Debunking the Creationist Earth-Moon separation nonsense.

I went to way too much trouble for this! (Earth-Moon separation vs. time)Earlier today on another thread our newest post and run Creationist 'evolutionbuster' trotted out the time honoured Hovindism about the Moon having been too close to the Earth in the past thus producing huge tides making life on the Earth presumably impossible. I challenged him to produce calculations supporting this nonsense. Of course (and at least he admitted this) he could not do so. But of course he was confident that his sources had this capability and thus the statement was legit.So I, being bored this evening, decided to calculate this myself from first principles. Especially since he asked if I could provide calculations. Well here goes. (this does get a little involved and so I'm sure it will turn people off this thread but what the heck!)The problem of calculating the Earth Moon separation as a function of time is not a trivial problem - as I discovered trying to calculate the bugger. Also let me state that this calculation I shall present is really only an approximation - a somewhat sophisticated one but an approximation nonetheless.In fact the true Earth Moon separation history will forever remain unknown in an accurate manner. Any calculation of this has some fundamental limitations which I shall mention below. But a plausible calculation is possible.CalculationThe aim is to derive a function describing the rate of change of the semi-major axis of the Moon's orbit as a function of time. The tides raised on the Earth by the Moon dissipate energy (from friction) due to tidal oscillations caused by the fact the Moon orbits in a different period than the Earth rotates. A corresponding phase shift of the Earth's tidal response thus ensues.The simplest (on a Saturday evening) method of tackling this problem is to model the Earth's response as forced harmonic oscillator.After about a page of algebra (omitted here because of the lack of typesetting for equations) the key result I get is thatsin(phase shift) = -1/Q.Q is the dissipation function of the oscillator which should be recognised by physics undergrads.Now the mean motion of the moon (denoted by n) is less than the Earth's angular velocity (W) therefore the tidal bulge is ahead of the Moon by an angle I = 2 x (phase shift).Therefore (as I think most people know) the tidal bulge is not aligned with the Earth-Moon direction. This means a tidal torque exists and thus a transfer of energy and angular momentum exists between the Earth and the Moon.We determine the torque T on the Moon by the usualT=r X F where the X is the vector cross product.And the Force F is determined by the gradient of the Earth's external potential V at the Moon's position.Now only the component of the force orthogonal to the Earth-Moon direction contributes to the torque and only the second order dipole term of the Earth's potential contributes to the force component.Now the work done by the torque increases the orbital energy of the system at the rate = T x n. By Newton's 3rd Law an equal and opposite torque acts at a rate T x W to decrease the rotational energy of the Earth. Since W > n then these rates are NOT equal and therefore the total mechanical energy of the Earth Moon system decreases at the rate = -T(W-n).This energy goes into heating the Earth and of course determines the evolution of the Moon's orbit over time. This is what we want.Thus by now applying an energy argument I can calculate the separation as a function of time.Total Earth-Moon mechanical energy is :E = (1/2 * I * W^2) + (-G M m/2 a) I= Earth moment of inertia M = Earth massm= Moon mass and a = semi major axis of Moon's orbit.Therefore differentiating with respect to time:E(dot) = I W W(dot) + 1/2 * (M * m /(M + m)) * n^2 * a * a(dot)where (dot) means the time derivative. I used Kepler's 3rd law above.Looking at the total system angular momentum we get:L = I W + (M m /(M +m))* a^2 *n (and is conserved of course)L(dot)=0 which implies I W(dot) = -1/2 * (M *m/(M+m)) *n a a(dot)Putting this in the E(dot) expression gives us:E(dot) = -1/2 * (M*m/(M+m)) * n a a(dot) (W-n).Thus a increases while W decreases. As we observe currently for the Earth Moon system.Now putting all this together and using the standard Newtonian tidal potential V = -3/5 R^4 (constant) g (1/r)^3 * P2(cos H).R=Earth radius P2=second order Legendre polynomial r=Earth-Moon distancewe finally get that the a(dot) - which is our goal is:(I have omitted quite a bit of algebra here and above in the V expression)a(dot) = 3 (Love #) * (m/M) * R^5 *(a^-4) * n/Q and n=(G*M/a^3)^0.5Now the Love # is a number based upon the elasticity of the Earth and I cheated (because I don't know how to calculate it) and found it's value is 0.3.But the real problem for any calculation to proceed is the tidal dissipation function Q.The current value is approx. 12. But this value depends on the position of the continents and the fact that the Earth's oceans are in near resonance with the Moon. That is the phase shift I mentioned at the start is a small angle. In the past when the Earth was rotating faster the value would have been higher.This is where uncertainty crops up and I found a reference Webb (1982) paper in Geophysical Review of Royal Astron. Society that a mean value for the entire Earth's history is approx. 34.Thus we can integrate the above a(dot) expression and find the a as a function of time.This gives us (finally !!!!!!!!)a(final)^6.5 - a(initial)^6.5 = 39*(0.3)*(G/M)^0.5 * R^5 * m * (Time)where G=Newton Grav. constant.ResultsI wrote a quick C program to calculate this and some numbers kicked out are:Current Moon a = 3.844 X 10^10 cmGoing back 1 billion years I get a = 3.698 X 10^10 cm
Going back 4 billion years I get a = 2.731 X 10^10 cm.As we can see the Moon is nowhere near the Earth. Closer yes - but not that close. I have seen Creationists say that the Moon a billion years ago would be so close as to break up at the Roche limit which is only some 2 X 10^9 cm - what a joke!!!!As for the height of the tides - I used the standard equlibrium calculation in any udergrad mechanics text.
Currently the Moon on average raises a tide of approx. 35 cm on the Earth. The Sun raises about 15 cm for comparison. So the current total is about 50 cm.
According to my calculations, 4 billion years ago the tide from the Moon would have been about (3.844/2.731)^3 = 2.78 times greater.
Thus the Moon would have produced a tide of about 100 cm (2.78*35) and the Sun's would have been the same as above for a total of 115 cm.
So this supposed doom of HUGE tides is typical Creationist bs. The total is just over twice the current level. Annoying for coastal areas but not Earth threatening.All in all - another example of Creationst nonsense.I realise this is way too much effort for a message board but heck it was kind of fun.

Well if that is how physics is - I want no part of it - I'm glad I never studied it!

it has everything to do with the formation of the moon.
the creationist argument is that they moon must have been formed in the last 6000 year because of it's recession from the earth. good calculation, of course, shows this to be in error, and puts that formation date, where the moon lies outside the roche limit, to be about 4 billion years ago.is this not what you calculated?

i was just pointing out that your data doesn't precisely coincide with the "official" data, but is certainly sufficient in disproving any creationist claim of a young earth-moon system.

the rate of recession/distance, however, along with angular momentum, the rotation/revolution lock, shape, mass, and composition of the moon all play a roll in determining the moon formation theory. if for instance, the moon did not have the rotational lock with the earth due to it's shape, it had to have formed independently of the system, out of hard bodies. however, the facts indicate liquid formation. if the moon were closer, and receding faster, it might indicate capture if the formation happened while life was present. if the moon were formed with an iron core, it would place its age a little older, with the formation of the solar system. instead, it appears to be formed from PART of larger mass (the earth) that had already been sorted by density.