Applying Physics to The Avengers

(WARNING: The following post contains physics as well as spoilers for a certain film.)

A couple months ago, I was watching The Avengers for the third time, and when the portal opened to start the alien invasion, I noticed that they kinda ignored the physics of the whole thing. The most obvious one (at least for me) was that for some reason none of the air was escaping into the vacuum of space. In addition, the Earth should have a gravitational pull on the space station, yet that doesn’t appear to be visible. And so, for whatever silly reason, I decided to actually crunch the numbers on the whole thing.

Before we begin, we have to make a few assumptions about the portal itself. Judging from the fact that the aliens only enter the atmosphere from one side, we can assume that one can’t approach it from “below” (in space) or “above” (above Earth). (Well, either that, or the aliens just have no tactical ability, which can’t be ruled out.) Judging from watching the film, the portal appears to be about 1100 metres off the ground and 200 metres in diameter, and was opened for 1400 seconds (assuming that there aren’t any jumps in time during that sequence of film). In addition, Stark Tower is about 300 metres tall, or about the height of one of the taller buildings in Manhattan.

Now it’s time to go to the actual physics! When the portal is created, there is atmosphere on one side and space on the other. The air escapes at a velocity equal to the speed of sound (about 340 m/s) into the vacuum above. This process will slowly drain the atmosphere in a manner similar to that of exponential decay. Since the other side is a pure vacuum, conditions will asymptotically approach that of a vacuum around Earth. The time it takes for this to happen can be approximated by the formula

where V is the volume of the air, A is the area of the hole, and pi and pf are the initial and final pressures, respectively. (Source) For the atmospheric volume, I just took the mass of the atmosphere and divided it by the sea level density. Plugging the numbers, we would have to wait about 15,000 years before half the air in the atmosphere is sucked out. In the duration that the portal was open, about two-billionths of the total mass of the atmosphere was released into space, which is still ten billion kilograms.

At one point in the movie, Iron Man redirects a nuclear missile headed to Manhattan and sends it to the alien space station instead. We assume that the missile has a constant velocity, the magnitude of which is not affected by Iron Man. He probably does accelerate it a bit, but trying to incorporate that introduces too many variables, and wouldn’t have too much of an effect on the final results anyway. We aren’t taking drag into account, since the missile is very aerodynamic, the speeds are relatively low while in the atmosphere, and in space there really isn’t any air to slow it down. It takes the missile 6 seconds to climb the 800 metres from the top of Stark Tower to the portal, 20 seconds from the portal until Iron Man lets go, and an additional 10 seconds before it explodes at the space station. Furthermore, it takes Iron Man 50 seconds to fall back through the portal. Creating a system of equations of motion, we can find that Iron Man falls about 12.5 km above the portal, and the space station is about 22 km above. So no worries, Felix Baumgartner, your record is still intact.

Of course, the space station itself is under the effects of the Earth’s gravity. It would be in free fall for the entire time that the portal is open, and would be accelerating at an increasing rate as it gets closer to Earth. Surprisingly, the equation governing free fall is actually extremely complicated, and is

where y0 is the initial separation, y is the current separation, t is the elapsed time, and μ is the standard gravitational parameter. (Source) Distances in this case refer to the distance from the object to the center of the Earth. Plugging in the numbers, the space station must have originally been about 4100 km above the Earth’s surface when the portal was opened. When the portal closed, on the other hand, the space station would be moving at about 7000 m/s, and would have crashed into the portal three seconds later.

Of course, those numbers don’t really make sense in context. The more realistic (Hah!) possibility is that the portal was attached to the space station in much the same way that the other end of the portal was attached to Earth. If that were the case, then the space station would just accelerate at Earth’s gravitational rate, but would stay at a constant distance away. In this case, by the time the portal had closed, the space station would be moving at a velocity of about 14,000 m/s, or about half the speed of Earth’s orbit around the sun. Needless to say, the space station would be way off-course. Let’s hope Thanos invested in a powerful set of rockets.

There is one last issue to be sorted out. When Iron Man falls back towards Earth, he will have to fight a massive updraft of all the air escaping from the atmosphere. This is much higher than the terminal velocity of a human, which means that poor Tony Stark will be pushed up, unable to make his way back through the portal, and consigned to a fate similar to that of Darth Vader at the end of A New Hope.

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