### New Scientist - Last Word contributions by Dr Hugh Hunt

8 September 2007

Q: Stop the world If you used, for example, the engines of the space shuttle to do it, how long would it take? And what would be the effect on the planet, in particular the weather and the tides?

A: This is an excellent question for practising numeracy. All that is needed is some basic mechanics, made a tad more difficult for being rotational. I have rounded up a few of the figures.

The mass of the Earth (M) is 6 x 1024 kg and its radius (R) is 6.6 x 106 m. Assuming it to be a solid homogeneous sphere, its moment of inertia (J) is given by 0.4 M R2. It works out at 1038 kg m2.

The planet spins once in 24 hours (86,400 seconds) so its angular velocity ( w ) is 4.16 x 10-3 degrees per second, or, more properly, 7 x 10-5 radians per second.

Earth's angular momentum (h) is the product of the moment of inertia and angular velocity (J x w ), which gives 7 x 1033 N m s. This is the momentum the shuttle engines will have to counter.

The thrust (F) of the shuttle engines on take-off is around 4 x 107 N and, if acting tangentially at the surface of the Earth, the torque (T) - or rotational force - about the Earth's centre is F R, which gives 3 x 1014 N m.

This torque acting over time (t) will change the Earth's angular momentum by an amount T t. The time needed to reduce it to zero is h/T or 3 x 1019 s, or 840 billion years.

This is some 60 times the age of the universe, and by the time the shuttle had done its job there would be no weather or tides worth having. There is one other wrinkle: if the fuel needed comes from the Earth, the planet will get lighter and lighter. The whole of the Earth's mass will be expended as fuel long before the Earth stops spinning.

Hugh Hunt, Dynamics and Vibration Research Group, Department of Engineering, University of Cambridge, UK

(there were several other contributions - see the full New Scientist article at 8 Sept 2007)

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