Message 2 of 3 (821506)
10-08-2017 4:48 PM
Earth differentiated into gabbro (upper mantle) and peridotite (lower mantle). Earths moon Theia differentiated even further into granodiorite and dunite (olivine).
3 billion years ago Theia's decaying orbit reached the Roche limit and over the next 1 billion years slowly deposited all of its mass onto a ring of mountains circling the earth's equator.
First the ice on its surface was deposited. This formed Earths ocean. Since Earth had no continents at that time the surface of the Earth was completely flooded.
Then the granodiorite was deposited. The granodiorite metamorphosed into the various rocks of the continental crust.
Then 2.4 billion years ago the dunite was deposited. This created the banded iron formations. The dunite sank to the bottom of the mantle where it now forms the d" layer.
Earth rotational angular momentum = orbital angular momentum of moon sized object at Roche limit (18,000 km)
sqrt(G*earth mass/18000 km) = 4.7 km/sec
moon mass * 4.7 km/sec * 18000 km = 6.21 * 10^33 J*s
rotational angular momentum of Earth = 5.86 * 10^33 J*s
For simplicity's sake let's just say Earth has one unit of angular momentum.
Our moon currently has 5 units of angular momentum
Therefore the total angular momentum of the earth-moon system is six units
A moon at the roche limit orbits in 6.7 hours
Therefore if Earth day 1.9 billion years ago (at the point that Theia had completely deposited all it's mass onto the Earth) was 6.7 hours then the Earth had 3.6 units of angular momentum and our current Moon had 2.3 units of angular momentum. (Earth couldn't have been spinning any faster because if it had then Theia would have receded away)
That means our moon had half as much angular momentum as it does now and its orbit was therefore 4 times closer to the earth 384000/4 = 96000 km Its orbital period was 0.25^1.5 * 28 days = 3.5 days
Which puts it well outside the orbit of Theia which was orbiting at the Roche limit which is 18000 km.
The current rate of lunar recession puts the Moon 72,000 km closer to Earth 1.9 billion years ago. 3.8 cm * 1.9*10^9
In fact it was 4 * 72,000 km closer. This suggests that rate of tidal recession follows an inverse Cube law
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