Spinning the Earth

Newton’s Third Law: “To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.”

Every time you take a step, you are pushing yourself forward at the expense of something else going backward. In this case you’re pushing the Earth. Since the Earth is rotating eastward, if you take the step at the equator and also head east, you are slowing the Earth’s rotation down. If you heard west, you are speeding it up. Let’s see if everybody walking at the same time in the same direction can affect the Earth’s rotation!

First we list some of the numbers we’re going to use (rounded for simple calculations):

• A person’s mass: 1 e2 kg (average is closer to 70kg)
• Number of people: 1 e10 (closer to 6.7 e9; source)
• A person’s acceleration at beginning of sprint: 3 m/s^2
• Earth’s Radius: 6 e6 m (actual ~ 6.378 e6; source)
• Earth’s Mass: 6 e24 kg (actual ~ 5.9742 e24; source)
• Earth’s Anuglar Mass: 8 e37 kg*m^2 (source)

And some formulas:

1. angular mass = mass * radius^2
2. force = mass * acceleration
3. torque = radius * force (assuming ? of 90)
4. torque = angular mass * angular acceleration

From this we can calculate that if everybody stands at the equator and starts sprinting in the same direction at the same time, they exert ~ 2 e19 N*m of torque:

1. torque = radius * force
2. torque = radius * (mass * acceleration)
3. torque = (6 e6) * (((1 e10)*(1 e2)) * 3)
4. torque = (6 e6) * ((1 e12) * 3)
5. torque = (6 e6) * (3 e12)
6. torque = (1.8 e19)
7. torque ~ (2 e19) N*m

We modify one of the equations to tell us how fast the Earth would rotate with this much torque:

1. torque = angular mass * angular acceleration
2. angular acceleration = torque / angular mass
3. angular acceleration = (2 e19) / (8 e37)
4. angular acceleration = (2) / (8 e18)
5. angular acceleration = (1) / (4 e18)
6. angular acceleration = 0.000 000 000 000 000 000 25 rad/s^2

In this example we simplified the numbers and rounded them in the conservative side. If everybody on earth were to run in the same direction at the same time, we still wouldn’t budge the Earth one bit. Ok, maybe a tiny tiny tiny bit. But way too small to be of any significance.

Another way to alter the Earth’s spin: Water Reservoirs