The moon is drifting slowly away from the Earth. If it is getting further away, then at one time it was much closer. The Inverse Square Law in physics states that if the moon was half the distance away, its gravitational effect on our tides would be quadrupled. One third the distance and it would be 9 times stronger. We would all drown twice a day. 1.2 billion (1,200 million) years ago, the moon would have been touching the Earth.
http://www.allaboutcreation.org/age-of-the-earth-c.htm
In attempting to find evidence for a young universe, Creationists seem to mention the drifting of the moon away from the Earth. A friend of mine recently gave me a paper on evidence against evolution, and among his arguments was this one. My plan is to address it in an order easily understood, and as to leave no doubt of its fallacy. I also will include some basics on the orbit of the moon learned through my research.
The Orbit of the Moon
The moon is approximately 384,400km away from the Earth, and is almost perfectly circular, being tilted slightly (5°). It takes 27 days to orbit around the Earth. The moon does not orbit around the center of the earth. Instead, it revolves around something known as a barycenter, which lies inside the Earths crust but not the middle. Why? Both the Earth and the moon have gravitational pull. The Earths gravitational pull is much greater however, than that of the moons. So, the barycenters position can be described as the Earths gravitational pull on the moon to its center minus the moons gravitational pull on the Earth (Love 2005.) Wikipedia places the barycenter for the Earth-moon relationship at 4,671km from the center of the Earth. The moon, as stated in the claim, is drifting away from the Earth. Ive seen Creationists put figures as high as 5.8cm/yr though (DeYoung 2004.) but the real figure is 3.8cm/yr or 1.5in/yr. The reason for the drift is simply that the Earths rotation is slightly faster than the orbit of the moons, and so when the moon exerts its gravitational pull on the tides, the Earths rotation carries this ahead of where the moon placed it. The Earth slows down a bit because of this tide displacement, allowing the moon to drift away from us.
The Inverse Square Law?
The Inverse Square Law is a physical law that basically states objects that can radiate their influence will do so according to this law. Mathematically described, intensity is equal to radius divided by area of sphere.
In regard to gravity, the equations do not change much, the figure looks very similar as well:
Now it is time for some calculations: G = Gravitational Constant, M = mass of the Earth. I think we all know what r means. For an example, lets use the formula to find out the acceleration on moons surface caused by its gravitational field.
R = 1,738, and M = 7.347673x10^22. The equation that follows is:
The answer I receive is: 1.62246789m/s/s. This makes sense because the Earths gravitational pull (9.81m/s/s) is approximately six times stronger than that of the moon. What is the moons effect on the Earths surface then? The moon is 384,403km away from Earth, which means it is going to have 221 times less gravitational effect on the Earth. Unfortunately for the argument the Creationists present, the Inverse Square Law is not a method for calculation of tidal movement. If it were, the numbers one would get from the equations would state that the Earths tide should move about one centimeter vertically per day due to the moons pull. The law is good for finding power of the gravitational field of an object, but for tidal movement it is not of value.
The mathematical formula needed for finding the estimate tide size is as follows: (Johnson 2002.)
Once again I plug in values:
What does this number mean? It represents the distortion the moons acceleration puts on our Earths acceleration. How much is it? About 1/900,000,000 of that of the Earths. Now, since we do not have water at the center of the Earth, this measurement is going to be distorted as well (the measurement we got referred to the Earth's center, not where the water is.) The Earth is about 6,400,000m thick, so we take our distortion rate and divide it by that amount and get 2/3rds of a meter. This is the height of the tide. Due to the shape of the Earth and whatnot, the height is somewhat less than this, the site I found puts it at around 20.
So, after all the fancy mathematics all we have found is the bulge of the Earths tides that the moon causes on us today. Still, with 3.8cm/yr as the drift rate, the tide does seem like it would be very high. We can use it to tell us past tides as well. If I place the moon 100,000 km closer to Earth, it will effect the tides such that the bulge is 66". How long ago would the moon be this close assuming a constant rate of drift? 2,631,578,950 years ago. Using a more lenient drift rate like 2.5cm/yr (as you shall see the drift rate is not constant) would put this type of tidal action at 4 billion years ago.
Oops, the moon hasnt always been drifting by 3.8cm.
The current rate of moon drift does not accurately reflect the moons previous drift. Why is the rate of drift not constant? The accumulation of momentum transferred from tides to the moons rotation is responsible for this. The further away from Earth the moon gets, the less it is going to be held back, because the gravitational attraction between the two objects will be lessening. The momentum transferred from the tides to the moon will be letting the moon travel faster and faster until it ultimately flies out of orbit and into space. How can scientists know what the rate is? Layers of sediment. The thin layers of sediment scientists look at (called sedimentary cyclic rhythmites) show scientists the ebb and flow of the tide, and from this the length of the day can be inferred, and from this, the drift of the moon can be inferred (Williams 2000.) George E. Williams in the journal
Reviews of Geophysics places the rate of drift during the Proterozoic (2450-620MYA) around 1.24cm/yr and 2.17cm/yr during the Neoprotozoic (~620MYA). So then, how does this effect our calculations? The numbers already show that the moon is drifting away not at a steady rate, but faster and faster. The numbers supplied by Mr. Williams show that for the
1.8 billion years of the Proterozoic Era, the moons yearly drift changed by 1.9cm. In only
620 million years (From the Neoprotozoic age to now) the moons drift changed by 1.63cm. The drift rate increased threefold!
This is critical. Unfortunately, it makes calculation very, VERY tedious. Too tedious, in fact, for me. Im by no means a mathematical wizard, but one can see that the moons drift rate gets asymptotically smaller as one delves farther and farther into the history of the Earth-moon system. If one wants to see this for himself, take 38440300000cm (the moon' distance from the Earth) and divide it by 3.8cm/yr. The result? 10,115,868,400 years. That's right. If the drift rate was constant, the moon would outdate the Solar System before it ran into Earth (which makes no sense). The moon has always been a safe enough distance away from the Earth so that tides were not so huge as to drown every living species that didnt breathe water.
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For some of you who want to nitpick: please do. Ive checked the math to the best of my ability, but I wouldnt doubt if it was wrong. If anyone sees an error within this please let me know so I can correct it A.S.A.P. Thanks.
EDIT: I finally found out why I was getting strange values for some formulae. Remember kids, always make sure your units aren't being mixed.
Bibliography
http://www.synapses.co.uk/astro/moon1.html
http://ncsdweb.ncsd.k12.wy.us/planetarium/synchronous.html
http://mb-soft.com/public/tides.html
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000RvGeo..38...37W&db_key=PHY
