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Ready, Set … Jump!

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Ready, Set … Jump!

Post by The Catalyst on Sun Feb 26 2012, 01:38

If every person in China climbed to the top of a six-foot (two-meter) ladder and then all jumped off at the same time, could it nudge Earth into a different orbit?

No, but it sure would create a windfall for Chinese podiatrists.
I suppose that everybody picks on China when they ask this question because China is the most populous country on Earth, containing 2.5 billion potentially sore feet.
There are really two questions here, aside from the question of why people who ask this question don't have anything better to do. (Just kidding; it's fun to wonder about such things.) The first question is how strong the jump-thump would be, and the second question is whether any size thump at all could change Earth's orbit.
It's easy to calculate the amount of energy from a gravitational fall. (And don't tell me they're not falling because China is upside down.) Assuming a population of 1.2 billion Chinese weighing an average of 150 pounds (68 kilograms) each, their collective pounce would hit the ground with an energy of 1.6 trillion joules. (A joule is just a unit of energy; don't sweat it.) That's just about the amount of energy released in a medium-sized earthquake measuring 5.0 on the Richter scale. Such earthquakes have been occurring for millions of years, and there is no evidence that they have nudged Earth into different orbits.
But no amount of earthquake or footquake energy could change the orbit anyway, so both earthquakes and Chinese ladders are irrelevant. Planet Earth continues circling the sun because it has a certain amount of momentum, which means that it has a certain amount of mass and a certain velocity, because momentum is a combination of mass and velocity. Our planet carries along with it everything that is attached to it by gravity, including jumping Chinese and acrobats on trampolines. We're all one big package of mass, and no amount of jumping up and down can change Earth's total amount of mass. Nor can it change the planet's velocity, because all the Chinese are being carried along through space at the same speed as the rest of the planet; we're all in one big, interconnected spaceship. You can't change the speed of your car by pushing on the windshield, can you? Nor can you lift it by pushing on the inside of the roof.
We might put it in terms of Newton's Third Law of Motion, which you must have heard a million times (and will again, if I have anything to do with it): “For every action there is an equal and opposite reaction.” Push on a brick wall and the wall pushes back. If it didn't, your hand would go straight through. When the Chinese land, their feet hit the ground with a certain amount of force, but at the same time the ground hits their feet with an equal amount of force in the opposite direction. Thus, (a) there is no net (unbalanced) force that could affect our planet's motion and (b) their feet hurt.

The Catalyst

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