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Episode 45: The Moon's Changing Recession Rate

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Recap: A young-Earth creationist claim is that the Earth-Moon system can be no more than 1.4 billion years old because, at that time, the Moon would have been touching Earth. Find out if this dooms "evolutionary theory," or if the YECs are wrong.

Solution to Episode 43's Puzzler: The solution is ... NO! Earth moves through space, around the Sun. Only an object on an orbit directly opposite Earth - which is unstable - would not be visible from Earth over the course of a year, let alone the at least decade that this claim has been around. The orbital dynamics work such that even if a Planet X just became visible when it was behind the sun as seen from Earth, it would still be approaching the sun from the same direction and Earth would eventually get around the Sun and we'd see it.

In fact, my explanation for this episode's Q&A covers this idea, too. Even if a Planet X were locked with Earth in a 1:1 resonance so that one may naïvely think that it would always appear near the sun, it wouldn't. It would move.

So Planet X people who make this claim cannot have it both ways -- either their photo or video of Planet X is real and NONE of the others that have been around for years are real, or it's yet another lens flare.

Solution to Episode 44's Puzzler: The solution to the first part, the logical fallacy, I agree with both Chew and Warwick, who sent in different fallacies. Chew's was an enthymeme, where you have an unstated assumption that must be true for the premises to lead to the conclusion. In this case, the unstated assumption was Hubble could view the sites. The premise was that it hadn't, and the conclusion was therefore the sites don't exist.

Warwick's argument from silence I think is the main one here, though. The argument from silence, or argumentum e silentio, is when a conclusion is drawn based on the absence of evidence rather than the existence of any evidence. I think this is effectively the same as the more commonly stated, "absence of evidence is not evidence of absence."

For the second part of the solution we go to trigonometry and basic optical theory. You need two equations. The first gives you the angle of an object based on its size and the distance to it, which is grade school trigonometry, and the second equation is the diffraction limit of an optical system, which is what I was thinking of when I said that this may be a Googleable answer.

For the second part of the solution we go to trigonometry and basic optical theory. You need two equations. The first gives you the angle of an object based on its size and the distance to it, which is grade school trigonometry, and the second equation is the diffraction limit of an optical system, which is what I was thinking of when I said that this may be a Googleable answer.

Both Chew and Warwick correctly calculated that IN OPTICAL light, including the entire range of Hubble which goes from near UV to near IR, the smallest object Hubble could resolve is still several times larger than the size of any Apollo relic. Same goes for the largest optical telescopes on Earth.

What I was going for with this puzzler and what no one explicitly sent in except a bit for Warwick, which is why I said these were partial, was to look at other telescopes on Earth that operate in other wavelengths of light to see what they could do. None of them can resolve Apollo, but I thought it would be an interesting exercise.

For example, the Very Large Array can get up to 36 km in size. But, it operates at radio bands, where the smallest wavelength would only let you resolve something about 200 meters across on the Moon.

The James Webb Space Telescope, which hasn't been built yet, will have a mirror 6.5 meters in diameter and operate at infrared wavelengths. It will only be able to resolve objects up to around 110 meters across. GALEX, an ultraviolet space telescope, has a mirror half a meter across and could only resolve features about 250 meters in size at the moon.

This also assumes that the relics would reflect light at these wavelengths, which they don't really do. A flag isn't really visible to radar.

If we ignore that and talk about theory, if the two Keck telescopes on Mauna Kea COULD be operated as an interferometer, then they would be able to resolve the landing sites. Similarly, the Very Long Baseline Interferometry project could image the Apollo sites in radio, except for the problem of the sites not being visible in radio.

So, the conclusion is, no.

Puzzler: There is no puzzler for this episode.

Q&A: This episode's question comes from Kwisatz Haderach, AKA Febo, from the SGU message boards who asks: "There is a bit from an old episode of Q.I. that has been bothering me for years. In it, Steven Fry claims that the Earth has a second moon, called "Cruithne." A few years later, he claimed that there are actually like 8 or 11 or 13 or something similar moons. What is the deal with Cruithne and other similar objects?" [YouTube Clip]

The short answer to Febo's question is that he is wrong.

The longer explanation has to start with the definition of a moon, which would be an object (probably a natural object) that orbits a planet or an asteroid. Since Phobos and Deimos orbit Mars, as in, Mars is at one of the two foci of the ellipse that defines their orbits, then Phobos and Deimos are moons of Mars.

Cruithne orbits the Sun; the Sun is at one focus of its ellipse, Earth is not at the other. Its orbit takes it closer to the Sun than Mercury and farther from the Sun than Mars.

Cruithne does, however, have a 1:1 orbital resonance with Earth meaning that for every one orbit of Earth around the Sun, Cruithne orbits once, too. This kind of resonance is almost certainly caused by Earth perturbing it over the years, but that doesn't mean that it's in orbit around Earth.

The same goes for these other objects.

They are sometimes called "quasi-satellites," but they are definitely INcorrectly referred to as "moons."

Additional Materials:

Transcript

Claim: It is a fact that Earth's Moon is, today, moving away from Earth at a rate of about 3.82±0.07 centimeters per year, as measured by the Apollo Lunar Laser Ranging experiment over the past 40 years, though that value comes from a paper from 1994. That means that since the end of the Apollo era, astronauts would need to travel, on average, about 1.6 meters farther to get there. Young-Earth creationists use this value to say that the Moon today is about 384,400 km from Earth, and so if you trace the current recession rate back, it would have had to sprung from the planet like Athena from Zeus's head only 10 million years ago. That's the naïve approach - if you actually use differential equations to do this more accurately, they claim it would be about 1.4 billion years ago. Obviously, the case is made, this means Earth and the Moon can't possibly be 4.5 billion years old even though "the evolutionists" say it's 4.5, therefore God created everything 6000 years ago.

Background: Changing Recession Rate

This is another case, much like Episode 43, where the explanation of background information shows the fallacy of this claim. To jump to the final answer, the recession rate was slower in the past. Why and evidence for this is the remainder of this episode's main segment.

For the claim, creationists rely upon the idea that everything is now as it was then, as in, they adopt a uniformitarian outlook even though they normally use catastrophism and mock normal scientists for using uniformitarian approaches.

Anyway, what I mean by this is that they assume that the day has always been 24 hours. They also assume that the Moon's recession rate can be modeled by a simple differential equation that takes the rate today along with basic laws of gravity and works the rate backwards through time.

Geologists, physicists, astronomers, and other scientists say otherwise. They say the day has been different in the past, and that the Moon's recession rate is more variable through time. If I can provide evidence that the Moon's recession rate was different in the past, then that would be evidence against the creationist claim.

Theoretical Approach

First, I'm going to take a theoretical approach. The Moon is moving away from Earth today because it is being pulled forward in its orbit, gaining energy from Earth's own rotation, and so moving to a higher orbit.

The mechanism is tides. Earth's tidal bulge is ahead of the Moon. Draw a circle in the center of a piece of paper for Earth, a circle above it for the Moon, then a larger circle to represent the Moon's orbit around Earth. Draw an arrow pointing along that orbit counter-clockwise. If you draw a straight line between Earth and the Moon, the bulge on Earth caused by the Moon's tides would be ahead of that line in the Moon's orbit.

The extra gravity from the bulge pulls the Moon along, and so it adds energy to the Moon's orbit at a cost of Earth's own rotational speed. So our day actually is slowing down as the Moon moves farther away, though it's by a very tiny amount.

So that's the basic idea here with theory: Tides are directly proportional to how fast the Moon moves away. If my explanation was in any way confusing, and I know it was, I've linked up to a Talk Origins article that explains it in much more detail, but because of the more detail, it's easier to understand.

Now change the distribution of the continents. The tides are going to change. This means that the amount of energy that gets added to the Moon's orbit to let it go to a higher orbit changes, which means that the recession rate must have changed, as well.

That is, of course, assuming that continental drift is correct, which many young-Earth creationists don't believe.

I should also mention before leaving the theoretical part of this discussion that I have glossed over a lot of details. Enough details to fill over 400 years of physics dating back to Newton's Theory of Tides. Suffice to say, a simple mathematical and physical situation, this is not.

Observational Evidence

Now there's the question of, is there any evidence for this? What could evidence be that tides were different in the past, or the lunar recession rate was different in the past?

One slightly hand-wavey answer is to get at the recession rate indirectly and look at the length of the day. If the day was faster, then the water level for any given tide would have to be different because there wasn't enough time for the tidal bulge to get as high as it otherwise would be for any given location. This, in addition to changing the continent layout, combines to give less of a tidal effect and hence have a slower recession rate.

So, what's the evidence the day was shorter? One of the best is to look at ancient corals. Coral skeletons produce both daily and yearly patterns, and so the skeletons can be used to count how many days per year there were in the past. Work done in the 1970s show that fossil corals from 180-400 million years ago grew in years that had 381-410 days, meaning that an individual day was faster, only around 22.5 hours long.

Similarly, the growth of mollusks and stromatolites show the same results, as do sediment deposition patterns. All the measurements that we can make to determine how long the day was hundreds of millions of years ago points to the day being shorter, and Earth's rotation slowing by roughly 2 seconds every 100,000 years, or 2 milliseconds every century.

Note that this is also a non-linear process, though, too. But, that's the average for at least the last 650 million years.

So Earth's rotation has been slowing, meaning that tidal bulges would have been smaller. The continents also have been rearranged, which results in different tides, too. Computer modeling shows that in previous arrangements such as Pangea, which was the configuration around 300 million years ago, the tides would have been smaller, as well.

We can also directly measure what are called tidal rhythmites, also known as tidally laminated sediments. These are laid down due to tides, as their name suggests. A study in 1990 showed that 650 million years ago, the lunar recession rate was 1.95±0.29 cm/year. The same study showed that from 650 million to 2.5 billion years ago, the rate was 1.27 cm/year. The same researcher re-analyzed his data in 1997 and calculated a value of 2.16 cm/year between 650 million years ago and now.

If you accept these results from the rhythmites, then even if you're a young-Earth creationist, you have to explain why the recession rate was SLOWER just a few thousand years ago (due to the compressed geologic time) than it is now, when the basic differential equation you used shows it should have been faster.

Don't believe corals nor the rhythmites? What about Babylonian records?

The ancient Babylonians recorded on what we would now say was April 15, 136 B.C., a solar eclipse. In fact, it's the only solar eclipse the Babylonians recorded.

The problem is, if you run the clock backwards assuming the day as it is now, the eclipse should have passed through Europe, about 2500 miles or 47° on Earth away from Babylon. Meanwhile, if you calculate how much Earth's rotation rate should have slowed if you assume a constant tidal force that we get now, then the eclipse should have been 22° off but in the OTHER direction.

Summary

Getting back to the main issue at-hand, what does this mean? It means that we have written records that prove Earth's rotation rate is slowing. And these records prove that the lunar recession rate is not constant because the recorded solar eclipse would have been in a different location on Earth.

We also have fossil and geologic evidence that Earth's days have lengthened.

This means a changing tidal bulge which means a changing tidal force on the Moon.

A lessening tidal force means the Moon's recession rate has increased in the geologically recent past, that it is not constant, and its change is different from the differential equations it would otherwise follow.

This means that the calculations done by the young-Earth creationists do not model reality, and so they cannot be used to show the Moon has to be less than a billion years old.

Therefore, this line of alleged evidence that creationists use, is not valid.

But despite all this, they still make this claim. Just four years ago, Jason Lisle while at Answers in Genesis but now at the Institute for Creation Research, wrote: "Secular astronomers ... must invoke other explanations ... . For example, they might assume that the rate at which the moon was receding was actually smaller in the past (for whatever reason), but this is an extra assumption needed to make their billions-of-years model work."

Similarly, Brian Thomas of the Institute for Creation Research wrote just last month: "To explain the moon recession problem - it would have been touching the earth and making life impossible at only a fraction of the earth's supposed billions of years - many suggest with no evidence to back the claim that the moon's current drift rate away from earth is abnormally fast these days."

Sorry guys, we didn't just make this stuff up. Many lines of independent evidence converge to show that the Moon's recession rate from Earth today is faster than it has been in the past.

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