Evidence that flight MH370 crashed in the southern ocean: Doppler effect and math.
The Evidence That Flight MH370 Crashed Isn’t Wreckage. It’s Math.
The citizen’s guide to the future.
March 25 2014 8:25 PM

How Can Math Decide That Someone Is Dead?

The best evidence that flight MH370 crashed in the southern ocean.

Australian Maritime Safety Authority Emergency Response Division General Manager John Young speaks to the media about satellite imagery of objects possibly related to the search for Malaysian Airlines flight MH370 March 20, 2014 in Canberra, Australia.
A U.K.-based satellite company, Inmarsat, has deployed a new kind of mathematical analysis to determine the plane’s trajectory.

Photo by Stefan Postles/Getty Images

For the relatives of passengers aboard Malaysia Airlines Flight 370, the announcement by the Malaysian Prime Minister Najib Razak on Monday must have registered as a double shock. First there was the fact that their loved ones were dead: “The past few weeks have been heartbreaking; I know this news must be harder still,” Najib said at a press conference after families were notified. More surprisingly, the announcement was made even though no bodies or wreckage had been recovered. Instead, the passengers’ fate had been determined by math alone. A U.K.-based satellite company, Inmarsat, had deployed a new kind of mathematical analysis to determine that the plane’s trajectory had carried it deep into the southern Indian Ocean, a region where there are were no landmasses upon which a plane can set down. Ergo, the passengers were all dead.

In Beijing, family members reacted with outrage, staging an impromptu march on the Malaysian embassy. One can only imagine how frustrating it must be to be told to abandon hope, to grieve in the absence of any material evidence of loss. They must have wondered if they could really believe what they were being told. Unreliable information has been reported throughout the search process, with assertions made about the flight only to be later refuted, modified, or quietly dropped. Amid all the uncertainty, how much credence should be given to this new mathematical formula, which seemed so complicated that hardly anyone could understand and whose underlying data remains veiled in secrecy?

That’s what I wondered when I heard the news, but after reviewing Inmarsat’s publicly released information with an expert, I’ve come to the conclusion that its findings are most likely sound. With caveats.


Since Inmarsat’s data is the only source of information we have about the fate of MH370, it’s worth reviewing how the system works. Inmarsat is a communications satellite in geosynchronous orbit over the Indian Ocean. Every hour or so, it sends out a short electronic message to subscribers that says, “Hey, are you out there?” The message contains no information as such; the satellite just wants to find out if that particular subscriber is out there in case it wants to talk. Kind of like picking up your telephone just to see if there’s a dial tone. On the morning of Saturday, March 8, MH370 replied seven times to these pings, saying, in effect, “Yes, I’m here.” The line was open for the plane to communicate with the outside world. But the system that generates the messages themselves, called ACARS, had been shut off. So nothing else was communicated between the satellite and the plane.

All the same, those pings tell us something important about MH370: They narrow down its location. Because light travels at a certain speed and electronics take a certain amount of time to generate a signal, there’s always a length of time between the satellite’s “Hey!” and the airplane’s “Yo!” The farther away the plane is, the longer it takes to respond because it has to wait for the signal from the satellite to travel that extra distance.

Imagine you and I are in a darkened room. You have no idea where I am, except you know that I’m holding one end of a taut 20-foot rope, and you’re holding the other. Therefore I must be 20 feet away. You don’t know where I am, exactly, but you know that I must lie somewhere along a circle that’s 20 feet in radius, with you at the center.

MH370 was in an analogous situation. When Inmarsat pinged it at 8:11 a.m. and received MH370’s reply, the amount of time it took the plane to respond allowed investigators to calculate its distance from the satellite. This did not correspond to a specific location but to an arc of possible locations across Central Asia in the north and the Indian Ocean to the south. This information was announced to the public on Saturday, March 15, by the prime minister of Malaysia.

This result was a huge breakthrough for the investigation, and it raised a question: Could analysis of the six earlier pings narrow down the route that the plane had taken? The U.S. National Transportation Safety Board obtained the data from Malaysia and set to work.

The process is fairly straightforward. The first ping coincided more or less with the time when MH370 slipped out of range of Malaysia’s military radar. So we have a starting point. By knowing the interval to the next ping, and by estimating the plane’s speed, we can arrive at a distance traveled during that time. Given the radius of the next arc, it’s a simple matter to calculate a route by angling the distance traveled to meet up with that arc.

When the NTSB ran the numbers, the resulting plot showed the plane winding up in a remote part of the Indian Ocean, and that’s where searchers began focusing their efforts. Soon after, satellite photos showed large pieces of debris floating in the water, and the Australian Prime Minister Tony Abbott jumped to the obvious conclusion: He announced on Thursday, March 20, that that investigators had found their first hot lead. “This is the first tangible breakthrough,” he said. “This is a very serious lead in the way that nothing else so far really has been.”

  Slate Plus
Political Gabfest
Oct. 6 2015 11:18 AM The “How Do You Punish This Company?” Bonus Segment Emily Bazelon, Jamelle Bouie, and David Plotz discuss reprimanding Volkswagen for ethical misconduct.