## Background

In personal correspondence, a creationist claimed that that the rotation of the Earth has been slowing down at a rate of 30 seconds per century, and that extrapolating back 4.5-billion years from this would give us a rotation rate that would have disintegrated the planet. Thwaites and Awbrey (1982) discuss a creationist publication that alleges a 1 second per year slowing rate, from which it extrapolates massive deformation rather than disintegration.

## The shorter answer

The actual rate at which the rotation of the Earth is thought to decrease poses no problem for an old Earth.

## The longer answer

### I. The actual rate

Apparently, both of the rates given by the creationists above are wrong. According to Thwaites and Awbrey (1982), the rotation of the Earth is decreasing at a rate of 0.005 seconds per year every year.

### II. What the actual rate would entail

Given the rate supplied by Thwaites and Awbrey, and assuming its constancy over the entire history of the Earth, we can calculate the length of a rotation on Earth 4.5 billion years ago.

The first critical thing to understand is that the Earth’s rotation rate and revolution rate are independent of one another: it always has taken the Earth about 31,536,000 seconds to complete a revolution around the Sun, no matter how fast or slow the Earth has been rotating.

The second critical thing to understand is what scientists mean when they claim that the Earth’s rotation rate is slowing by 0.005 seconds per year every year. They do *not* mean that one year ago, a *rotation* took 0.005 seconds less than it does today. To express *that*, they would say that the rotation rate is slowing by “0.005 seconds per *rotation* per year.” The actual rate of slowing means is that if the Earth today can complete 365.25 rotations in 31,536,000 seconds (that is, one revolution), then one year ago the Earth would have required only 31,535,999.995 seconds to complete the same number of rotations. Since this is 0.005 seconds short of a full revolution, that means that one year ago, there were slightly more than 365.25 rotations in a revolution. There was an extra tiny bit of a rotation equal to \( 0.005 \text{ s} \cdot \frac{1 \text{ hr}}{3600 \text{ s}} \cdot \frac{1 \text{ rotation}}{24 \text{ hrs}} \), which is close to 600 millionths of a rotationâ€”truly tiny.

The slowing rate means that every time the Earth makes a trip around the Sun, you can cram another 600 millionths of a rotation into the trip. 4.5 billion years ago, you had 4.5 billion extra such little bits in the year, which add up to 260.42 extra rotations. These are *extra* rotations, so the *total* number of rotations in a year all the way back then was the sum of the current 365.25 rotations and the extra 260.42 rotations: namely, 625.7 rotations per year.

Now, if, 4.5 billion years ago, there were 625.7 rotations in a year, and there are always 31,536,000 seconds in a year (because, recall, the rotation rate has no impact on the revolution rate), then we can figure out how many hours there were in a rotation back then by dividing the 31,536,000 seconds by 625.7, and then converting the result into hours. In the end, this gives us 14.01 hours per rotation.

Thus (assuming, of course, the constancy of the slowing rate), a rotation on Earth 4.5 billion years ago would have been about 14 hours long. Comparing this with Jupiter’s ten-hour rotations, Thwaites and Awbrey conclude that a 14-hour rotation would not cause the Earth to deform significantly, much less to disintegrate.

### III. Confirmation of rate from corals

Chris Stassen has pointed out to me that given the slowing rate of 0.005 seconds per year every year, there would have been around 400 days per year in the Devonian Period, and that this corresponds nicely with the approximately 400 daily growth layers per year that one finds in Devonian corals.

### IV. Possible non-uniformity of rate

Stassen also points out that it is uncertain whether the slowing rate has been constant. He says that the rate becomes “much less accurate with increasing time (particularly back to near the origin of the Earth). There are still arguments over the forces which dominate the slowing, and how much stronger or weaker they would have been when integrating backwards in time” (Stassen, personal correspondence, 1997).

Stassen recommends as resources Thwaites and Awbrey 1982, Cazenave 1982, Bursa 1982, and Mignard 1982.

## References

Brosche P and Sunderman J (eds.). 1982. Tidal Friction and the Earth’s Rotation II. Berlin: Springer-Verlag.

Bursa M. 1982. On some topical problems of the dynamics of the Earth-Moon system. In Brosche and Sunderman 1982:19-29.

Cazenave A. 1982. Tidal friction parameters from satellite observations. In Broshce and Sunderman 1982:4-18.

Mignard F. 1982. Long time integration of the Moon’s orbit. In Brosche and Sunderman 1982:67-91.

Thwaites W and Awbrey F. 1982. As the world turns: can creationists keep time? Creation/Evolution IX:18-22.

## Acknowledgements

Chris Stassen, as should be obvious from the text, graciously helped me with this claim early on. Any defects that remain are, of course, entirely my own responsibility.