating the satellite’s position means that the plane’s electronics failed to correctly compensate for its own velocity. When the plane first disappeared from radar, the angular distance between where the satellite was and where the plane thought it was amounted to about 3 degrees, enough to generate a velocity error of 20 miles per hour.
As the hours passed and the plane got farther away from the satellite, this effect became less pronounced. At the same time, however, a second source of error was growing: The satellite was accelerating on its path toward the Southern Hemisphere. This would cause it to receive an unexpectedly higher frequency from a plane flying south of the equator, and an unexpectedly lower frequency from a plane flying north of the equator. What’s more, this effect would become more pronounced the further the plane was from the equator. A plane traveling north at 450 knots would be traveling away from the satellite at 16 knots more than expected by the end of its flight. For one traveling south at 450 knots, the error would be in the other direction, to the tune of 18 knots.
Understanding all this, we can at last make sense of the mysterious BFO chart from March 25. Just after the plane disappeared from radar, the plane’s position error would have made a northbound plane’s transmission frequency too high, then after a few hours the satellite velocity error would have made it increasingly too low. Conversely, in the early hours after its disappearance position error would have made a southbound plane’s frequency too low, but then satellite velocity error would have gradually made it get higher.
Because the satellite’s velocity error becomes so dominant toward the end of the flight, and because that error varies strongly with the latitude at which the plane happened to be, the BFO value basically tells you where along the final “ping arc” the plane was when it neared the end of its flight. And this, we can assume, is why the authorities have been searching the particular stretch of ocean they’re looking at now.
For those like me, who thought it possible, even likely, that the plane might have gone north, this comes as bad news. It seemed to me that there were lots of potential motives perpetrators might have for taking a plane north; what’s more, if the plane went north, one could entertain hope that the passengers might still be alive. At the time I first made that suggestion I was roundly criticized by those who preferred the theory that the plane’s change of course was a result of mechanical mishap. The fact is that none of us had enough information to prove our case, but we were making good-faith efforts to make sense of limited data. Indeed, even now the flight path that we’re left with is difficult to make sense of, since it jibes with neither a deliberate action nor a mechanical failure. Perhaps, as some have suggested, the disappearance took part in two phases: first, a deliberate diversion of the plane to a westerly course, and then, at around 18:25 GMT, an accident or act of violence that sent it heading south as a ghost ship.
To be sure, then, the solution of the Inmarsat data mystery leaves plenty of questions to be answered. If the plane did go into the ocean, why hasn’t any debris been found? If it tracked south over Indonesia, why wasn’t it picked up on radar? And if the final BFO value should give such a clear indication of where the plane wound up, why have the authorities shifted the search area multiple times—and why are experts within the search, as reported yesterday by the Wall Street Journal, continuing to debate the significance of factors like airspeed and fuel burn?
For me, though, the most perplexing question is why the authorities released the Inmarsat information the way they did. For nearly three months now, the public, and in particular the passengers’ families, have struggled to understand why the authorities were so adamant that the plane had gone south. Instead of simply explaining the facts, which as I describe here seem to be pretty straightforward, they obfuscated, delayed, and bluffed. When they finally did reveal the truth, they tucked it away inside a ream of data so as to make its revelation as difficult as possible.
At any rate, the end effect is the same: We the public finally understand the official stance on the fate of the plane. But Inmarsat and the Malaysian authorities could have gotten us to this point without seeming mean-spirited and obstructionist.
This article is part of Future Tense, a collaboration among Arizona State University, the New America Foundation, and Slate. Future Tense explores the ways emerging technologies affect society, policy, and culture. To read more, visit the Future Tense blog and the Future Tense home page. You can also follow us on Twitter.