Extra Credit Blog

How Great Is Earth's Momentum?

“What would happen if everyone on Earth stood as close to each other as they could and jumped, everyone landing on the ground at the same instant?” was asked by Thomas Bennett specifically, but it is a premise that has been wondered by many over the course of history. This question was a topic of much speculation and optimism, and it wasn’t until Rhett Allain used the laws of conservation of momentum and energy that the world had a definite answer.

Allain is an Associate professor of Physics at Southeastern Louisiana University, and, when cogitating this problem, he made a couple of assumptions and estimates. First, he rounded the worldwide population to be 7 billion, and then he assumed that the average weight (given that there will be kids and the elderly doing this as well) to be 50 kg. Lastly, he made the generous assumption that everyone was able to jump 0.3 meters in the air.

Through the work at the bottom of the page, Allain came to the conclusion that everyone jumping at once would not have any significant effect on the Earth. In fact, the velocity that he calculated the Earth moving in towards its core due to this experiment (2.6 x 10^-13 m/s) is so minuscule that it is still only about one hundredth the radius of a single hydrogen atom. This is not to say that everyone in the world jumping and landing at once does not create a lot of energy, it is just that the momentum of the Earth is so much greater. The Earth has a total mass of approximately 6 x 10^24 kg, and it moves at a speed of 460 m/s. For all the people in the world to counteract, or even equal this momentum (upholding the assumption of an average weight of 50 kg), they would have to achieve a collective velocity of 7.89 x 10^15 m/s. That is 7.89 quadrillion meters per second, which is more than 26 million times the speed of light. As a side note, for Allain's calculations for the momentum generated by everyone jumping at once to be maximized, the crowd would have to be fit into as small as an area as possible. Rhode Island was found to be ideal. If everyone in the world were to be standing shoulder to shoulder as this experiment demands, the crowd would fit almost perfectly into the state of Rhode Island.

An experiment similar to this was actually conducted in 2012 at the Reading and Leeds Festival in the U.K. Here, a man named Greg Foot got everyone in the crowd of around 50,000 people to jump at once, an impact that he measured using a seismograph 1.5 kilometers away. The impact registered as a 0.6 on the Richter scale. For something to have an effect on the spin of the planet, it needs to measure at least an 8 on the scale. After crunching the numbers, Foot calculated that you would need 7 million times the current population of the Earth to even come close to such an amount of energy.

To put things in perspective, the earthquake in Japan in 2011 registered as an 8.9 on the Richter scale, which has an equivalent energy release to around 1.8 trillion kg of explosives. This earthquake moved so much of Earth’s mass towards the center, and therefore increased Earth’s rotational speed, that every day since has been approximately 1.8 microseconds shorter.

So, to answer the question “What would happen if everyone jumped at once?”; Well, nothing significant, at least as a direct consequence. The Earth’s mass is so great and is spinning so fast that, even with an impact of 7 billion people, nothing really happens. If such a situation were ever simulated, however, the process itself would result in near-mass extinction. The situation was pondered by the website “What If” and, if everyone in the world were to gather in Rhode Island to conduct this outlandish experiment, within weeks after the experiment, Rhode Island would be “a graveyard of billions”. This is because the T.F. Greek airport in Warwick only has the capacity to handle a few thousand passengers a day, and “they could run at 500% capacity for years without making a dent in the crowd”. The roads would be so overpopulated with people and cars that they would become unnavigable, and food and water stocks would quickly dissipate. For those that were able to escape, “any two people who meet are unlikely to have a language in common, and almost nobody knows the area”. Crime and violence would be unfiltered, as every type of law enforcement in the world is in Rhode Island, and an environment that truly is survival of the fittest would be created.