From grandparents to children, we all look up at the Moon - and we always have : some more intently than others. When we look at the Moon, it raises all sorts of questions in our minds, some of them disarmingly simple.
One of those seemingly simple questions is "How high is the Moon in the sky tonight ... and why ?". This "simple" question was at the heart of the most difficult presentation I ever had to put together for a RASC Ottawa meeting, back in 2012 I believe.
Another seemingly simple question might be "How far away is the Moon ... and how did it get there ?". However, that "simple" question raises a whole host of other, potentially complex, second-order questions, as we seek to provide an answer to the initial "simple" question. One of those second-order questions is : "How has the Earth-Moon distance evolved over time ?".You probably know that the present orbit of the Moon is elliptical, which means that the Earth-Moon distance varies at the scale of months to years. Hence all the media hype about "Super Moons" !
The usual average distance in the literature is ~385,000 km, that you can round out at ~400,000 km. However, you are also aware that current thinking derives the Moon by a "collision" between the very early Earth and a Mars-sized planet (Theia), which means that the Moon must have started off very close to the Earth some ~4.5 Gy ago. So what's it doing way out there at ~400,000 km distant ? Well, obviously the Earth-Moon distance has increased with time since ~4.5 Gy ago, but how ? - and why ? : more supposedly "simple" questions !
A recent paper, published in Dec 2024, set out to address these very questions. Notice the title : it doesn't even mention the Earth-Moon distance ! Why ? Because we have no way of directly measuring the history of the Earth-Moon distance in the past, but there are proxies ! What's a proxy ? A proxy is something you can observe and/or measure that has a known (or inferred) relationship to something you cannot directly observe and/or measure. Well, it turns out that the Earth-Moon distance, and the length of Earth's day, and the rate of precession ("wobble") of the Earth's spin axis, are all related. So, if you can work out the rate of change through time of one of these phenomena, you can at least get an estimate of the rate of change of the other two. Now, you might think that this is getting unnecessarily complicated. Most of you probably already know that the length of Earth's day was shorter in the past (Earth spun faster), and that it has slowed to ~24 hours as the Moon has drifted further away from Earth, due to an exchange of angular momentum - also known as "Tidal Drag". However, you may not know is that this evolution of length of day and Earth-Moon distance has not occurred at a constant rate. Look at the end of the title of the paper : Earth's precession ("wobble") rate changed rapidly towards the end of the Proterozoic Era, between 1000 and 500 My. ago, and that's where the complications come in.
In this figure from the paper, moving to the right on the horizontal axis is getting closer to the present day, and the precession rate is getting slower as we move down along the vertical axis. Note the modern rate of precession today : 50"/year. Keep this number in mind. However, before we look at this slide, what exactly do we mean by "precession" (wobble) and the rate of precession ? (wobble rate).
You are all familiar with the behaviour of a spinning top, and many of you know what a gyroscope is. As a spinning top slows its spin, it begins to wobble. Technically, its spin axis begins to "precess". So precession can be thought of as the "wobble" of the axis of spin of a rotating body, including that of a planet !
... and that goes for the Earth too. A full Earth wobble takes ~26,000 years today. So its current precession rate can be described as 360 degrees/26,000 years, or 1 degree every 72 years, or 50 arcsecs/yr (remember that number ??).
However, this diagram shows us that Earth's precession rate was different in the past : you can't fit all the data points here on a single line ! Something changed between 1000 and 500 Ma, either slowly - or rapidly at ~600 Ma. But what might have caused that change ? Before we can answer that question, we need to know where the data points in this slide come from in the first place.
... and the key word here is Cyclostratigraphy.
What is Cyclostratigraphy ? These are images of layered sedimentary rocks, originally deposited in water. Not just any old layers, but rhythmic layers reflecting seasonal cycles in the way the sediments were laid down though time (younger going up !). Keeping things (overly) simple : if the visible layers were to represent years, then the really thin layers within the visible layers could represent days. If we can count the daily layers within annual layers, then -since Earth's orbit has not changed significantly over time (a year is still a year !) - we can determine the number of days in the year, and hence the length of the day at that time.
What is Cyclostratigraphy ? These are images of layered sedimentary rocks, originally deposited in water. Not just any old layers, but rhythmic layers reflecting seasonal cycles in the way the sediments were laid down though time (younger going up !). Keeping things (overly) simple : if the visible layers were to represent years, then the really thin layers within the visible layers could represent days. If we can count the daily layers within annual layers, then -since Earth's orbit has not changed significantly over time (a year is still a year !) - we can determine the number of days in the year, and hence the length of the day at that time.
Remember, the length of the day is linked to the rate of precession of the Earth's spin axis. So, if we know the age of the sequence of sediments that yield data on the length of the day at that time, we can put a data point on the graph. As an example, it turns out that 1.4 Gy ago, the length of day of was ~18.5 hours (cf. 24), a precession cycle took ~14 Ky (cf. 26), and the Earth–Moon distance was ~340,000 km (cf. ~400,000).
You can also do the same thing using seasonal growth rings in fossils such as corals and stromatolites, You all know what a coral, so here's an example of stromatolites that can be found at the foot of the Confederation Bridge on the Quebec side of the Ottawa River when river levels are low. What you are looking at is a 450 My old reef of mounds of bacterial mats bevelled by erosion, so you can see the concentric growth rings inside the mounds that can be used to determine how many days there were in a year - and how long those days were at the time.
So, OK : now we know how to tell the length of the day at some specific time in the geological past. How does that help us to determine the rate of precession at that time ?
Yes, I know ... it's an equation. However, once we stop panicking and look at it, it starts to make sense. Start on the left hand side of the equals sign : small k is the rate of precession, i.e. the rate of "wobble" of the Earth's axis of rotation. Now go to the right hand side and we find all the variables you would expect to influence the orbital mechanics of the Earth/Moon system :
Yes, I know ... it's an equation. However, once we stop panicking and look at it, it starts to make sense. Start on the left hand side of the equals sign : small k is the rate of precession, i.e. the rate of "wobble" of the Earth's axis of rotation. Now go to the right hand side and we find all the variables you would expect to influence the orbital mechanics of the Earth/Moon system :
- X is the length of the Earth day
- a is the length of the long axis of the Earth's elliptical orbit
- ee*and em* are the ellipticities (circular to elliptical) of the Earth's and the Moon's orbits, respectively
- i is the inclination of the Moon's orbit wrt the ecliptic
- Mm* and Ms* are the masses of the Moon and the Sun, respectively
* : subscripts !
By doing this for a number of dated geological formations, we can then plot the evolution of the precession rate of the Earth through time. However, what about those "necessary assumptions" ?
Well, we don't actually know the true values for a number of the variables in the equation, especially those relating to orbital eccentricities and inclinations. So many older studies simply assumed a circular orbit for the Moon in the same plane as the Earth's rotation, and modern day values for the inclinations. However, one of the major contributions of the authors of the work I am describing to you here is that they used a neat statistical analysis to go beyond these assumptions ... and put some realistic numbers on these variables, but we can pass on the details here
The other assumption most workers make is that the only influence on the orbital mechanics of the Earth/Moon system is Tidal Drag. I'll bet dollars to doughnuts that this is what you were all taught in school too !
Well, we don't actually know the true values for a number of the variables in the equation, especially those relating to orbital eccentricities and inclinations. So many older studies simply assumed a circular orbit for the Moon in the same plane as the Earth's rotation, and modern day values for the inclinations. However, one of the major contributions of the authors of the work I am describing to you here is that they used a neat statistical analysis to go beyond these assumptions ... and put some realistic numbers on these variables, but we can pass on the details here
The other assumption most workers make is that the only influence on the orbital mechanics of the Earth/Moon system is Tidal Drag. I'll bet dollars to doughnuts that this is what you were all taught in school too !
Here's a quick reminder on what we mean by "Tidal Drag". Both the Moon and the Sun exert a gravitational influence ("pull") on the Earth which is most readily seen by examining the ocean tides, but the Moon is closer, so its gravitational influence is more important than that of the Sun. The Moon's gravity raises a tidal bulge of water on the Earth that follows the Earth's rotation and gets ahead of the Moon, which orbits more slowly than the Earth turns on its axis. This leads to a Tidal Bulge Offset, with the tidal bulge leading the Moon and "pulling" it forward (and speeding it up on its orbit) and the Moon trailing the tidal bulge and pulling back on the Earth (and slowing down its rate of spin).
Now, the same tidal interaction occurs between the rocks of the Earth and those of the Moon. However, because rocks are stronger and stiffer than water, the effects are visually less spectacular, but of greater magnitude in terms of angular momentum. Now, remember your thermodynamics. For every action (or interaction) work has to be done and energy exchanged and, in the case of the Earth/Moon system, this results in an exchange of angular momentum from Earth to the Moon whereby the rotation of the Earth gradually slows down, the precession ("wobble") rate of the Earth also slows down and the Moon speeds up in its orbit and migrates away from the Earth. In a nutshell, this is the story of Tidal Drag that many of you will already be familiar with, except perhaps for the "wobble" part of the story.
The problem with the assumption that all this is due only to Tidal Drag is that in order to account for the change in precession rate of the Earth at ~600 My ago, the Tidal Drag effect has to take 40 times longer than it does today (40 times weaker), but we don't have an explanation as to why ! So, this paper challenges the assumption that change in precession rate of the Earth at ~600 Ma is all due to Tidal Drag and asks what other factors could influence the precession rate.
Earlier in this presentation I compared the precessing Earth to a wobbling top or gyroscope.
However, this is an over-simplification. In reality, the Earth's outer layers are not uniform, as you can see by looking at the distribution of less dense continental rocks vs denser ocean floor rocks, plus the distribution of the mass of ocean water. If you like, you can think of the Earth as a weighted spinning top weighted in the same sense that the cheating gambler's dice might be weighted to come up with sixes as opposed to a random result.
To add to this complication, continental drift due to plate tectonics means that this weighting effect has changed through time (compare today and 250 million years ago). However, the authors of the paper felt that such changes occur too slowly to account for the observations.
I disagree : The 400 My time window (1000-600 My) within which the change in precession rate may have occurred potentially offers ample time for the plate tectonic configuration of the Earth to change significantly ... unless of course, the change in precession rate was very rapid within this time window.
I disagree : The 400 My time window (1000-600 My) within which the change in precession rate may have occurred potentially offers ample time for the plate tectonic configuration of the Earth to change significantly ... unless of course, the change in precession rate was very rapid within this time window.
The paper then addressed the possibility that redistribution of surface mass due to formation and melting of polar ice caps through geological time - or perhaps a planet wide ice sheet ("Snowball Earth") - might have affected the precession rate. However, as the authors point out, once you remove the ice, the planet should return to its pre-perturbation precession rate - and Earth did not do so !
So then the paper looked at changes in the interior of the Earth at the scale of the planetary core and mantle. As a reminder, Earth is a differentiated planet : differentiated into a thin outer crust, a thick rocky mantle and a metallic core that is liquid on the outside and solid on the inside. So could the formation of the metallic core have affected the Earth's precession rate at about 600 Ma ? No ! There is firm evidence that the metallic core had already formed 4 billion years ago ! So what about the crystallisation of the solid inner core from the liquid outer core ? That doesn't work either because the transition from liquid to solid is a phase change, not a transfer of mass.
So what about a disturbance of the Solar System itself ? This would lead to major changes in orbital eccentricity (circular to elliptical) that would leave very obvious evidence of major climate change in the sedimentary record. Now you might wonder if that's what Snowball Earth was all about at ~600 Ma, except that we should then see similar disturbances in the other planets ... but we don't.
So, finally - for completeness - the paper looked at how lunar-driven tides in the Earth's atmosphere might contribute to changing the Earth's precession rate, and - unsurprisingly - drew a blank. The atmosphere is simply not viscous enough to affect precession.
So, what did the authors of the paper conclude ? What's their take home message here ? Well, having eliminated all the other potential influences on the Earth's precession, they are left with the unpalatable conclusion that the change in the precession rate has to be essentially due to Tidal Drag, even though they have no mechanism for explaining why the time required for the Tidal Drag to be effective at ~600 My ago has to be 40 times longer than under modern day conditions.
So, what's my take home message here ? To quote the old adage : "All models are wrong, but some are more useful than others", and combine it with a direct quote from the authors regarding their own analysis ("... there are many uncertainties in the uncertainties") this paper well illustrates how much we still do not know about our nearest astronomical neighbour, even with respect to some of the "simple" questions we might ask of it.
Clearly, there's still much to be learned about the Earth-Moon system !
So, what's my take home message here ? To quote the old adage : "All models are wrong, but some are more useful than others", and combine it with a direct quote from the authors regarding their own analysis ("... there are many uncertainties in the uncertainties") this paper well illustrates how much we still do not know about our nearest astronomical neighbour, even with respect to some of the "simple" questions we might ask of it.
Clearly, there's still much to be learned about the Earth-Moon system !