Hat tip to Talkshop contributor ‘OldmanK’ for alerting us to an interesting website written by physicist Carl Johnson some years ago. Among the many interesting articles, there are a few on gyroscopes and the angular momentum of precession which directly relate to our study of solar system organisation, and which provide clues as to how the energy transfer which organises the stability of the orbits occurs. I have a hunch that this can potentially lead to several advances for us, in understanding the relations not only of orbital periods and their effects on neighbouring orbits, but also of orbit to spin-rate energy transfers. This will help unlock the mysterious numerical ‘coincidences’ Stuart and I have discovered between planetary rotation rates and their neighbours orbital rates. It may also further our understanding of correlations I discovered between Z-axis motion of the Sun relative to the centre of mass of the solar system and sunspot production, and changes in Earth’s length of day.
It will also help us understand why the important Z-axis discovery recently made by Paul Vaughan is Geo-effective, as evidenced by the appearance of the relevant periods in paleo-proxy records. As Paul points out, the implication is that two key cyclic periods, the Gleissberg and De Vries cycles, may be more to do with Earth’s orientation variations caused by Gas giant motion than solar activity variation, though it’s possible both are involved in the climate changes indicated by the proxies. This would be because the gas giant planets affect the Sun as well as the Earth directly.
From Carl Johnson’s website:
It has been assumed by all astronomers and Physicists that planets can perturb several parameters of the orbits of each other, BUT that they could never alter the semi-major radii of each others’ orbits. That conclusion WOULD be true IF all the objects in the Solar System orbited in exactly the same Plane. But they certainly do not.
The Solar System objects move in various planes. This fact results in effects that are similar to the non-Conservation of Angular Momentum of the toy gyroscope. Examples are the Earth’s Precession, the Regression of the Nodes of the Moon’s Orbit (and all other orbits), and any other perturbations where the Z-axis is involved. Planets ARE causing precessional effects in each other. Now that the precessions are all established, no significant violations of Conservation of Angular Momentum SEEM to occur, but whenever each of those precessions CHANGES, that is, they ACCELERATE, they certainly represented clear violations!
For example, the earth has an equatorial bulge that is rotating in a plane where each of the Sun and Moon nearly always are acting to gravitationally try to tilt that plane (trying to stand the Earth more upright), which causes the Precession that the Earth experiences. There seems to be a common misconception that this Precession of the Earth is constant, and we all learned of the 26,000 year time period of the (wobble) Precessional motion in Elementary School. However, that is not even close to being true! TWICE each year, the precessional effect of the Sun on the Earth entirely vanishes, at the instant when the Earth’s orbital motion causes the Sun to appear to exactly cross the celestial Equator (around March 21 and September 21 each year). The Precession of the Earth due to the Sun ENTIRELY STOPS on those two days each year! After that, the precessional speed ACCELERATES during the following three months, up to a point where the precessional SPEED is greatest around June 21 and December 21 each year. After that, there is a DECELERATION of the precessional speed during the next three months, to get back down to the zero precessional speed.
Also, consider a “new earth” exactly like ours but not precessing at all. It would (somehow) START to precess, in other words, the Precessional motion of the earth would ACCELERATE up to the rate it is now at. A motion which takes 26,000 years to occur might seem to not involve very much energy, and so it seems that it has always been neglected by Researchers regarding energy considerations. But the Earth is quite massive and since that Precessional motion starts and stops twice every year, there is actually an enormous amount of energy involved.
This represents a good deal of kinetic energy of the Precessional motion, and the Conservation of Energy insists that a source for that energy have provided it. The energy that would supply that motion comes from slight variations in the tilt of the Earth’s rotation axis, so Kinetic Energy would be conserved, even with the “precessional acceleration up to the new precession rate”. However, Angular Momentum in the Plane of the Ecliptic would NOT be conserved! New Angular Momentum would constantly arise and disappear in that Plane. The AVERAGE of this is the actual observed velocity of the Precessional motion.
In fact, a “new Earth” would be no different than our current Earth, since our precessional motion (due to just the Sun) entirely STOPS twice every year! That significant amount of Kinetic Energy involved in the Earth’s precessional motion is CREATED and then CANCELLED OUT twice every year! The processed being discussed therefore involve significant energy transfers! These energy transfers occur because of the gravitational field of the Sun (and Moon).
In fact, since the precessional effects of various solar system bodies on each other are constantly CAUSING ACCELERATIONS AND DECELERATIONS in the precessional speeds, this necessarily indicates that the Earth and other planets are also doing a very slight tilt-axis dance that has always simply been considered a part of Solar Nutation! It is quite a small effect, but experimentally measurable!
The same effect occurs as planets perturb the orbits of other planets and satellites, sometimes also referred to as precession but more commonly called Regression of the Nodes. These effects are commonly presented as though they are constant effects, but they are NOT constant at all! As a perturbing planet varies from being above or below the orbital plane of a perturbed planet, it crosses that orbital plane twice in each synodic period. This causes the precessive effect to constantly be oscillating, from zero effect to a maximum, during the synodic period of the two bodies. This effect occurs for BOTH of the orbital motion and the rotational motion, and affects both bodies involved. This indicates that there must certainly CONSTANTLY be MANY small violations of Conservation of Angular Momentum occurring.
The effect described here is fairly small, and the cumulative effects are very slow. In all practical situations, Conservation of Angular Momentum will be seen to appear true. It is only where Euler’s equations transfer energy from one plane to another that any variances with that Conservation can occur. Conservation of Energy appears to still always be true.
If we consider that on March 21 of any year, the Earth has NO Precessive effect due to the Sun, we can easily calculate some things here. We first calculate how much kinetic energy there is in our AVERAGE precession. It is 1/2 * I * ω2. We know that the rotational inertia (I) of the earth is 8.07 * 1037 kg-meters2. We know that ω is one precessional revolution in 25,800 years or one radian in 1.296 * 1011 seconds. Therefore, the AVERAGE kinetic energy the Earth has in precessing is around 2.4 * 1015 joules. In planetary dynamics, that is not very much, but it still is kinetic energy that did not used to exist!
The AVERAGE kinetic energy of the precessional motion is that amount. However, we know that around Mar 21 and Sep 21 each year (considering only the Sun’s contribution) that amount is briefly zero, and arould Jun 21 and Dec 21, it is much greater than that average amount. Actually, since the Precessional MOTION is twice as fast at those instants, there was FOUR TIMES AS MUCH kinetic energy transferred.Note that this means that around 10 quadrillion joules of energy is ADDED to the Earth’s (Solar driven) Precessional motion in a three-month interval, and then the same amount is REMOVED from the Earth’s precessional motion in the following three months! This is a significant transfer of energy into and out of that motion, on a very regular basis! The Moment (torque) of this constantly fluctuating amount of Precessional Kinetic Energy is related to a slight axis tilt change of the Earth’s spin axis. The double Integration of the Euler Equations shows that the energy involved is always Conserved, but that it is simply transferred back and forth between a slight fluctuating tilt of the Earth’s rotation axis and the varying Precessional speeds.
Ten quadrillion joules might sound like a lot, but since it is spread out over a three-month interval, that is about an average of 1,250,000 kiloWatts (because a watt is a joule/second). That might not be worth the bother regarding trying to build any equipment to try to capture it! But it gets WAY better!
In addition, similar calculations show that around 40 quadrillion joules of energy is ADDED TO the Earth’s (Lunar driven) precession in about a WEEK, and then the same amount is removed during the following week! Many people have noticed and measured the very small-scale wobbling that the Earth does (collectively called Nutation) but I have never seen that anyone has realized that it was actually (primarily) due to a side effect of the constantly varying Precessional effect.
It might be noted that the energy transfer due to the Moon’s effect here is relatively significant from a human perspective! There is about 40 quadrillion joules transferred in a period of about one week (or 637,000 seconds) which means that an average power transfer of that quotient is occurring, or about 63 billion joules/second or 63 billion watts or 63 million KiloWatts! That 63,000 Megawatts is comparable to the entire output of electric power from ALL US nuclear generating plants! But I do not see how it could ever be captured by anything that we humans could ever do! Maybe some human far smarter than me can see some way to capture that energy, and we would then have an enormous supply of power, essentially forever!
The puny little Moon causes this effect around 50 times greater than the enormously massive Sun does! Interesting!
More significantly, each time when the Precession Effect is non-zero, there is Angular Momentum that did not used to exist! This fact means that one of the two pre-conditions that Laplace, LaGrange and everyone else have always applied is often (slightly) invalid. In short-term motions or perturbations, these effects are not seen, as they are comparatively small amounts of energy and angular momentum involved, and Angular Momentum appears to be conserved. However, over very long periods of time, these effects of continuously modifying small amounts of “new” angular momentum ALLOWS planets to mutually alter their semi-major axes! (Which is currently assumed impossible.) This then allows some very slow perturbation effects that are so small that they have not been yet detected (or understood). However, they certainly occur, because there is extensive evidence of near-commensurability in orbits of planets, satellites, asteroids, ring particles, and more. These are therefore not mere coincidences, but the very long-term effects of this new category of mutual perturbations where the semi-major axes are altered. Again, the Hamiltonian remains true, and Energy is Conserved, but slight changes in Angular Momentum certainly occur.
We have known for thousands of years that the Moon causes and creates spectacular amounts of energy that exist in the Oceans’ Tides (every day). We know that this is due to some gravitational effects of the Moon on the Earth and on the waters of the oceans. Here, we are discussing a DIFFERENT gravitational effect of the Moon on the Earth, which is actually due to the Earth having an Equatorial Bulge so that a Precessional motion can be caused on the Earth by the Moon.