Earth is whipping around quicker than it has in a half-century

In astronomy, there are solar eclipse records used from Assyria and Babylon that indicate a slowing down of Earth's rotation as well as solar eclipse observations since the 1880s and the Moon slowly moving away from Earth. The Giant Impact model for the origin of the Moon features different models used to show the initial rotation of the early Earth or proto-Earth (perhaps when it was 65% to 90% present mass and size). Some indicate an initial length of day some 2-3 hours that slowed down. Tracking all of those length of day changes through geologic time and showing strata evidence is more than challenging :)
 
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I think the latest models put Earth's rotation after impact of close to your numbers, but I think it's 4 to 6 hours -- I may be thinking of orbital time for the proto Moon admittedly -- though that means accuracy going back several billion years and it's clear that things were more like a pinball machine at times back then.

One requirement is that the very close orbiting proto-Moon (or moons) that formed after the impact had to be slower than the Earth's orbit, otherwise tidal action would have dragged it back down.

This is why Venus has no moon, even Mars is a problem. Venus has very little rotation so even if it grabbed a moon it would tidally force it to auger-in. Mars has almost the same rotation rate as we do, but it may have had it long ago, so it is, and was, very limited in what it could capture and hold. Phobos isn't "long for this world". Well, ok, it isn't long for that world. :)
 
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The article says:
> "That's not particularly alarming — the planet's rotation varies slightly all the time, driven by variations in atmospheric pressure, winds, ocean currents and the movement of the core. "

They forget to mention that the most significant factor is the lunar cycle, which shows up in the length-of-day measurement strikingly. This is data going back to 1962, with the main factor being the 13.66 day lunar fortnightly tidal cycle.

Baa0cQ.png
 
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The lunar tidal cycle and slowly expanding orbit of the Moon moving away from Earth is very difficult in the tidal dissipation parameter calculations. The giant impact model for the origin of the Moon has the proto-moon form near the Roche limit near 3 earth radii but some new models indicate perhaps 4 earth radii or so to avoid difficulties. 'Supercomputer simulations could unlock mystery of Moon's formation', https://www.sciencedaily.com/releases/2020/12/201204110254.htm, Dec-2020. Also, 'The effect of pre-impact spin on the Moon-forming collision', https://academic.oup.com/mnras/article/500/3/2861/6007797, "ABSTRACT We simulate the hypothesized collision between the proto-Earth and a Mars-sized impactor that created the Moon..."

[My observation, this report and computer model is very interesting. Many things can go very wrong in the giant impact model to make the Moon we see in the sky here on Earth. The PDF paper is attached. The paper is 10 pages and says on page 9, "The simulation with Theia not spinning initially yields an orbiting proto-Moon with a periapse at 4.5 R⊕, well outside the Roche radius of ∼3 R⊕. It has a mass of 0.01 M⊕
0.81 M...On page 4, Table 1 is provided showing a proto-earth with 3 hour day or so. The effects of a spinning Theia are presented and on page 5, here are some stats provided, "We consider an impact between a target proto-Earth of mass 0.887 M⊕ and an impactor, Theia, of mass 0.133 M⊕. Both are differentiated into an iron core and rocky mantle, constituting 30 per cent and 70 per cent of the total mass, respectively, modelled using the Tillotson (1962) iron and granite equations of state." As computer models advance in the giant impact model, more and more special initial conditions seem needed now to make everything work :)]

At present, I am not aware of any tests that verify the Moon orbited the proto-earth so very close as 3 to 5 earth radii, the simulations seem to require this.
 
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[...The paper is 10 pages and says on page 9, "The simulation with Theia not spinning initially yields an orbiting proto-Moon with a periapse at 4.5 R⊕, well outside the Roche radius of ∼3 R⊕. It has a mass of 0.01 M⊕
0.81 M...On page 4, Table 1 is provided showing a proto-earth with 3 hour day or so.
That also is the view found in the new book, "The Earth Had Two Moons", contrary to what I had thought, but cautioned I could be wrong.

It is the proto-Moon that is assumed to have about a 6 hour orbit.

The rule of thumb for terrestrial planets puts the Roche limit at about 2.5R, so a minimum of 3R is safer for the limit. This is the forming region the author took for discussion in his book.

It seems logical that when an impact occurs the majority of the mass lifted up will fall back down. Less and less material will reach higher and higher altitudes and orbits. Thus, the bulk of the mass that survives in orbit would be just outside the Roche limit, IMO.

[Getting a bit astray of the OP, but interesting, is that this event would have created two strong Lagrange points allowing for Trojans. A large mass could have formed at an L4 or L5 or both. Later, as they moved outward due to tidal action with Earth (first hypothesized by George Darwin in 1879), then the instability would have caused the smaller body to impact the Moon.

But the impact velocity of a Trojan would likely be about that of the slow esc. velocity of the Moon (2.4 kps) and a talps (splat spelled backwards, Belton) event. This gentler class of impact seems to explain the farside's thicker crust and thinner KREEP.]

As computer models advance in the giant impact model, more and more special initial conditions seem needed now to make everything work :)
Yep, initial conditions are always critical to cosmogony and celestial mechanics.

What is amazing is that there are hypotheses that can match most of what we see. But I don't think anyone suggests we have it nailed down yet.
 
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FYI, ref. Helio post #7. I used my astronomy spreadsheet and plugged in a proto-earth 0.9 earth mass, proto-moon 0.9 moon mass and eccentricity = 0 with semi-major axis = 4.5 earth radii. I get ~ 14 hour orbital period, similar to the giant impact models in use. Parameters like this in the model are not directly verifiable.
 
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Your so smart I don't understand what you are saying

I understand. Two books I purchased long ago from Sky & Telescope have greatly helped me in orbital dynamics and astronomy. Jean Meeus, Astronomical Algorithms 1991, and Fundamentals of Celestial Mechanics by J.M.A. Danby 1992. These books help define how you can understand and calculate an elliptical orbit or a circular orbit about another body in space---Rod
 
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My view on astronomical simulations - they can be very useful but must also be followed up using real world or natural world observations to support. The origin of the Moon model popular today is the Giant Impact Model and shows various initial parameters for the Earth-Moon system that is not directly observable today like the planet's original length-of-day, very different than our 24 hour day. Some components of the model may be testable, other components like a Moon with a 6 to 14 hour orbital day around Earth is not verified.
 
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Your so smart I don't understand what you are saying

When it comes to Earth-Moon interactions, it's actually quite simple -- the moon's gravitational force will induce a rotational and axial torque on the earth and thus either slow down or speed up the earth's rotational speed, and also create a wobble in the earth's rotation. The latter is apparently not understood as no one has discovered yet that the earth's precessional wobble (the so-called Chandler wobble) matches precisely the known lunar cycle. The 3 green arrows below are predict precisely from the moon's draconic (or nodal) cycle, which provides the strongest declination torque when applied in conjunction with the sun's semi-annual nodal declination.

x2YRb5.png
 
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Interesting. What are the units along the y-axis for each graph?

They are all essentially arbitrary units indicating the strength of the interaction, which is routine for signal processing analysis. The top panel is the strength of the lunar declination, showing the 13.606 day draconic fortnightly cycle, and the longer term 18.6 year nodal modulation. The second panel is the projection of the extent of the Earth's wobble on an equatorial planar axis, showing the 433 day period interfering with an annual cycle. The bottom panel is the power spectrum of the second panel, which if the log is taken would be in dBs. The inset shows the strength of the sun's semi-annual declination, indicating a difference in the torque applied for northern vs southern declination.

The geometry is shown in the figure below
ViIcq9.png
 

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