# The Doppler shift and Flight 370

The following report from CNN (http://www.cnn.com/2014/03/24/world/asia/malaysia-airlines-satellite-tracking/index.html?hpt=hp_t1; the video from CNN can be found at http://www.cnn.com/video/data/2.0/video/world/2014/03/24/lead-foreman-satellite-data-mh370.cnn.html) discusses in layman’s terms how applied mathematicians were able to track the final moments of Flight 370. Here are the relevant paragraphs:

The mathematics-based process used by Inmarsat and the UK’s Air Accidents Investigation Branch (AAIB) to reveal the definitive path was described by McLaughlin as “groundbreaking.”

“We’ve done something new,” he said.

Here’s how the process works in a nutshell: Inmarsat officials and engineers were able to determine whether the plane was flying away or toward the satellite’s location by expansion or compression of the satellite’s signal.

What does expansion or compression mean? You may have heard about something called the Doppler effect.

“If you sit at a train station and you listen to the train whistle — the pitch of the whistle changes as it moves past. That’s exactly what we have,” explained CNN Meteorologist Chad Myers,who has studied Doppler technology. “It’s the Doppler effect that they’re using on this ping or handshake back from the airplane. They know by nanoseconds whether that signal was compressed a little — or expanded — by whether the plane was moving closer or away from 64.5 degrees — which is the latitude of the orbiting satellite.”

Each ping was analyzed for its direction of travel, Myers said. The new calculations, McLaughlin said, underwent a peer review process with space agency experts and contributions by Boeing.

It’s possible to use this analysis to determine more specifically the area where the plane went down, Myers said. “Using trigonometry, engineers are capable of finding angles of flight.”

My understanding is that even though the pings from a satellite to the plane and back were occurring, even though the plane’s location was not being transmitted. From the Doppler shift of those pings, the plane’s trajectory could be reconstructed.

Someday, for teaching purposes, I hope that a formal write-up of this procedure is published. The details will probably be over the heads of most students, but this is a eye-catching, though indescribably tragic, example of how mathematics can be creatively used to solve a mystery.

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