Are Rocket Booster Tests Slowing Down (or Speeding Up) the Rotation of the Earth?

Seeing the recent solid fuel rocket booster test got me to thinking about how much this might change the rotation of the Earth and thus the length of our day. What if it shortens the day?! It would be "Give us back our 11 days" all over again.

Anyway, The calculations seemed simple enough and follow for your viewing pleasure. (Note: if you find any major errors I'll just fix the blog and pretend it was right all along).

First, the change in angular momentum of the Earth is (F)(d)(t), where 'F' is the force of the rocket engine, 'd' is the distance from the axis of rotation, and 't' is time. For this blog I'm going to try and get the maximum effect, so we'll assume the engine is set parallel to the ground at the Equator (i.e. perpendicular to the radius), and facing East (or West).

The change in angular momentum = (moment of inertia)(delta omega) where 'omega' is the angular rotation of the Earth in Radians/sec.

For this calculation I'm going to assume a big rocket thruster produces roughly 10,000,000 Newtons force (the one linked to above may be slightly larger) and runs for a minute. The moment of inertia of the Earth is about 8 x 10³⁷ kg m², and the radius of the earth is roughly 6500 km. Putting this all together gives:

(8 x 10³⁷ kg m²)(delta omega) = (10,000,000 kg m/s²)(6,500,000 m)(60 s)

Doing the math:
(delta omega) = 4.9 x 10^-23 rad/sec

Seems pretty big so far - after all 4.9 is no small number. But it would be useful to see just how much the x 10^-23 affects it. (Side note, this reminds me of Avogadro's number which is 6.02 x 10²³)

So how much of an effect is this? How long will it take the Earth to slow down or speed up enough to add or subtract another second to the day?

1 second is 2(pi) / (24)(60)(60) radians
so 4.9 x 10^-23 (t) = 2(pi)/(24*60*60)
t=1.5 x 10¹⁸ seconds or roughly 4.7 x 10¹⁰ years (or approximately 10 times the age of the earth!)

Maybe not quite such a large effect!

20150316 Update: Seems that similar calculations have been done ('stopping the world' using Space Shuttle boosters) and the numbers are similar - with the caveat that it's only really valid if the Earth has no atmosphere! Oh well, it probably only works for spherical chickens in a vacuum (Big Bang Theory reference to the spherical cow metaphor).