[LEAPSECS] Far past and far future

Rob Seaman seaman at noao.edu
Tue May 24 19:33:48 EDT 2011

Hi Clive,

I see Steve Allen has just responded.

> Lunar laser ranging says that the length of day is increasing by about

> 2.3ms per century in the long term.

Well, laser ranging data can be folded into a complex model of the angular momentum coupling of the Earth-Moon system to make such an estimate. Steve has some discussion of this:


The link to his Morrison & Stephenson (2001) reference seems to be broken. It would indeed be delightful if an expert in this field would participate on the list.

> But how long term is that? Does anyone have figures on how far back or

> forward I can project based on that figure? What was the length of the day

> in the time of the dinosaurs?

A figure that has been tossed about is that the LOD was 22 "SI-hours" (such a unit is an abomination, of course) during the Devonian "Age of the Fishes", 350 million years ago. So during the mid-Jurassic, 175 MYA, the length-of-day might have been 23 SI-hours (82,300 SI-seconds). The abstract to the reference in Steve's reply rather suggests a number of 22 SI-hours at 620 MYA (ymmv). You might ask a coelacanth to comment.

By definition, of course, the length of a day is always 86,400 seconds, or 24 hours of 60 minutes of 60 "natural seconds" :-)

> Oh, and to stop me having to reconstruct the formula from first principles,

> does anyone have the relationship between length of day and distance to the

> moon?

One should never spurn the option of constructing from first principles - but such principles are quite hairy here. However, the back of the envelope numbers are that length-of-day increases by about 1 SI-second per 50,000 years and that the Moon's orbital radius increases by 1 mile over the same span. So about 20 SI-seconds and 20 miles per million years. By all means somebody refine these numbers.

The lunar ranging measurement is that the Moon is receding 3.8 cm per year.

We had a spirited discussion here sometime in the last few years making the point that leap seconds (or equivalent adjustments) are not tightly coupled to tidal deceleration, rather the more stochastic (probably not the right word) shorter term geophysical variations that are flamboyantly pictured on Steve's page above create a requirement for timekeeping corrections all on their own. And without a Moon to temper the Earth's motions, the EOP values might be much more variable. So we might stop blaming the Moon for this timekeeping issue - it is intrinsic to life on Mother Earth.


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