The Receding Moon

The moon is moving away from earth at a measurable rate. Running the clock backward gets uncomfortable.

The moon is moving away from earth. Slowly — about 3.82 centimetres per year — but steadily and measurably.¹ We know this because of the laser reflectors the Apollo astronauts left on the lunar surface in 1969–72. From observatories on earth, we bounce laser pulses off those reflectors and time the round trip. The distance is now known to a few millimetres. Decades of those measurements give us the recession rate.

The mechanism is well understood. Earth’s gravity raises a tidal bulge in the oceans (and a smaller one in the solid earth itself). Because earth rotates faster than the moon orbits, that bulge is dragged slightly ahead of the line connecting the two bodies. The bulge’s gravity then tugs the moon forward in its orbit, adding angular momentum to the moon and subtracting rotational energy from earth. Result: the moon gradually spirals outward, and earth’s day gradually gets longer.²

This is all uncontroversial. Where it gets interesting is what happens when you run the clock backward.

The arithmetic

The recession rate is roughly constant on human timescales. If you assume it has been constant on geological timescales, the arithmetic is straightforward:

Ten billion years — more than twice the age of the earth. So a naive constant-rate extrapolation does not put the moon at earth’s surface within the geological lifespan. So far so good for deep time.

But this is the wrong calculation. The recession rate isn’t a constant — it depends, very sensitively, on the distance between earth and moon. The tidal force varies as the inverse cube of distance. As you push the moon closer to earth (running the clock backward), the tidal force gets much stronger, the recession rate gets much faster, and the moon hits earth’s surface much sooner.

The proper integration of the tidal evolution equation, using present-day tidal dissipation rates, gives a “Roche-limit time” — the time it would take to push the moon to within the distance at which earth’s tides would tear it apart — of roughly 1.5 billion years.³

That number is the problem.

The moon is supposed to be 4.5 billion years old. The standard model of lunar origin (the giant-impact hypothesis) has a proto-moon condensing from a debris disk at three to five earth radii from the planet’s centre, around 4.5 Ga. From that starting position, the moon must have receded continuously to its current orbit at sixty earth radii.

But the tidal-recession math, running at present rates, only gives you 1.5 Ga of recession before the moon comes back into earth. You are 3 Ga short. The moon, on the standard timescale, should not be where it is.

The standard response

Mainstream geophysics is well aware of this problem. The standard response is to argue that the tidal dissipation rate has not been constant over geological time — that the past few hundred million years have been an anomalous period of unusually strong tidal friction, and that for most of geological history the dissipation rate was much lower, so the moon receded much more slowly.

The argument is that the configuration of the continents matters to tidal friction. Today, the Atlantic Ocean has a width close to a tidal resonance for the M2 tide, which amplifies friction. In the past, when continents were in different configurations, the resonance condition was not met, and friction was much weaker.⁴

Mathematical models of paleo-tides can be tuned to produce a recession history compatible with a 4.5 Ga lunar age. Kirsten Brosche’s and Bills & Ray’s papers in this tradition are the standard references.

Why I find the response unconvincing

This is a coherent move, and I want to take it seriously. But it has features that should make any honest reader hesitate.

One: the variable-rate hypothesis is invoked specifically to preserve the 4.5 Ga timescale. It is not derived from independent evidence and then applied to the lunar recession problem. The direction of inference is backward.

Two: the geological evidence we do have for past tidal rates mostly points the other way. Tidal rhythmites — laminated sediment patterns that record daily and monthly tidal cycles — preserve information about the length of the lunar month and the length of the day at the time the sediment was laid down. The rhythmites from the late Precambrian (~620 Ma in the standard chronology) record a slightly longer day than today, which implies the moon has receded less in that interval than constant-rate extrapolation would suggest — meaning the rate in that interval was actually slower than today, not faster.⁵ If you take the rhythmite data at face value and combine it with the present rate, you get a recession history that gets you to the moon’s current orbit in less time than deep time requires, not more. The standard model has to dismiss this awkwardly.

Three: even granting an unusually high tidal dissipation rate now, the mechanism cannot have run backward in time without limit. As soon as you place the moon close enough to earth, ocean tides become catastrophic — kilometre-high water surges that would scour the surface clean. Yet the geological record is not the record of a planet repeatedly stripped to bedrock by lunar tides.

What it means

The lunar recession is one of several measurable rate-based clocks on our solar system. Taken at face value, it gives an upper bound on the moon’s age that is much shorter than the standard 4.5 Ga timeline — by a factor of three even on the most generous assumptions, and much more if the variable-rate hypothesis is discounted.

This does not, by itself, give a young-earth chronology. A 1.5 Ga upper bound is still a billion years longer than the six-thousand-year reading of Genesis. But it puts the standard model in a difficult position: the timescale that is asserted as the scientific consensus is in tension with a measurement made to four decimal places by laser ranging.

The young-earth reader notes that the present recession rate is consistent with a much younger moon, that the rate-variation rescue is ad hoc, and that the data we have from independent sources (tidal rhythmites) does not actually support it.

Next: the salty oceans — another rate-based clock with a similar problem.