By Timothy Cho
Editor-in-Chief

On Tuesday, Nov. 24, Turkish jets shot down a Russian Su-24 military jet near the Turkey-Syria border, and both governments have disputed the specific details of what exactly occurred. Both presidents have issued statements of the matter, defending their actions while accusing the other of hostile behavior.

Russian President Vladimir Putin claimed the jet was on its way to attack the Islamic State in Syria (ISIS) and publicly accused Turkey of shooting down the jet to protect secret oil trade with ISIS. Turkish President Recep Tayyip Erdogan publicly stated that the Russian jet violated Turkish airspace, entering Turkish territory without authorization; he further stated that he will resign from his position if Russia can prove its claim.

Amidst the politics, two Belgian physicists published an online article on the blog “Ku Leuven,” disproving both Turkey and Russia’s statements with their mathematical calculations. According to the co-authors, Tom Van Doorsselaere and Giovanni Lapenta, the evidence Turkey and Russia provided are scientifically false.

Here’s where physics enters the scene.

Based on video footage of the jet plummeting towards the ground after impact with a Turkish missile, its estimated descent took approximately 30 seconds. Calculating the height immediately after explosion incorporates the time the jet took to descend, the gravitational constant and assuming the jet had no vertical motion, its gravitational force balancing with its lift.

According to Newtonian physics, the equation y = vot – 1/2 gt2, when applied here with substitution of the initial vertical velocity, zero, the amount of time the jet took to descend, 30 seconds and gravitational constant, 9.81 meters per second squared, will yield the height of the jet immediately after the missile collided with it.
Using the previous equation, the height immediately after explosion is 4,410 meters (14,469 feet). Doorsselaere and Lapenta, according to their published article, calculated a height of 4,500 meters (14,764 feet) while the Turkish government stated the jet was at a height of 5,800 meters (19,029 feet).

Turkey has also claimed that the jet traveled eight kilometers (26,247 feet) after it was hit by their missile, of which two kilometers (6,562 feet) occurred over Turkish air over the course of 17 seconds. However, physics proves otherwise.

The jet’s initial velocity was composed purely by the velocity in the horizontal direction and, given the total horizontal distance, the jet’s initial velocity can be calculated and used to prove whether or not the jet truly took 17 seconds to travel 2 kilometers (6,562 feet).

Newtonian physics state that horizontal velocity can be found with Vx= X/t, with “X” equal to the distance and “t” equal to how long the jet took to travel that distance. Substituting 8,000 meters (26,247 feet) and 30 seconds, Vx equals 266.67 meters per second (597 miles per hour).

The equation Vx= X/t results in a time value of 7.5 seconds; with X as 2,000 meters (6,562 feet) and Vx as 266.67 meters per second (597 miles per hour), time is calculated to be 7.5 seconds, compared to Doorsselaere and Lapenta’s calculated 7.5 seconds.

Comparing the calculated 7.5 seconds to Turkey’s claimed 17 seconds, the physics disproves the politics.

However, Russia has its own problems with the evidence it provided; Russia distributed maps of the jet’s hypothesized route, but there lies a problem—approximately four miles east of Turkey’s south-western border with Syria, the Russian jet took a sharp near-90 degrees turn to swerve clear of the border. The problem arises when considering that for the Russian jet, a Su-24, weighing at a maximum 43,755 kilograms (96,463 pounds), moving at its speed requires a massive external force to turn at such an angle.

A moving object requires an external force to change direction and in the case of a jet, the pilot may change the jet’s direction. However, the pilot reportedly ejected out of the plane prior to the jet-missile collision, which leaves only an external force to change direction. The impulse, instantaneous change in momentum, required to change the direction of a Su-24 jet moving at such a high velocity would be extremely high. For a missile and its explosion to change the jet’s direction in such a drastic way is improbable.

Therefore, while the discourse between Russia and Turkey continues, one thing is certain: According to physics, both are already wrong.

Eureka.