Lunar recession and Earth receding from the sun

There is geological and paleontological evidence that Earth rotated faster and that the Moon was closer to Earth in the remote past. Tidal rhythmites are alternating layers of sand and silt laid down offshore from estuaries having great tidal flows. Daily, monthly and seasonal cycles can be found in the deposits. This geological record indicates that 620 million years ago there were 4007 solar days/year.The current rate of lunar recession which has been measured very accurately by mirror's placed on the moon indicates that there should have been 426 days in a year 620 million years ago. The usual explanation is that the moon was receding more slowly in the past. This makes no sense. If anything the moon should have been receding faster in the past.However, the current rate of lunar recession is consistant with the observation that there were 400 days in a year 620 million years ago if the Earth was closer to the Sun (because the year would be shorter). Its orbital radius would have to have been 0.9589 au at that time.Recession rate of Earth = 6.85 * 10^-11 au/yr (10.25 m/yr)Assuming that rate did not change, that puts the Earth at 1-(1- 0.9589) *7.5 = 0.69 at 4.5 billion years agoIf the rate of recession is inversely proportional to the cube of the orbital radius then that puts the Earth just inside the sun 4.5 billion years ago.Year lengthens by 3.24 seconds per 1000 years

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*sFor simplicity's sake let's just say Earth has one unit of angular momentum.Our moon currently has 5 units of angular momentumTherefore the total angular momentum of the earth-moon system is six unitsA moon at the roche limit orbits in 6.7 hoursTherefore 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 daysWhich 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*10^9In fact it was 4 * 72,000 km closer. This suggests that rate of tidal recession follows an inverse Cube law

Hi Granpa,Paragraph 1 is a cut-n-paste from Tidal acceleration at Wikipedia, and paragraph 2 is a cut-n-paste from Lunar Recession at Hypography.The Forum Guidelines state (among other things):

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Grandkids around the world are crying now. Please clean up your act.Thread proposal rejected.