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Torque of the Earth 
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Post Torque of the Earth
Torque of the Earth

The spin wobble period of the earth, the 25,800 year period known as the Great Year or Platonic Year, provides a precise measurement of the torque forces operating on the earth.

Celestial Mechanic wrote the precession dialogues which explain the science of the torque of the earth.

I'm posting this to enquire further regarding the exact science of the torque of the earth. More than 99% of the precession is understood as resulting from lunisolar torque. I would be interested in scientific comment on the remaining factors causing precession and its rate of change.

Any puns on torque of the earth would be welcome, such as from Mahler or the talk of the town, all torque and no binary.

Late heavy bombardment and earth's spin wobble
G. Jeffrey Taylor of Hawai'i Institute of Geophysics and Planetology wrote a paper in 2006, Wandering Gas Giants and Lunar Bombardment, arguing that outward migration of Saturn might have triggered a dramatic increase in the bombardment rate on the Moon 3.9 billion years ago, an idea testable with lunar samples. Dynamic graphics are available at Planetary Science Research Discoveries Archives.

Taylor states "This portrait of planetary migration explains the late heavy bombardment, the orbital parameters of the outer planets, the present orbital distribution of main-belt asteroids, and the presence of Jupiter's Trojan asteroids."

Did the events of the late heavy bombardment set earth's spin wobble period?

My question is asking whether the suggested 1:2 resonance event of Jupiter and Saturn is scientifically proven, whether the resulting stabilisation of the solar system included stabilisation of the earth-moon system, and if more is known about the effect of this event on the motion of the earth and moon.

Could it be possible that this event, the stabilisation of the gas giants, gave the earth a dynamic stability which it has retained ever since?

Robert Tulip
rtulip.net



Sat Dec 12, 2009 4:27 pm
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Post Re: Torque of the Earth
You may as well be torquing in tongues for all I know about this subject Robert….


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Robert Tulip
Sat Dec 12, 2009 8:51 pm
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Post Re: Torque of the Earth
I am not torquing through my hat. Here is a conversation on this topic with an astronomer.

Quote:
The precession-driving torque follows the same inverse cube law as the raising of tides. Jupiter has about 1/1,000 of the Sun's mass and is about 5 times farther away, so its torque component should be roughly 1/100,000 of the Sun's component. The contribution from Saturn is down another factor of roughly 20, and the contributions of Uranus and Neptune are tiny compared with that of Saturn.
Many thanks Hornblower. As you know from our previous conversations, my knowledge of astrophysics is patchy, so the fact the torque of the earth follows the same inverse square cube law as the tides is very helpful for me to understand what is going on.
Quote:
The Earth is lumpy, gooey, and partially fluid. The variations in magnitude and direction of the lunar and solar gravitational vectors are all over the place. I am not surprised at small discrepancies between the calculated and observed precession rates.
Thanks, I had thought the discrepancy was due to torque forces of other planets, but as you point out these are miniscule.
Quote:

I would expect most of the impacts on the Earth and Moon to be from small bodies in prograde, highly eccentric orbits. They would overtake the Earth, and the impacts should push it into a slightly larger orbit. That would reduce the Sun's gravitational torque and slow the precession down slightly.

Okay, so the late massive bombardment would have had some direct effect on the parameters of precession. No more recent event could have bumped things around on such a scale.
Quote:
We would need an estimate of the total mass of impacting bodies during the bombardment to estimate the effects on the Earth's orbit. It might be roughly analogous to shooting at an elephant with a machine gun. The hail of bullets would kill the beast but not move it much. As a swarm of planetesimals passes through the Earth/Moon system, some will hit the Moon prograde and others will hit it retrograde. I would expect them to largely balance out and cause relatively little net change in the Moon's orbital radius. The ones that hit on crossing paths might change the eccentricity a bit. Once again, bullets hitting an elephant.


So the likely direct effect could be very small. I wonder, could the bombardment have shifted earth enough to change our orbit by a whole day, ie in range 364.25 - 366.25 days, or is the elephant so much bigger than the bullets that likely shift would be more like seconds or minutes?
Quote:
I don't see this as "shuddering", but rather as numerous tweaks and nudges that gradually shift the orbits of the outer planets over a period of some 200 million years, the interval noted in the paper. Once again, the violence at the inner planets is from impacts by deflected planetesimals, not from direct gravitational perturbation by the outer planets.
Here are some more detailed questions on the “shuddering” theme.

The posited resonance between Jupiter and Saturn in the early solar system occurred when the Saturn orbit period was double the Jupiter orbit period, for a time lasting about 200 million years around 3.9 billion years ago, about 700 million years after the sun came alight.

To understand this 1:2 resonance, consider Saturn orbital period as 28 earth years and Jupiter orbit as 14 earth years. Jupiter has since moved closer to the sun to its current 11.85 year orbit and Saturn, now at 29 years, has moved further away. Jupiter and Saturn combined their energies during this resonant phase to expel Neptune far beyond the orbit of Ouranos. This JS resonance appears to have lasted for millions of years, until the early cosmic ‘egg’ of the solar system exploded with the expulsion of the planet Neptune to the far depths of outer space, in the stable orbit in resonance with Pluto where it has remained to this day.

The 14:28 year JS phasing would have had large effect on the solar system barycentre, causing a very regular wave function due to the repeat of the JS amplitude cycle having such simple regularity at the same exact spot on the ecliptic. Other planets crossing this JS alignment point would have been perturbed in their orbital cycle period over the movement of their perihelion against the multi-million year period of the JS resonance. Did something have to break?

We can imagine Neptune orbiting outside this JS pair with their one-two routine. When all three are lined up in a syzygy with the sun, the JS conjunctions pull Neptune closer to the sun.

Were the perturbations this resonance introduced into Neptune’s orbit enough to toss it to the current edge of the planetary disk?

For earth, now orbiting 164 times faster than Neptune, the 14:28 year JS resonance would have had real orbital effects. The conjunctions and oppositions of Jupiter and Saturn would have opposite gravitational effects on earth’s orbit, not same direction effects as with Neptune.

When Jupiter and Saturn are conjunct at earth’s perihelion or aphelion, would this move earth’s orbital position appreciably closer to Venus or Mars, with stronger or weaker gravitational interaction between the inner planets occurring as a result?

Could Earth’s orbital period have been significantly different before the Neptune escape cataclysm in the early days of the solar system?



Mon Dec 14, 2009 12:17 am
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Post The Arrow of Odysseus
The Arrow of Odysseus

An analogy to describe the events of the early solar system can consider the expulsion of Neptune as similar to an archer pulling a bow and firing an arrow.

The solar system is a disk or lens. When Jupiter and Saturn were in 2:1 resonance for two million years four billion years ago, their combined gravitational energy worked like an archer pulling a bow, with the sun at the central point of the bow and Ouranos marking the points where the string is tied to the bow at each end. As the arrow of Neptune was pulled back (by Odysseus the archer, to continue the mythic meme), strain was placed on the entire bow. As Neptune was released when the string was fully drawn and the arrow was fired, also somewhat like a baby born from it's mother's womb, the tension of the string, fueled by Jupiter and Saturn, was released, also causing the bow to return to an unstressed state. The bow, with the Sun at the notch point of Odysseus' hand, has the inner planets Mercury, Venus, Earth-Moon and Mars as its jewels. These four jewels, spaced up and down the limbs of the bow, return from stress when Neptune is released. The planets, unlike jewels on a bow, are held together only by gravity, so the upheaval of the whole system allows them to move freely in response to the forces unleashed by the release of tension at the expulsion of Neptune.

A further analogy for how the Jupiter-Saturn resonance affected the whole solar system is a coin in a tin can. You can rattle the can either round and round like a centrifuge or from side to side like a bell. When Jupiter and Saturn were in 1:2 resonance, the can rattled like a bell, with the solar system barycentre rhythmically shifting every decade between two exact points on the ecliptic for two hundred million years. This bell ringing booted Neptune out. Since then, the barycentre has had a stable 'centrifugal' shape, like shaking a coin around the inside perimeter of a tin can. This shape embeds the number 144 in the relation between the torque of the earth and the whole solar system. Jupiter, Saturn and Neptune form the Solar System Barycentre wave function with period 178.9 years, precisely one one hundred and forty fourth of the earth torque period of 25765 years.

Are the above metaphors of the bow of Odysseus and rattling the tin can accurate descriptions of the astrophysics of the solar system?



Mon Dec 14, 2009 8:22 pm
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