Following the recent downing of a Russian military jet by Turkish forces somewhere along the border of Syria and Turkey, both nations offered very different accounts of what happened. Two astrophysicists at the Belgian university KU Leuven have used simple Newtonian mechanics to show why both countries’ accounts cannot possibly be correct.

Last week, a Russian military jet was shot down by Turkey, who claims that it violated their airspace for 17 seconds, and ignored 10 warnings in the space of five minutes. Russia claims that it was shot down over Syrian airspace, and that it never violated Turkish territory. Two Belgian researchers decided to review the video footage of the incident to try and ascertain which account is more accurate.

When the first jet is hit, it begins tumbling to the ground, falling for 30 seconds before it impacts the hillside. Assuming the pilot lost control of the plane immediately, the downwards movement is only dependent on gravitational acceleration. Backtracking this acceleration downwards, they calculated that the plane was traveling at a height of 4,500 meters (14,800 feet) when it was hit – roughly consistent with Turkish accounts at this point.

Turkey claimed a specific crash site, 8 kilometers (5 miles) from where it was hit. This means that it must have been traveling at an initial speed of 980 kilometers per hour (610 miles per hour). Turkish officials say that the jet was traveling through 2 kilometers (1.24 miles) of Turkish airspace for 17 seconds.

At this speed, however, it would have only taken seven seconds. In addition to this, if the jet was traveling at that speed, it would cover a distance of 80 kilometers (50 miles) in five minutes – making the Turkish military’s statement of “ten warnings in five minutes” seem highly implausible; the warnings could not have all fitted into just seven seconds. The warnings made would therefore have been based on mere speculation as to whether or not the plane was crossing the border.

Image credit: An airstrike on Kobane, a town close to the Syrian-Turkish border. Orlok/Shutterstock

Although this makes the Turkish claims fairly suspicious, the Russian claims are also quite dubious, according to the researchers. The Russian map that apparently shows the jet not violating Turkish airspace at all shows that it changed course by 90 degrees when it was hit by the missile. “A change of course of 90 degrees can only be achieved with an object that’s many times heavier or faster than the jet,” the physicists note on their blog.

A surface-to-air missile would not have caused this to happen, implying the 90-degree turn was caused by the pilot’s own maneuvering. Therefore, despite Russia’s claims to the contrary, the jet was likely not actively avoiding Turkish territory.

So, according to science, both Turkey and Russia are, to some degree, contriving falsehoods.

[H/T: Motherboard]