Everyone Jumps!

What would happen to the motion of the earth if all of the people in the world gathered in a single place and then jumped at the same time? This is an age old question that many scientists have pondered.There are roughly 7 billion people on Earth, with a total weight of approximately 800 billion pounds (363 billion kg) so there needs to be a place that would fit everyone in the world. Since people are spread out around Earth;s surface, if we all jumped in place, nothing would really happen. All go out impacts and jumps would cancel each other out. This would result in a net force of zero on the Earth. However if everyone gathered in the same place, there could be a very different outcome.

The first issue that would need to be contemplated is where everyone would gather. If everyone in the world stood shoulder-to-shoulder, we could all fit into a space the size of Los Angeles—that’s more than seven billion people packed into 500 square miles (which is a pretty tight squeeze). But even if we all jumped at once in that small area, not much would happen. Our collective mass is extremely heavy. However, it is just not as heavy as compared to the mass of the Earth.

Using the laws of conservation of momentum and energy, we can calculate what would happen to the 6-trillion-trillion-kilogram Earth under these circumstances. Assuming each human could jump one ft (30cm) in the air and that we would all be jumping from the same point, we can prove that the Earth would only move slightly.

Calculations

After solving for velocity, I plugged in the values of earth and the people. I estimated that the number of people on earth were 7.4 billion people with an average weight of about 62 kg. The weight of all the people combined would be about 458.8 billion kg and the height each person would jump would be 30 cm. The weight of the earth would be 6 x 10^24. 

After plugging in these numbers into my equation I found that the velocity would be 2.6 x 10^-13 m/s. So, in one second, the earth would move about a hundredth of the radius of a hydrogen atom. This just goes to show that our weight is insignificant compared to the grand size of the earth. 

Now, if instead of gathering in LA, we could gather in Rhode Island. RI would fit the crowd much more comfortably. However, the problem with having all these people come to Rhode Island would be getting them out. 

TF Green airport handles only around a few thousand passengers per day. If the airport increased its efficiency and ran at 500% capacity for years, it would only make a trivial indent in the crowd. If TF Green continued at this pace it would take almost 2,000 years to ship all the people back to their homes and by then all those people would be dead. Some people could probably make it into neighboring states, but resources would be used up very quickly because there wouldn't be enough resources to go around. The only thing that would work is if more airports were built in RI in order to fly everyone back to their homes. 

Sources:
https://www.livescience.com/33383-everyone-on-earth-jumping-at-once.html
http://mentalfloss.com/article/54836/what-would-happen-if-everyone-jumped-once
http://www.businessinsider.com/what-happens-if-everyone-on-earth-jumps-at-the-same-time-2016-6