UPDATED: See end for description of possible northern route

On Saturday, March 15, Malaysian authorities released an analysis of satellite data that dramatically narrowed the possibilities for where missing Malaysia Airlines Flight 370 had gone after it disappeared from radar on March 8. Over the course of the following week, Inmarsat released further information that not only showed where the plane went, but also indicated how it got there. The results are shown on this chart. We still don’t know if the plane headed north or south, but if it went north, it made landfall near the western India-Bangladesh border and proceeded along the Himalayas to Central Asia. If it went south, it passed over western Indonesia and out over the southern Indian Ocean.

How are we able to determine this? The procedure requires a bit of explanation. Inmarsat is a communications satellite in geosynchronous orbit over the Indian ocean. That means it remains in the same place in the sky, like it’s sitting on top of an invisible pole. Because it’s so high up, it has a straight line-of-sight to virtually the entire eastern hemisphere. That’s great for radio communications: if you can see it, you can send it a message, and it can send that message along to anyone else in the eastern hemisphere, or to a base station that can then relay it to anywhere in the whole world.

Every hour, Inmarsat 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, “Yup, 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 allow us to 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 further away the plane is, the longer it takes to say “Yo!,” 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 like somewhere along a circle that’s 20 feet in radius, with you at the center:

Now, it happens that in this room there are walls and pieces of furniture, so you’re able to rule out certain spots based on that, so instead of a whole circle, you have pieces of circle, or arcs.

MH370 was in an analogous situation. When Inmarsat pinged it at 8.11am, the amount of time it took the plane to reply allow us to calculate its distance from the satellite, just as if it was holding a taut piece of string. Instead of furniture, factors such as speed and fuel capacity provide other limitations of where it could be, so its range of possible locations is also not a circle but a series of arcs:

Note that these arcs do not represent the path that the plane took, but the range of possible locations at 8.11am. That particular ping tells us nothing at all about how the plane got to wherever it happened to be. So at this point all we know is where it started (it disappeared from Malaysian military radar at 2.15am at a spot between the Malay Peninsula and the Andaman Islands) and where it ended up. It could have taken any of a zillion routes to get from its start point to to its final recorded location somewhere on that last arc.

Remember, however, that Inmarsat received six earlier pings as well, and from them we can narrow down the range of possibilities dramatically. The first was received at 2.11am, just before MH370 disappeared from Malaysian military. Its length indicates that the plane must have been somewhere on the green circle at that moment:

Of course, thanks to radar we happen to know in this case pretty much where the plane really was at this time — around the area of the pink dot.

On Friday, March 21, an Inmarsat spokesman told me that “the ping timings got longer,” meaning that the distance between MH370 and the satellite grew increasingly bigger, and never smaller. That means that at no point during its subsequent travels did MH370 travel any closer to Inmarsat. So from the 2.11am ping data alone, we can rule out every spot within the green arc:

MH370 never traveled anywhere in the shaded area. (Of if it did, didn’t stay there for long; by the end of the hour it had to be outside.) We also know that it never was further away from the satellite than it was at 8.11am, so we can exclude everything east of that, as well. Finally, we can rule out some chunks close to its starting point for other reasons:

So just from the 2.11am and the 8.11am pings, we know that MH370’s route of flight must lie within either of these two broad swaths — one lying to the north, and the other to the south. Bear in mind, the reasoning that we’ve just gone through doesn’t tell us anything about whether the plane went to the north or two the south. Because of the symmetry of a circle, the possible paths are mirror images of one another. However, we’ve vastly reduced the range of flight routes that MH370 could have taken. For instance, a popular theory circulating on the internet posits that MH370 tucked in close behind a Singapore Airlines flight, “SIA68,” in order to hide in its radar shadow:

This new Inmarsat data rules out that possibility. It also rules out the idea that MH370 flew south through the middle of the Indian Ocean to avoid military radar. If the flight went south, it would have had to have gone through Indonesian radar coverage.

Interestingly, on March 19, the website Antara News reported that “Indonesian Defense Minister Purnomo Yusgiantoro said the Indonesian military radar placed in the country’s western-most city of Sabang did not detect an airplane flying over Indonesian territory.”

On March 22, 2014, CNN reported that China, India, Pakistan, Myanmar, Laos, Kyrgyzstan and Kazakhstan have told investigators that “based on preliminary information, their nations had no radar sightings of missing jetliner.”

So far, we haven’t talked about what we can deduce from the remaining five Inmarsat pings, the ones received at 3.11, 4.11, 5.11, 6.11, and 7.11. It should be possible, based on the presumed speed of the plane and the distance between the successive arcs, to make some reasoned guesses about how the plane traveled from one to the other. I haven’t seen the data yet—I’m working on it—but earlier this week the Washington Post published a map that showed what appeared to be the results of just such analysis as applied to the southern route, carried out by the NTSB:

This appears to be why the nations assisting the investigation have poured so many assets into searching that particular stretch of southern ocean. If MH370 took the southern route, it would have had nowhere to land, so it must have crashed and its debris must still be floating somewhere in this area.

Of course, the information we glean from Inmarsat data about MH370’s flight route is, by itself, symmetrical around an axis that runs from the spot on the ground underneath Inmarsat to the point where the aircraft was last observed. So assuming that the NTSB’s interpretation of the southern route was only based on factors of speed and arc spacing, it should be applicable in mirror form to the northern route as well. I’m working on that right now.

UPDATED 3-23-14: Okay, I feel a little slow on the uptake on this one, but it turns out that if you flip the NTSB’s guesstimated southern route, you come up with a northern route that looks pretty much like this one published in the Daily Mail (I know, I know):

Basically, you make landfall in the vicinity of Bangladesh, skirt along the border between India and Nepal, then cut across northeastern Pakistan and Afghanistan before winding up in Uzbekistan or Kazakhstan. This may be why Malaysia recently asked Kazakhstan if it could set up a search center there.

Kazakhstan would not be a bad place to try to hide an airplane. It is larger than Western Europe with a population of just 17.7 million. Its expansive, sparsely populated steppe and desert terrain make it perfectly suited as a touchdown spot for Soyuz space capsules. The country gained independence from the Soviet Union in 1991 but its communist-era ruler, Nursultan Nazarbayev, remains in power. He is a close ally of Putin, and two days after MH370 disappeared told the Russian premier “that he understands the logic of Russia’s actions in Ukraine,” according to Reuters.