MadSci Network: Astronomy

Re: Is it possible to change the earth's rotation with man-made

Date: Sun Sep 26 15:08:37 1999
Posted By: Pauline Barmby, grad student, Harvard University Astronomy Dept.
Area of science: Astronomy
ID: 937943235.As

Hi Zane,

Your intuition that we can't change the Earth's rotation with rockets is correct. Here's a calculation to show this:

The angular momentum of the Earth is its moment of inertia, I, multiplied by its rotational velocity, omega. The moment of inertia for a sphere is 0.4MR^2 where M is the sphere's mass and R its radius. ("^" is supposed to represent an exponent, ie R^2= R x R). Assuming the Earth to be a sphere (not quite true, but good enough for this example) gives I = 9.8 x 10^37 kg m^2. Omega is (2pi radians/day)=7.27 x 10^(-5) rad/s.

Changing the rotational velocity of something requires exerting a torque on it. Let's assume that we exert the torque where it will have the maximum effect on the rotation, that is, at the equator, exactly against the direction of rotation. Then the torque is just tau= R x F, where R is the Earth's radius and F is the force applied.

How much force would we need to apply to change the Earth's rotation velocity by 1 percent? From the number I gave above, the change would be 7.27x10 ^{-7) rad/s. The angular acceleration alpha = tau/I = (change in omega)/(time torque is applied). We want to know F, which is (change in omega)x I/(time x R). Let's assume that our rockets fire for 10 seconds. Then the force required is: (7.27x10^(-7) x 9.8x10 ^37)/(10 x 6.4 x 10^6) = 1.1 x 10^(24) Newtons

This is a HUGE number! The Saturn V rockets -- the most powerful ever built -- produced 3.33 X 10^7 Newtons of thrust at takeoff. But this is pretty much zero compared to what you would need to change the Earth's rotation sped even a little bit.

As for having people jump off chairs, that doesn't work too well either. This MADSci answer estimates the force produced by everyone in China jumping off a chair. It's actually greater that what you might get from a single rocket, but still way too small to have an effect.

The Earth actually is slowing down very slightly: Because the Earth really isn't a perfect sphere, the Moon exerts a torque on it. This torque is very small, and the only reason it will eventually have a measureable effect is the fact that it acts over a very long period of time.


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