Mark I. Vuletic

Last updated 21 March 2008

Background

The creationist contention as posed to me in personal correspondence is 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.

Analysis

(i) 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) 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 day on the Earth 4.5 billion years ago. The manner in which Thwaites and Awbrey cast their calculations has proved confusing to my readers, so I will recast them in what I hope will be a clearer form, though the differences are merely in presentation and not in substance.

To start out with, remember that a year (for the Earth) is the time it takes for the Earth to complete one full >revolution around the Sun. It is critical to recognize that changes in the Earth's rotation rate have no impact on its revolution rate, so the number of seconds in a year will always be the same as it is now: about 31,536,000 seconds.

To start out with, remember that a day (for the Earth) is the time it takes for the Earth to make one complete rotation about its axis.1 A year is the time it takes for the Earth to make one complete revolution around the Sun. It is critical to recognize that changes in the rotation rate have no impact on the revolution rate: the number of seconds it takes for the Earth to complete a revolution around the sun is always the same as it is now: about 31,536,000 seconds per revolution.

The second critical thing to understand is what scientists mean when they say that the rotation rate of the Earth is slowing by "0.005 seconds per year every year." They do not mean that one year ago, a day was 0.005 seconds shorter than it is today. To express that, they would say that the rotation rate is slowing by "0.005 seconds per day per year." The actual rate given means that if the Earth today can complete 365.25 rotations in 31,536,000 seconds (that is, one revolution), then the Earth one year ago 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 year. There was an extra tiny bit of a rotation equal to (0.005 s)(1 hr/ 3600 s)(1 rotation / 24 hrs), which is close to 600 millionths of a rotation: truly tiny.

The slowing rate means that every year, you can cram another extra such little bit of rotation (or minuscule fraction of a day) into a revolution (or year). 4.5 billion years ago, of course, 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 day 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 day.

Thus (assuming, of course, the constancy of the slowing rate), a day on Earth 4.5 billion years ago would have been about 14 hours long. Through comparison with Jupiter's ten-hour days, Thwaites and Awbrey conclude a 14-hour day is insufficient to cause significant deformation (much less disintegration) of the Earth.

(iii) 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, which corresponds nicely to the approximately 400 daily growth layers per year present in Devonian corals.

(iv) Stassen also points out that the assumption of a uniform slowing rate is uncertain. 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

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

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

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

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

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

Notes

1 Actually, as a reader pointed out to me, this is not true if we stick to SI units, since the system defines a "day" as precisely 24 hours, and a full rotation of the Earth currently takes a little bit longer than 24 hours. For the purposes of this discussion, however, it should be understood that I will be using the word "day" in the same colloquial, day qua rotation, sense as the creationist argument relies upon.

Acknowledgements

Chris Stassen graciously provided me with help with this claim early on. The math on an eariler version was generated using MathCast (v 0.86), Tom Chakam's fine open source equation editor.