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If I jump, will the entire earth move a little bit?
Category: Earth Science
Published: June 4, 2013
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and physics professor at West Texas A&M University
It's true that every force has an equal and opposite force. Newton's Third Law of Motion states that to every action there is an equal and opposite reaction. When the earth pushes on you to send you into the air after jumping, you also push on the earth with the same force. But forces are different from accelerations. A force F is a push or pull on an object. The acceleration a is the change in speed of the object that results from the force. According to Newton's Second Law of Motion, the force and resulting acceleration are related according to the equation F = ma, where m is the mass of the object. This means that if we hold the force constant, then the bigger the mass, the smaller the acceleration. The mass of the earth is so huge, that the acceleration caused by the force of one person jumping is ridiculously small. It's small, but in this simplified picture, it's not zero. The earth would therefore move a ridiculously small amount when you jump (at least in this simplified picture). To move the earth a noticeable amount, you would need a bigger force, such as a collision with another planet. Even though you have, in principle, moved the earth, the mutual gravitational attraction between you and the earth would quickly bring you back together again. You fall back to the earth and the earth falls back to you, and once you are reunited, any displacement of the earth that you might have created is gone.
This simplified picture would only be true if you were the only object in the world pushing on the earth. In reality, the earth is covered with billions of people and creatures all jumping, walking, bumping, tumbling, or breathing on the surface of the earth at the same time. Being distributed somewhat uniformly over the earth's surface, the forces on the earth from all these creatures tend to cancel each other so that the earth feels no net movement, not even a ridiculously small one. Even if we take into account all the people and creatures in this way, our picture is still too simple to get at the truth.
In reality, the earth is not perfectly rigid. Even the hardest bedrock is somewhat elastic. This means that when you jump, you don't actually exert a force on the entire earth at once. Being elastic, the entire earth does not accelerate all at once away from you when you jump. Instead, you just deform a tiny bit of earth right under your feet. If the ground you are standing on is loose and weak, such as sand or mud, then the deformation caused by jumping only travels a few meters. If you jump while you are standing on bedrock, then the deformation will ripple away for several meters in the form of very weak seismic waves. The seismic waves caused by humans jumping are so weak that they are quickly overpowered by the seismic waves caused by more powerful forces such as ocean waves, wind, and earthquakes. The local earth movements caused by people walking, cars on the highway, a truck rumbling down the road, a train pummeling down the track, etc. are called "ambient vibrations" and are considered noise on a seismograph. The seismic wave created by a person jumping is far too weak to travel all the way to other side of the earth and therefore be considered as having moved the entire earth in any sense of the phrase. A stronger force, such as is due to an exploding nuclear bomb, a volcano that has blown its top, or an earthquake, does create seismic waves that are strong enough to travel to the other side of the earth. But the center of earth does not change in these cases, because the ground is just vibrating and is not permanently displacing.