Just out of curiosity I've been trying to find out just how far away the Moon was from the Earth when it formed 4.5 billion years ago. Lots of sites saying it is moving away from us at about 38mm a year, but also pointing out that this was slower in the past. But none give a distance. Anyone know?
The moon must have formed outside the Earth/Moon system's Roche limit, or it would have fallen apart again directly. This lower limit of the early Moon's orbit is between nine thousand and eighteen thousand kilometers from the centre of the Earth, depending on exactly how fliud the Moon was as the time. And the Moon was probably quite fluid, as it would have been very hot when it first coalesced. So we can be fairly certain the newly formed Moon has never been much closer than eighteen thousand kilometers from Earth. After that the Moon has been moving outwards at varying speeds according to the variable effects of tidal forces; these are variable because the continents are moving around on the Earth's surface, so tidal flow in the oceans is not constant over time; I expect other effects may be even more important, for instance the cooling and solidification of the Moon's interior.
If Earth had oceans and continents like they are today, do you have info on amplitude the tides? (I seem to recal 1000 meters or more.) I have never seen any discssion of how larger tides would have effected evolution - quite a lot would I think. How high were the tides when fish began to crawl up on land or, as I am guessing, got stranded there, and some of the "genetically deformed ones" survived better, until the next tide came, which would be only a few hours later as Earth was spinning more rapidly. What was the length of the day when first "fish" were left "high and dry" for a few hours? 16 hours? etc. I am not sure they crawled up on land with little "fin legs" etc until AFTER they could get oxygen by some "Darwinian propigated deformity" that now has become our lungs.) I know nothing about this. - Can someone who does, pick up this ball and run a little with it?
Can't find a definite answer, but 1 billion years ago the Earth rotated in 18 hours. More info here: http://www.space.com/scienceastronomy/moon_mechanics_0303018.html Note solar tides contribute about 1/3 of the tidal force slowing the Earth's rotation; it isn't all the moon. You are confused about the meaning of "tidal force". This does not merely mean the rise and fall of the Earth's oceans. Info here: http://en.wikipedia.org/wiki/Tidal_force Since the amount of water in the oceans is about the same as would cling to a globe if you dipped it in water and pulled it back out, it's safe to say the mass of the oceans is negligible compared to the entire mass of the Earth, and therefore the placement of the continents has no measurable effect on tidal retardation of the Earth's rotation.
I have not yet read your referrence, but think eburacum45's text more near the truth than yours above. If there were no lag in the positions of the tidal bulges, then there would be no torque (perhaps "thrust" is better term?) on the moon to change its orbit. The extent of the lag is a strong function of the continental shapes and ocean depth etc. If Earth's dry land mass were all in constant-width, Everest-high, ring around the equator, then the moon would be moving away at a much slower.
The Wiki article doesn't truly describe what is going on in tidal retardation of the Earth's rotation rate. The article talks about forces but not torques, and it is the gravity gradient torques by the Moon and Sun that slows the Earth's rotation rate. Ignoring high-order terms, this torque is 3 GM/||R||^5 R cross I*R where M is the mass of the Moon (or Sun) R is the vector from the Moon (or Sun) to the Earth's center of mass I is the Earth's inertia tensor. There would be no gravity gradient torque if the Earth were a perfect sphere. It is the Earth's equatorial bulge, not the oceans, that give the Moon and Sun something to grab.
It is my understanding that the varying disposition of the continental masses, which are islands of different density in the crust, *and* the flow of ocean tides and currents work together to make the changes in tidal effects unpredictable. These are small effects, but enough to make the tidal braking of the Earth/ Moon system a non-linear effect, so that the rotation of the Earth can't be calculated by projecting backwards or forwards in time using current rates of rotation change.
eburacum45, The small effects you are talking about are *very* small. Those effects definitely come into play in determining whether a leap second has to be added to a year; that calculation can only be made six months in advance. On the other hand, a reasonably good estimate of the length of a day 100 million years ago can be made just by considering the J2 contribution and ignoring everything else. You are correct regarding extrapolation using the current rate of change. The problem of determining the length of a day 100 million years ago is a highly non-linear problem. The gravity gradient torque itself is non-linear because it varies with 1/R^3. This is compounded by the rate of change of the Moon's orbital radius; this too is non-linear. Finally, as the Earth's spin rate has decreased, so has the Earth's oblateness. The Moon and Sun had a lot more to grab on to 100 million years ago.
This page might hold some interesting information; http://jason.kamin.com/projects_files/lunarrecession.htm During the periods when a supercontinent occupied one hemisphere of the Earth tidal flow will have been quite different to other periods when the continents were dissociated; so I think this variable factor would make exact modelling of rotational change practically impossible.
That link is bogus. Averaged over time, the water on the surface of the Earth is going nowhere with respect to the surface of the Earth. The *tiny* frictional forces average out to nil on both the Earth and the Moon. I really don't want to derive the gravity gradient torque equations in a LaTeX-free forum, but I will if I must. The gravity gradient torque is the true cause of the tidal locking of the Moon's rotation rate to the Earth-Moon orbital rate, and eventually will tidally lock the Earth's rotation rate to the same. Gravity gradient torque is a well-understood process that acts on artificial satellites. There is nothing unnatural about this torque; it acts on natural satellites as well as on artificial ones.
Yes, but do artificial satellites change shape over time? Do you have equations which take into account fluid flow and mass redistribution?
More links http://bowie.gsfc.nasa.gov/ggfc/tides/intro.html Which says that solid earth tides are more important than the ocean tides, by the way, but I supsect that continental drift will have an influence there as well; http://en.wikipedia.org/wiki/Tidal_acceleration#Qualitative_explanation
