What is the relationship between Earth's rotation and its mass?

[kernelpenguin]

On the UserFriendly forums I saw a message a few days ago from two people that had lost some weight. It went something like: "If you've noticed that the Earth is spinning faster, it's because X and Y have lost N pounds!"

Okay, logically, an object should start spinning faster if it sheds some mass, but does it, in this case, shed any mass at all?

I got into a debate about this with my friend.

My point of view is that the Earth is a closed system when it comes to particles with mass. Even if they did lose N pounds, that still hasn't left Earth or its atmosphere, so Earth should be spinning at exactly the same speed.

His point of view was that Earth is not a closed system since it gets sunlight and sheds heat radiation. But these shouldn't affect mass, should they? Then he went on saying that some of it is deposited in the atmosphere and thus doesn't contribute to Earth's rotation.

It's a fun little problem, methinks. Anyone care to cast their opinions? :)

 

[Gonzolo]

Don't forget to think in terms of mass distribution too, not just total mass! Is the rotation of the Earth the same once someone has sweated off 1 pound? Or has eaten a carrot that was underground?

 

[Everett]

This is like the stereotypical ice sk8er problem, but instead of arms and legs moving in toward the center, is it not(X and Y)

 

[krab]

In a closed system, it is not the spin that is conserved, but the angular momentum. Therefore, if mass is re-distributed to be closer to the axis, the spin rate will increase. Like a skater pulling his arms in.

 

[LURCH]

Earth is not a closed system, and does indeed receive sunlight and radiate heat. This will have an effect on the overall mass of the planet because the lost weight was lost as calories burned by biological activity. This mass was converted to heat, which can leave the Earth and its atmosphere.

 

[selfAdjoint]

Earth also radiates just because of its temperature, as anybody does. It doesn't require biology to do that. Indeed the Earth can be seen as a system in near thermal equilibrium, losing as much heat by radiation as it gains from insolation. If the greenhouse effect prevents heat from being radiated, it will reach equilibrium at a higher temperature, as has happened to Venus.