In part one we discussed the basics of lunar recession including the most basic backwards projections. In this part we will look at three more realistic backwards projections that is based on the measured slowing of the earth rotation. The difference here is a result of the actual shape and composition of the Tarth. The second backwards projection is based on a common mistake made when trying to refute lunar recession as an issue for an old earth, where they simply try to project the observed slowing rate of the Earth's rotation backwards. The third projection assumes a constant rotation rate for the earth.
A backward projection based on the observed slowing of the Earth's rotation.
This is a backward projection of the number of days in a year based on forces acting on Moon and Earth.
This is a backwards projection of the distance of the moon based on forces acting on Moon and Earth.
This is a backward projection of the relative proper secular breaking of the Earth's rotation and lunar recession data made assuming that the current relative proper secular acceleration of the Earth's rotation continued back. The relative proper secular acceleration is the difference between the relative proper secular breaking and the observed net breaking of the Earth's rotation. The reason given for this difference is the process of Earth rounding out following the Ice age. Once again, the current data is simply plugged into the math. as shown earlier. The result is that the Moos would have been locked in Geosynchronous orbit around the Earth at 16,000km 1.25 billion years ago. This is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth-Moon system cannot be anywhere near.4.5 billion years old.
Backward projection assuming a constant breaking of the Earth's rotation.
This is a backwards projection of the number of days in a year based on a constant breaking of the Earth's Rotation.
This a backwards projection of the distance of the moon based on forces acting on Moon and Earth based on a constant breaking of the Earth's Rotation
This is a backward projection of the number of days in a year and lunar recession data made assuming a constant breaking of the Earth's Rotation. This is not a reasonable assumption, but it is a common mistake. The result is that the Moon would have been locked in Geosynchronous orbit around the Earth 1.36 billion years ago. So even this extremely generous assumption produces a result that is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth-Moon system cannot be anywhere near 4.5 billion years old.
Backwards projection assuming the Earth's rotation is constant.
This is a backwards projection of the number of days in a year assuming no breaking of the Earth's rotation.
This is a backwards projection of the distance of the moon based on forces acting on Moon and Earth assuming no breaking of the Earth's rotation.
This is a backward projection of the number of days in a year and lunar recession data assuming that the Earth's rotation is constant. This is not a reasonable assumption in fact it is totally contrary to observation. The result is that the Moon would have been locked in Geosynchronous orbit around the Earth 1.55 billion years ago at 42,164 km. So even this extremely generous assumption produces a result that is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth-Moon system cannot be anywhere near 4.5 billion years old.
These results show that the forces on the moon are far more important than those on the Earth in determining a maximum age for the Earth-Moon system. The fact that you don't even get halfway to 4.5 billion years even when keeping the Earth's rotation rate constant is strong evidence for the Earth-Moon system not being any were near 4.5 billion years. We could potentially stop here but several arguments have been raised against such calculations and we need to deal with those arguments.
The key issue then we will deal with in part three is going to be showing the constraints paleontological data place on this problem for an old Earth.
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References
http://gscim.xyz/Articles/Advanced/Lunar_recession_and_the_Age_of_the_Earth/
http://gscim.xyz/Articles/Intermediate/Lunar_recession_and_the_Age_of_the_Earth/