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This is a verbatim quote from a young earth creationism video:
The rate at which the Moon is moving away from the Earth due to tidal friction places a limit on the age of the Moon of a few thousand years. If it were millions of years old it would have to had started very close to the Earth causing ocean tides so severe it would have drowned everything on land twice a day.
This argument relies on the listener not bothering to do even the most basic of fact checking, nor even think about it, and instead to take it completely at face value. Unfortunately many people who are eager to believe all arguments made by young earth creationists will swallow this type of argument whole.
Before even looking at the actual numbers (which isn't really the point of this article, but I'll nevertheless get to that later), let's think a bit about this.
How do we know that the Moon is receding from the Earth? Who came up with this fact? The astrophycisists who study these things. The math showed that the Moon should be slowly receding from us due to tidal forces. The exact rate of recession was later measured with a very high degree of accuracy, which confirmed the theory behind it. This is a completely accepted fact of physics, known by the entirety of the scientific community.
Now, thousands and thousands of highly educated competent scientists from around the world, from different countries and cultures, with different world views and ideologies, know this fact, and understand the math behind it.
This immediately raises the question: If the creationist claim above is true, how come none of these thousands and thousands of scientists has ever raised the issue? Why isn't this called "the Moon recession anomaly" or something similar? Why are all the scientists quiet about it?
"They don't talk about it because it contradicts established theories" is a completely ridiculous claim, which is even quite easy to demonstrate as false. For example the so-called Pioneer anomaly is the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft on their trajectories out of the Solar System. Even when taking account all possible variables and calculating the velocity at which these probes should be traversing, the math contradicts the observations.
Or take another example, the so-called flyby anomaly, which is a similar deviation that probes experience during Earth-flybys, which is unaccounted for in the math.
Are the scientists keeping quiet about these anomalies because they seem to contradict established science? Of course not. These are fully recognized, and work is being done to solve the mysteries and find out what is causing this.
Even if the scientists, for whatever strange reason, would want to keep quiet about it, how could they? As said, the scientific community of astrophysics consists of thousands and thousands of people from around the world, from different cultures. Somebody is going to raise questions if anomalies are found, and the rest of the community will have to deal with them.
So if it were indeed true that the age of the Earth-Moon system can only be a few thousand years, as claimed by the creationist video, how is it possible that the scientific community isn't discussing this? There are only two possible options, both of which are quite ridiculous:
In practice science works in the exact opposite way: Whenever an anomaly is found and corroborated, especially if done so by multiple independent observers, the awareness of the rest of the community is raised, papers are published, and research on the subject requested. Nothing would be more rewarding for a scientists than to publish a new discovery.
Of course there's a third option: That the claim is false.
If only the people who listen to these claims and swallow them without even the slightest of skepticism would do even the tiniest amount of research. You don't have to do a lot of research to corroborate or discredit the claim.
A quick google search reveals that the current rate of recession of the Moon is approximately 3.8 cm (1.5 inches) per year. This rate of recession has probably not changed much in the last few thousands of years, so it has been quite constant.
So let's just use 6000 years (which is the most common figure creationists use as the age of the Earth) and just plug in the numbers in the trivial multiplication, and we get: 6000 years times 3.8 cm/year = 228 meters (748 feet).
That's a laughably small amount. How small? Well, consider that the orbit of the Moon is elliptical, which means that its distance from the Earth varies during one orbital period (ie. one month). The closest distance from the Earth to the Moon is about 356400 km and the farthest is 406700 km. In other words, during one month the distance between the Moon and the Earth varies by over 50 thousand kilometers. This orbit was about 0.2 kilometers closer 6000 years ago.
In other words, the difference in distance from the Earth to the Moon varies during one month by five orders of magnitude more than those 228 meters.
So, assuming this recession rate has been about constant for a million years, how much closer was the Moon then? Again, plug in the numbers, and we get about 38 kilometers. That's still three orders of magnitude less than what the distance changes within one month.
A billion years? Now we are getting a bit closer: 38 thousand kilometers. This is about the same order of magnitude as the difference in distances within one month (which was about 50 thousand kilometers). Still doesn't sound like enough to cause "ocean tides so severe it would have drowned everything on land twice a day."
Of course that approximation of a billion years, and probably even the one of a million years, is not completely accurate because the math is much more complicated than that (for instance, the change in distance is not linear), and there's a myriad things that affect the recession rate (including things like the arrangement of continents, which affects the tidal forces applied to the oceans). However, this recession rate has probably not changed by any significant amount in the last 10000 years, and just using very simple math can show how ridiculous the original claim is.
The history of the moon recession physics is quite interesting in itself. There was some controversy decades ago about this recession speed, as initial calculations seemed to show a maximum possible age for the Earth-Moon system of about 2 billion years. Scientists didn't keep quiet about it, but the question was publicly raised.
Some creationists have jumped on that controversy to claim that the Earth cannot be over 4 billion years old. However, jumping from an estimation of 2 billion years to an estimation of 6000 years is an error of enormous proportion. It's the same amount of error as estimating that the width of the United States is 12 meters (40 feet).
(The problem was later resolved by more accurately taking into account all possible variables, including the fact that the continents have not always been where they are now. This has an effect on how tidal forces operate on the oceans, which affects how the system slows down. An age of over 4 billion years with respect to the recession rate of the Moon has not been considered a problem for many decades.)
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