# [LEAPSECS] Far past and far future

Rob Seaman seaman at noao.edu
Fri May 27 18:38:22 EDT 2011

Clive D.W. Feather wrote:

> Rob Seaman said:

>> Almost the definition of a moot point, but if the oceans boil into the atmosphere, how much of a change will that make to the Earth's moment of inertia - and in what direction?

>

> Wikipedia says that the current moment of inertia is 8.04e37, which is

> close enough to the numbers I get by calculating it, so let's go with that.

> The mass of the hydrosphere is, apparently, 1.4e21. It's all close to the

> surface, so let's say that the radius is 6.378e6. So the moment of inertia

> of the oceans is mr^2 = 5.7e34. That's less than 0.1% of the total.

>

> If it turns into atmospheric steam at, say, an average height of 1km, that

> adds a tiny amount to the MoI - about 0.03% of the water's total, or under

> 0.2 part per million of the earth's total. If it all escapes into space, it

> reduces the MoI by 0.1% or so.

I started paging though my undergrad planetary atmospheres texts for the table I remember somewhere of the timescale for escape versus molecular weight, but really the dense atmosphere of Venus is a sufficient proof of concept. The water vapor won't rapidly escape (but see "moot point" above).

So, if the moment of inertia increases by 0.2 parts per million, the angular velocity must decrease by the same amount to keep the angular momentum constant. If this unfortunate occurrence happened in the current day, length of day would thus increase by 0.017 SI-seconds. This would require a leap second six times per year to accommodate.

...and this is *still* within the scope of the current definition of UTC to accommodate - plus a comfy factor of two for monthly Shannon-Nyquist sampling.

Which is to say that even should Earth's oceans boil, the ITU's case for redefining the UTC standard has missed the boat.

Rob