The moon billions of years ago

[dcderek24]

this a creationist question. i am not a creationist but a creationist friend asked me this question. didn't have the answer.
the moon is moving away from us at a rate. billions of years ago at that same rate the moon would have been "touching us"?

don't know the answer.. was the moon always orbiting earth?
did the moon pull away more at a faster rate since it got to a further distance?

 

[Kevin_Axion]

The moon is in equilibrium with the Earth's gravity and it's orbital centrifugal force, as is the Earth with the Sun's gravity. The moon wasn't always there and is a product of a celestial collision between a primitive Earth and another large mass object. The object moved into the orbital zone it currently occupies, although it likely shifted.

 

[granpa]

this a creationist question. i am not a creationist but a creationist friend asked me this question. didn't have the answer.
the moon is moving away from us at a rate. billions of years ago at that same rate the moon would have been "touching us"?

don't know the answer.. was the moon always orbiting earth?
did the moon pull away more at a faster rate since it got to a further distance?

Even if all that were true the moon would never have been 'touching us'.
Eventually the Earth and moon would have been tidally locked.
Whether this occurs before or after the roche limit is reached I don't know.

http://en.wikipedia.org/wiki/Roche_limit#Roche_limits_for_selected_examples
http://www.ridgecrest.ca.us/~do_while/sage/v5i5d.htm

 

[granpa]

the angular momentum of the moon is

m*v*r=(1 lunar mass)*(86400 km/day)*384,400 km = 3.32 * 10^10​

the angular momentum of Earth is

(2/5)*m*v*r=(2/5)*(80 lunar masses)*(40,000 km/day)*6380 = 8.166 * 10^9​

for the Earth moon system as a whole, the sum of the Earth's and the moons angular momentum must be constant.
at the present time the vast majority of the angular momentum of the Earth moon system is in the moon.
If the moon was very close to the Earth then the vast majority of the angular momentum of the Earth moon system would be in the earth.

we assume as a first approximation that when the moon was very close to the Earth that the Earth spun around 4 times as fast and a day was 5.9 hours
then we need to determine where the moon would be if it were tidally locked at 6 hours

period of an orbit:

T^2 = Kr^3
t for an orbit just above the surface of the Earth is about 90 min​

so if the moon were tidally locked with the Earth at 5.9 hours then

(6 hours)^2/r^3 = (1.5 hours)^2/(6380 km)^3
r^3 = (5.9/1.5)^2 * 2.597*10^11
r = (16*2.597*10^11)^(1/3)
r = 16075 km
r = 2.5 Earth radii​

At this orbital radius the angular momentum of the moon at that time would be:

m*v*r=(1 lunar mass)*(5*2pi*16075/day)*16075 = 8.1182 * 10^9
therefore the moon would still have significant angular momentum.​

the Earth's angular momentum at that time would be:

present angular momentum of Earth + present angular momentum of moon - angular momentum of moon at that time
8.166 * 10^9 + 3.32 * 10^10 - 8.1182 * 10^9
which is about 4 times what it is now

so the Earth would indeed be spinning 4 times as fast
A day would indeed be 6 hours
thus agreeing with our assumed approximation​

the roche limit for the moon is

fluid=18,261 km
rigid=9,496 km​

​

conclusion:

the moon could never have 'touched us'.​

 

[granpa]

I screwed up the math at first but I think I got it right now

 

[Upisoft]

Current rate is 38mm per year. Earth is less that 5by old. In that time with that rate the Moon had to be 190 billion mm = 190,000 km closer. The moon is 384,400km away now, so in the hypothetical moment 5by ago the Moon was 194,400km away. It does not seem like touching.

 

[Janus]

Current rate is 38mm per year. Earth is less that 5by old. In that time with that rate the Moon had to be 190 billion mm = 190,000 km closer. The moon is 384,400km away now, so in the hypothetical moment 5by ago the Moon was 194,400km away. It does not seem like touching.

Not only that, but since the recession rate depends on tidal friction, and tidal friction varies with the distribution of the continents, there were periods in Earth's past when the tidal friction was much smaller and the recession rate of the Moon was lessened as a result.

 

[Ich]

http://www.talkorigins.org/faqs/moonrec.html

 

[D H]

billions of years ago at that same rate the moon would have been "touching us"?

As upisoft pointed out, assuming a constant rate would have meant that 4.5 billion years the Moon was a bit over half its current distance from the Earth. That is an erroneous result. The assumption of a constant rate is not valid. All other things being equal, the recession should be roughly a 1/r⁶ process. The better of the creationist arguments use a 1/r⁶ model coupled with the current recession rate to determine that the Moon was "touching" the Earth around 1.2 billion years ago.

So how to reconcile that 1.2 billion year value with all of the evidence that the Earth is about 4.6 billion years old and the Moon is about 4.5 billion years old? Simple: Just as using the current recession rate in conjunction with a linear extrapolation yields the wrong answer, so does using the current recession rate in conjunction with a better nonlinear model. That 1.2 billion year result is still wrong because of its assumption that the current recession rate is solely a function of the distance between the Earth and the Moon. Use the wrong assumptions and you will get a wrong answer. Garbage in, garbage out.

All other things being equal, decreasing the distance between the Earth and the Moon would make for a larger recession rate. All other things are not equal. The configuration of the continents also contributes to the recession rate. There presently are two huge barriers to tidal flow in the oceans, the Americas and Africa+Eurasia. To make matters worse, the configurations of the oceans are such that they amplify various tidal nodes. The current configuration makes the current recession rate anomalously high.

This has not always been the case. There were times when the recession rate would have been closer to some average rate, and other times when the rate would been anomalously low. The continents have come together five different times to form supercontinents. The lunar recession would have been anomalously low at those times. At other times the equator was free of land. That too would have made for an anomalously low lunar recession rate. The fossil record contains various signatures of the length of a day, the number of days per month, and the number of months per year. Science now has a pretty good picture of the Earth-Moon system going back to 2.4 billion years. The Moon was never "touching" the Earth during that time. Not even close.That said, your friend was correct in one regard. The current best guess regarding the formation of the Moon is that the Earth and Moon did indeed "touch" one another a long time ago. Rather violently in fact. This is the "giant impact hypothesis." Per this hypothesis, a Mars-sized body collided with the proto-Earth. However, this collision would have occurred about 4.5 billion years ago rather than 1.2 billion. Per this hypothesis, most of the mass of that Mars-sized body simply added to the Earth's mass. Fragments of the collision went into Earth orbit. These fragments rather quickly coalesced to form the Moon somewhere above the Roche limit.

The current lunar recession rate is largely attributable to ocean tides. While there were no ocean tides at the time of that collision (there were no oceans at that time), there still were Earth tides (there still are Earth tides for that matter; google that phrase). The Earth tides caused by the Moon orbiting at a bit over the Roche limit would have been huge. Since the Earth isn't perfectly elastic, those huge Earth tides would have resulted in frictional heating of the Earth, and that in turn would have resulted in a transfer of angular momentum from the Earth's rotation to the Moon's orbit. So even without any oceans the nascent Moon would still have undergone recession from the Earth.

 

[granpa]

http://docs.google.com/viewer?a=v&q...xe-j5j&sig=AHIEtbRaMXPNzsx96oixrCVl6Lqtyoz9cQ

http://docs.google.com/viewer?a=v&q...1crDMG&sig=AHIEtbRsg-4lkHtL_572CU1bOPcPuaOLGA

 

[Upisoft]

The OP said "at that same rate" thus the linear assumption. Anyway the tidal wave speed also plays role. Currently 1 moon rotation = 27 Earth rotations. In the past when the Moon was closer to Earth it orbited faster and making the tidal wave speed lower. Any way the alleged "better" 1/r⁶ model is ridiculous as it suggests quite huge values for the point when Moon and Earth was tidally locked. At that point one should expect values near zero as the tidal wave speed is zero.