Can We Rotate the Earth with a Rocket?

[ibeukema]

Hi,

My roommate and I were wondering how much energy is needed to rotate the Earth about an equitorial axis. Just as a fun experiment to get Holland into the sun.

 

[mgb_phys]

Energy in a rotating body is 1/2 I w²
w is in rad/s so the Earth is rotating at about 2pi/24*3600 = 72uRad/s
I for a solid sphere is 2mr²/5

The mass of the Earth is 6x10²⁴ kg and the radius is about 6*10⁶m

So total energy is = 6x10²⁴*6*10⁶*6*10⁶ * 72*10^-6 *72*10^-6 /5 = 2²⁹ J

Edit, although if you don't want to stop it, just nudge the equator a little it would be a lot less.

 

[icelevistus]

his question was about rotating the Earth about an equatorial axis, not polar axis.

For this, you have to consider that you are going against the force of the Earth's angular momentum vector.

I haven't the desire to calculate it, but suffice to say that it is far more than all the king's horses and all the king's men would ever be able to conjure.