OC406: Vortexes & Spin Gravity

David Noel
Ben Franklin Centre for Theoretical Research
PO Box 27, Subiaco, WA 6008, Australia.

This is Number 6 in a suite of web articles about the Oort Cloud, the volume of space immediately outside our Solar System.

About vortexes
The type specimens for vortexes are the whirlpools or maelstroms sometimes found in the sea or other water bodies. But the vortexes most familiar to us are the swirls produced in the water when the plug is pulled in a bath or sink.

Fig. OC406-F1. Water swirling down the plughole. From [F1].

Why should these vortexes form, why doesn't the water just run straight down the hole? It's to do with the nature of vortexes. Here we'll just list a couple of important property of these objects.

Proposition OCF-P1. Nature finds that vortexes are an efficient way to move and store energy and mass.

Proposition OCF-P2. Vortexes suck.

So, why does the water swirl? Popular explanations go on about the Coriolis Effect, but although this effect is very important when it comes to weather patterns, it doesn't apply to small items like sink flows -- even if your house is on the Equator, where the Coriolis Effect is zero, your sink-water will still swirl down the hole.

When the water is in the sink, it represents a potential energy situation, as the water is above the plug. Pull the plug, and this potential energy is converted to energy of motion, most of it in the downward movement of the water. But a little is converted into spin, into forming a vortex. This is one aspect of will later be called "Spin Gravity".

If this phenomenon occurs with water, does it also apply with other situations, such as with a metal ball falling under gravity? One of the earliest known investigators of gravity was the Italian astronomer, physicist, and engineer Galileo Galilei, who lived from 1564 to 1642. He has been called the "father of observational astronomy", the "father of modern physics", the "father of the scientific method", and the "father of modern science" [F3].

Fig. OC406-F2. Galileo Galilei. Portrait by Tintoretto. From [F3].

Between 1589 and 1592, Galileo is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.

Fig. OC406-F3. Galileo and the Tower of Pisa experiment. From [F2].

Galileo was a polymath. He studied speed and velocity, gravity and free fall, the principle of relativity, inertia, and projectile motion. He also worked in applied science and technology, describing the properties of pendulums and "hydrostatic balances", inventing the thermoscope and various military compasses, and used the telescope for scientific observations of celestial objects. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, the observation of Saturn's rings, and the analysis of sunspots [F3]. He was accused of heresy by the Catholic Church for some of his descriptions of natural phenomena, and was held under house arrest for the later part of his life.

So, if water tends to twist as it falls under gravity, do metal balls also tend to twist when falling under gravity? I have been unable to find evidence of experiments testing this proposition, though it shouldn't be hard to set these up.

Weather vortexes
Weather vortexes form an essential part of the Earth's energy cycle, by which heat and light are received from the Sun (preferentially in the Tropics), and this energy is then distributed over the rest of the Planet's surface, before being radiated off into space (this topic was looked at in OC405).

The larger of these vortexes are usually called Cyclones, weaker examples may be called Atmospheric Pressure Lows. They can pack immense power and cause devastation over vast areas, since the outer edges of the vortexes show up as strong and hurricane-force winds.

Fig. OC406-F4. 2013 Cyclone Rusty over Western Australia. From [F5].

Tornados are smaller forms of weather vortexes, usually funnel-shaped and less than 1 km across, and often coming almost to a point at ground level. According to Wikipedia [F8], "A tornado is a rapidly rotating column of air that is in contact with both the surface of the Earth and a cloud. Tornados come in many shapes and sizes, and they are often visible in the form of a condensation funnel originating from the base of a cumulonimbus cloud, with a cloud of rotating debris and dust beneath it. Most tornados have wind speeds less than 180 km/h, are about 80 m across, and travel a few kilometres before dissipating. The most extreme tornados can attain wind speeds of more than 480 km/h, are more than 3 km in diameter, and may stay on the ground for more than 100 km".

Fig. OC406-F5. 2007 tornado near Elie, Manitoba. From [F8].

Tornados are most commonly met with in a strip of the United States going north from the Gulf of Mexico, popularly called "Tornado Alley", although similar vortexes, with a variety of names such as water-spouts, dust-devils, and willy-willies, occur elsewhere in the World.

Fig. OC406-F6. Tornado Alley, USA. From [F6].

Formation of tornados appears to depend on a favourable set of weather conditions, and may also depend on regional topography. They may be immensely destructive on the smaller scale, sometimes cutting avenues of destruction though the landscape.

Practical measures for countering the effects of tornados have not been widely researched. One analysis, Killing Tornados -- How To Stop A Twister [F7], contains two possibly novel suggestions -- that it might be possible to build artificial tornados of opposite polarity and merge these with natural ones so they neutralize each other, and that such artificial tornados could be a source of power.

Solar Systems
There is a useful concept for illustrating how the planets orbit with respect to the Sun, and other similar situations, called the Gravity Well. It takes the plane of the planets, and represents it like a wide flat rubber sheet.

Fig. OC406-F7. Earth and Mars in the Sun's gravity well. From [F10].

The heaviest object, the Sun, is thought of as heavy ball placed on the sheet, where it depresses the sheet in a large dimple, its Gravity Well. A planet is thought of as a lighter ball, travelling in a circle round the Sun, where it forms a small circular trough in the sheet. Because of the centrifugal force of its orbit, the planet continues to travel in the trough, rather than fall into the Sun.

The same situation can be looked at as a cross-section across a gravity well. The well can be for a solar system, a planet and its satellites (natural or artificial), or other similar assembly of cosmic objects.

Fig. OC406-F8. Earth's gravity well. From [F11].

Figure F8 shows a typical funnel-shaped gravity-well cross-section for the Earth. The vertical axis shows potential energy -- objects higher up the well, more distant from the surface, have higher potential energy. The dotted line at the top is the energy of Escape Velocity -- an object needs to be moving at higher than escape velocity if is to leave the Earth area permanently.

The lower blue line is for a satellite in Low Earth Orbit, only a few hundred kilometres above the surface. The higher blue line is for an object in geosynchronous orbit, an orbit about 36,000 km above the equator (where satellites appear motionless), much used for communication satellites. If our Moon was to be shown on this diagram, it would appear as a smaller funnel off to the right on the red line, at about 380 thousand kilometres, when the red line was still nearing escape velocity.

Similar funnel-shaped gravity-well cross-sections can be drawn for all the planets, as in Figure F9.

Fig. OC406-F9. The planets in the Sun's gravity well. From [F11].

The Gravity Well scenario is a useful one to give a visual grasp of the situation, but there are things to bear in mind. The graphics are 2-dimensional representations of a 3-dimensional situation, but the Wells don't have a particular location in space -- for the Solar System, any point on the whole of the surface of the Heliosphere could be thought of a gravity-well position.

Both Figure F7 and F9 also show the path of a comet (or any other solid object entering the Solar System from outside). Treating the System as a slowly-rotating funnel vortex, what happens to a comet or the like depends on its path and its velocity, which themselves depend on the comet's origin and what objects in the Oort Cloud it has previously encountered.

Many so-called "long-period" comets swoop in at high velocities and on highly eccentric paths. They will dip into the funnel, getting nearer to the Sun, but their impetus or velocity will carry them up the side of the funnel again and over the Rim of the Sun's escape velocity envelope (as where the red line in Figure F8 finally touches the dotted line). These objects will be one-time only visitors to the Solar System.

Less common entrants to the Solar System may come in with lower velocities, or on their paths they may interact gravitationally with some of the planets or asteroids. Sometimes they will not have enough impetus to get over the gravity well Rim, and will be permanently captured within the System.

This does reflect a property of vortexes noted above -- Vortexes Suck. As with the Maelstrom, which sucks ships and people down into its depths, vortexes tend to hold on to chance visitors and integrate them, in so doing themselves increasing in size. Only the most agile visitors will escape being captured, and the vortex will spontaneously give nothing up.

In this way, solar-system vortexes slowly increase their size by capturing occasional bodies which fall prey to their gravity, and planet-moon systems do likewise. This tendency is fostered by Equatorial Forcing, which slowly brings random objects orbiting a central large mass down into its equatorial plane, so the closer objects are more liable to gravity bringing them together.

This process explains why the satellites of larger planets like Jupiter and Saturn, each with about 80 known moons, are such a mixed bag as regards their masses, orbits, and constituent natures -- they defy any general theory of origin. Instead, they are just the trophies of a collection which has gone on over a few billion years.

For our Solar System, there is more detail on these process in P4: The Greater Averaged Universe (GAU): How the Solar System cannibalizes the Oort Cloud [F12].

Galaxies as vortexes
Galaxies are often beautiful and obvious examples of vortexes. One of these is the Whirlpool Galaxy, about 23 million light-years from Earth, and visible with binoculars under good conditions. Believed similar in general appearance and structure to our Milky Way galaxy, it is classed as a spiral galaxy. It is about 75,000 light years across, three-quarters the size of the Milky Way.

Fig. OC406-F10. M51A, the Whirlpool Galaxy. From [F13].

Its mass is estimated to be that of 160 million Suns, and like all spiral galaxies, it has an AGN or Supermassive Black Hole at its centre. Just like other celestial objects, galaxies are born, evolve, and eventually die. The AGN is responsible for the disk- or flying-saucer-shape of the galaxy, and is another example of Equatorial Forcing -- the AGN is rotating extremely rapidly and its Spin Gravity is reaching out to stars and solar systems some 38,000 light years out.

Being vortexes, galaxies seek to suck in stars and other objects from their surroundings, and achieve growth. This growth is countered by the mass and energy emitted from its Vortex Beams. So a spiral galaxy will grow and maintains its size as long as it can reach new objects within its region of Oort Space, but will eventually have exhausted available new resources and pumped much of its mass/energy out through its vortex beams -- this process may form the basis of a new, globular galaxy.

In the case of a medium-size galaxy like the Milky Way, the birth-evolve-death cycle has been calculated at about 20 billion years. Galaxy recycling forms part of the mechanisms by which the Universe maintains very-large-scale uniformity in perpetuity while its internal processes each have their own life cycles. There is more detail on this in UG101: Recycling the Universe -- Neutron Stars, Black Holes, and the Science of Stuff [F14].

Atoms as vortexes
Nowadays we are accustomed to think of atoms in what was originally called the Bohr Model -- with a central dense nucleus containing protons and neutrons, surrounded by a diffuse cloud of electrons. This model was developed in 1913 by the Danish physicist Niels Bohr. who described the simplest atom, Hydrogen. This contains only a single proton at its nucleus, accompanied by a single electron -- the Proton-Electron Model.

There are other models of the atom which can be described, based on different principles. One such is the Spindle-Vortex Model, which treats the atom as a vortex (Reference [F15]). This also uses a different way of looking at Mass.

The scientific equation which is best known to the general public is the Einstein Equation, E=mc2. It says that Energy and Mass are inter-related, so that if is a Mass "m" is converted into energy, the amount of this energy can be calculated by multiplying the Mass by the square of the speed of light, "c".

The conversion also works the other way, giving the amount of energy needed to create a given mass. Processes operating in this direction are seldom encountered, though they are active when AGNs (supermassive black holes) put out mass/energy they have accumulated in Vortex Beams, which contain particles as well as light.

Another way of looking at the situation is to say Mass and Energy are equivalent, merely different ways of naming the same thing. There is some familiarity with this concept, as when Light can be treated in two apparently exclusive ways at the same time -- sometimes saying Light is made up of Waves (energy), sometimes Photons (particles). This is quite allowable in science -- if there are 2 models of Light, either may be used to suit the circumstances,

So with atoms. The Proton-Electron Model treats atoms as containing Mass, the Spindle-Vortex Model treats them as containing Energy, in the form of rapidly-rotating vortexes. Take, for example, a Copper atom, as in Figure F11 following. It is represented as a rapidly-rotating ball. The figure is one frame from an animated GIF -- the animations can be seen in action in BS802: GEMMA -- The Spindle Vortex Model for Gravity, Energy, Matter, Magnetism, Antimatter. [F15].

Fig. OC406-F11. Copper atom in the Spindle Vortex Model. From [F15].

The same source also has a Simulator, one snapshot from which is shown in Figure F12. At the top is a Slider Bar which can can be dragged back and forth to simulate different rotation rates (equivalent to masses) for a sample range of atoms.

Fig. OC406-F12. Still from the Spindle Vortex Atom simulator. From [F15].

When the Slider is on the left of the scale, it shows a Hydrogen atom, which has a VRN (Vortex Rotation Number) of 1, and an AW (Atomic Weight) of 1 also. Moving it 7 places to the right brings up Copper, with a VRN of 8 and a AW of 64. This vortex rotates, in the animation, at 8 times the rate of the Hydrogen atom. Because the energy of a rotating body varies as the square of its rate of rotation, in the Spindle-Vortex Model, AW is equal to VRN squared.

Just as, in the Proton-Electron Model, only certain atomic weights (AWs) are allowed in nature, so in the Spindle-Vortex Model only certain VRNs are met with -- these may be fractional, the Simulator shows the nearest isotope to a whole-number VRN.

In some things, the Proton-Electron Model gives a more intuitive picture, thinking of the atomic nucleus as containing various numbers of black balls called Neutrons, and red balls called Protons, of very similar but not identical weight. But in others, the Spindle-Vortex Model is superior. One of these is the representation of how an atom emits a photon.

Fig. OC406-F13. Spindle Vortex atom emitting a photon. From [F15].

Reference [F15] also has an animation of an atom emitting a photon. It shows 2 photons, of opposite polarity, being emitted along the 2 axes of the spindle. An additional feature, which need not have any physical tie-up with what's happens in reality, is that incoming radiation energy gathers on, and swells up, the surface of the vortex, until at a given threshold, emission occurs.

The Spindle Vortex Model also gives interesting physical bases for a number of scientific phenomena, including Gravity (vortexes suck), Magnetism (misaligned vortex vectors), and Antimatter (vortexes rotating in opposite directions).

There is a parallel between how an atom emits photons along its axes, and how a Vortex Star emits radiation, and sometimes matter, as Vortex Beams along its axes. There is also a parallel between the magnitude (mass) of an item being a consequence of its rotational energy, and the magnitude (mass) of a Vortex Star also ultimately stemming from its rotational energy. This does provide an explanation of where the "Mass" may lie in Black Holes.

Matter in Neutron Stars is highly compressed, similar to that of the atomic nucleus alone, and that in Black Holes is thought of as even more compressed, by many orders of magnitudes, though its nature has only been speculated on. A nice comparison is that the Earth, mostly ordinary matter, has a diameter of about 12,700 kilometres. Calculations show that if the Earth was made entirely of the matter in Neutron Stars, its diameter would be about 330 metres. And if it was made entirely of black-hole substance, it would have a diameter of about 3 centimetres.

Conventional physics does not really have a suggestion on the nature of black-hole material. The models presented here suggest that the "Mass" of Black Holes is contained in their vortex rotational energy. There is more background to this in UG101: Recycling the Universe -- Neutron Stars, Black Holes, and the Science of Stuff [F14].

The representation of atoms as rotating balls in the Spindle Vortex Model is done purely for convenience in simulating their rotation, it is not suggested that they are necessarily spherical, nor that they have a solid internal axis. Figure F14 following shows another representation, more like a spinning children's top, which may be a closer parallel to a Spindle Vortex.

Fig. OC406-F14. Another concept of a Spindle Vortex. From [F17].

Is the Spindle Vortex Model new?
Surprisingly, the idea that atoms are vortexes is far older than the concept that they consist of tiny charged balls. Even Lucretius, who is supposed to have originated the concept of the atom in the first century BC, thought that "they are in perpetual motion at enormous speed" [F15]. And the Scottish physicist Lord Kelvin, who is remembered in the Kelvin scale of temperature, published several articles in which atoms were treated as vortexes.

But the real surprise comes from right back at the dawn of modern science, in 1644, from the French polymath Rene Descartes. In that year, the scientist, mathematician, and philosopher (after whom Cartesian Geometry is named) came up with a description of matter and space entitled "Aether vortices around celestial bodies", in which he postulated that matter consisted of vortexes.

Fig. OC406-F15. Rene Descartes. From [F16].

Even more surprising, he claimed that the vortexes were the source of Gravity. This was actually before Isaac Newton published his comprehensive theory of gravity in 1687, though the concept of gravity had been talked of before then. In a description of Descartes' work it was noted that "Due to centrifugal force, matter tends towards the outer edges of the vortex, which causes a condensation of this matter there ... this inward pressure is nothing else than gravity" [F15].

Vortexes as energy stores -- the Kilogram Power Wheel
The idea of storing energy in a rotating device, a "Flywheel", is not new. It was used in antiquity in the Potters Wheel, and a mechanical flywheel was used for water raising by the agronomist Ibn Bassal in Moorish Spain, as far back as the AD 1000s [F20].

In more modern times, mechanical flywheels have been used to power vehicles -- in Switzerland, flywheel-equipped buses without motors were used in the 1940s [F18]. They were able to boost their flywheels through electric points at passenger stops, and could travel as much as 6 km between charges.

Flywheels may have a promising future for domestic and industrial energy storage, possibly replacing electric-battery devices such as Tesla's PowerWall. A detailed proposal is in DS903: The KPW (Kilogram Power Wheel): A domestic power storage device replacing batteries [F18]. This envisages using one or two KPW devices, about the dimensions of a record player, for buffering household electricity usage. The KPW would use a magnetically-suspended flywheel in an evacuated casing (making it frictionless) to do the same job as the more bulky and expensive PowerWall.

In a possible further development, the KPW's flywheel would be replaced by a Torus -- a ring-doughnut shaped body, essentially a flywheel with a hole instead of an axle, made possible because the rotating part was magnetically suspended. It might look something like Figure F16.

Fig. OC406-F16. A notional Kilogram Power Torus. From [F19].

This illustration is actually of a Tokomak, a nuclear-fusion device. In the KPT, the purple torus would be the rapidly-rotating object storing the rotational energy.

Mass Gravity and Spin Gravity
In a recent poll of scientists on "Who was the greatest scientist to have ever lived?" the top position was gained by Isaac Newton [F22]. Among the many things that Newton is famed for, formulation of the Laws Of Gravity stands out. So much of modern science has these Laws as part of their foundation.

Fig. OC406-F16. Isaac Newton. From [F22].

Newton gave us the famous formula for calculating the force of attraction between two bodies, for example the gravitational attraction between the Earth and the Sun. Here is the formula.

Fig. OC406-F17. Newton's formula for the force of gravity. From [F23].

The formula says that the gravitational force between two bodies is found by multiplying their masses together and dividing the result by the square of their distance apart. It also includes a constant "G" (the Gravitational Constant) which depends on the units used for mass and distance.

For ordinary things (things not travelling at close to light-speed), such as the gravitational attraction between Earth and the Sun, the formula gives an exact answer. But if you want to know how things got to how they are now, it is not the full answer.

Newton's law of gravitational attraction, which we might call Mass Gravity, defines the current situation with two bodies. But it does not tell you how, or why, they got to that position. For that, we need to look at another aspect of gravity, which we can call Spin Gravity.

We have seen that the current orbits of the Planets have been modified by a gravitational force which has been called Equatorial Forcing. In Equatorial Forcing, a massive central rotating body exerts a force which seeks to make nearby bodies modify their motions to match the plane of rotation and direction of rotation of the central body. This force appears to depend on the mass of the central body and the distance of separation.

Equatorial Forcing may be regarded as a particular case of Spin Gravity, for the action of a massive central body on smaller bodies in orbit about it. Let's attempt to generalize the situation by formally specifying the interaction between any two rotating bodies.

Proposition OCF-P3. Under Spin Gravity, two bodies each seek to to make the other conform with their own rate, vector, and direction of rotation, and the forces involved are proportional to their masses and inversely proportional to the square of their separation distance..

Newton and the comets
Isaac Newton's ideas were most accessible through two major books which he published, and it is interesting to note the differences in the approaches of these two books, and how these approaches correlate with publishing today.

The first book, Philosophiæ Naturalis Principia Mathematica, was written in Latin, and first published in 1687. The Latin title means "Mathematical Principles of Natural Philosophy", and the work is usually referred to as Newton's "Principia". It included all his discoveries in mathematics (such as calculus) his Laws of Gravitation, and the application of these laws to the Solar System and elsewhere.

The Principia is what we would regard today as an "Academic Book", intended for an informed and specialist audience. It was written in Latin, because that was then the international language of science, and so was readily accessible to experts in Germany, France, Italy, and elsewhere in the World.

The second book, Opticks, was quite different in nature -- although it contained many far-reaching new concepts, it was what we would regard today as "Popular Science" (as is the article you are now reading). With the full title Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light, it was written in English. It contains details of many simple experiments, with prisms, lenses, and the like, which any interested reader could try and and confirm for themselves. The first edition of Opticks was published in 1707. It was very popular among the general public, and several later editions followed .

This popular book was crammed with simple explanations of a host of natural phenomena, but in later editions, Newton also included notes on things he had not been able to explain, not just in optics, but in the world at large. In the 1740 edition of Opticks [F25], Newton brought up the subject of the orbits of planets and of comets, and why they were different in nature. He said "Whence is it that Planets move all one and the same way in Orbs concentrick, while Comets move all manner of ways in Orbs very excentrick?" [F21].

His spelling is a little old-fashioned these days, but what he was asking was why all the Planets have almost circular orbits in the same plane, while comets come in on orbits which are quite random to this plane, and very eccentric (non-circular). We saw earlier how comets mostly originate in the Oort Cloud, the sphere of bodies outside the Heliosphere (for an illustration, see Figure F1 in OC401).

Fig. OC406-F18. Graph of inclinations of comet orbits. From [F24].

Figure F18 show inclinations of the orbits of comets according to the distances they reach from the Sun. The horizontal scale, marked "Semi-major axis", shows the maximum distance comets reach from the Sun in their orbits. Blue dots represent comets which orbit entirely within the Heliosphere (100 AU) -- most have orbits inclined at from 0 to 30 degrees to the plane of the Planets.

The red dots represent comets which have visited the Solar System, but travel on highly eccentric orbits mostly in the Oort Cloud, some going out as much as 100,000 AU -- a thousand times the distance of the Heliosphere. These comets have random inclinations of their orbits to the planetary plane. (Inclinations of greater than 90 degrees means "retrograde" orbits, circling the Sun in the opposite sense to the planets).

Newton's question, unresolved for some 300 years, now has an answer. It wasn't explicable with the Mass Gravity which he described, but is explained by Spin Gravity -- Equatorial Forcing has brought the planets down towards the Sun's equatorial plane, while the more distant comets have had very little taste of the Sun's gravitational power.

Spin Gravity theory and usage
Spin Gravity, as outlined above, does not appear to have accumulated much in the way of theoretical backing or mathematical analysis. One aspect which has found practical use, is in the use of Gravity Assist [F9] to modify the trajectories of space probes.

The principle behind Gravity Assist is that if you enable a space probe to fly past a planet or large moon, the Probe's energy of momentum can be increased or decreased, or its trajectory angle modified, by inserting the probe into a specific path vis-a-vis the Planet's rotation.

Say you just want to increase the velocity of a probe. You set up its approach to the planet so that it comes in at a specific height above the planet's equator, in the same plane as the equator, and in the same direction of rotation. Normally the planet will be rotating at a faster rate than the probe's flypast, so the Spin Gravity principle means that the planet will transfer a tiny amount of its momentum to the probe. Because the masses of the Probe and the Planet are so different, this will have a large effect on the Probe, while the effect on the Planet will be completely negligible.

Fig. OC406-F19. The trajectories that enabled NASA's twin Voyager spacecraft to tour the four giant planets and achieve velocity to escape the Solar System. From [F9].

Gravity Assist was used with both of the Voyager space probes to let them "tour the planets" on their way out of the Solar System -- both have now passed the boundary and are moving in the Oort Cloud. The manoeuvres greatly increased the amount of information which could be gathered.

Fig. OC406-F20. Plot of Voyager 2's heliocentric velocity against its distance from the Sun, illustrating the use of gravity assist to accelerate the spacecraft by Jupiter, Saturn and Uranus. From [F9].

Gravity Assist can also be used to decrease a Probe's momentum, or change the angle of its trajectory. To observe Neptune's moon Triton, Voyager 2 passed over Neptune's north pole, resulting in an acceleration out of the plane of the ecliptic and reduced velocity away from the Sun. Using successive encounters with Jupiter, Saturn, Uranus, and Neptune, Voyager was not only able to observe these planets close up, but also to build up enough energy, above the Sun's escape velocity, to be able to leave the Solar System completely.

Orbital Resonance in the Solar System
There is an occurrence in the orbits of Solar System bodies which is not explained by Mass Gravity, called Orbital Resonance. In Orbital Resonance, the times to complete orbits of two bodies lie in a simple whole-number relationship, for example the time it takes Pluto to complete 2 orbits is almost exactly the time it takes Neptune to complete 3 orbits [F27]. This can be called Pluto:Neptune 2:3 resonance.

Another example is the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and a further case involves the moons of Pluto.

Fig. OC406-F21. Diagram of the orbits of Pluto's small outer four moons, which follow a 3:4:5:6 sequence of near resonances relative to the period of its large inner satellite Charon. From [F27].

Pluto and its innermost satellite, Charon, actually form a double dwarf planet, since their centre of gravity does not lie within the larger body, but between the two. Four smaller moons orbit around this joint centre of gravity, as in Figure F21, These four outer moons follow a 3:4:5:6 sequence of near resonance with the inner moon Charon.

The point here is, that the positions of these planets and satellites conform exactly with the laws of Mass Gravity, but the latter does not explain how their orbits came to be amended to produce Orbital Resonance. An explanation requires the use of Spin Gravity theory.

Spin Gravity is governing the fate of Pluto and its moons in two quite opposite ways. First, it preserves them by setting up Pluto:Neptune 2:3 resonance, which means that although on occasions Pluto actually comes closer to the Sun than Neptune does, it does so only when Neptune is at the opposite side of the Sun, distant from a gravitational clash. Eventually, however, Spin Gravity will bring Pluto's orbit down closer into the planetary plane, when Neptune is likely to capture the lot as six extra moons.

Movement of Moons away from their Planets
A final example of a situation where Spin Gravity lore is needed is in considering the movements of moons away from their parent planets. Earth's Moon is slowly moving away from us, as its average distance increases each year by about 38 millimetres. We know this, because the Apollo astronauts placed a mirror on the Moon's surface facing toward Earth, so its distance at any time can be determined by firing a beam of laser light towards this mirror, and timing how it takes for the reflection to return to Earth.

Recession of the Moon from the Earth is usually put down to an effect of Tides sapping energy from the Earth, and there is a body of mathematics dealing with tidal theory. But the idea that tides are created by the Sun drawing water in the oceans towards it does not sit easily with intuition -- it explains tides rising at a spot on the Earth's surface during the day, when the spot is facing the Sun, but not them rising on the opposite side of the Earth, at a place facing away from the Sun.

Nevertheless, tidal theory mathematics, even if not wholly applicable, can be used to give useful information in considering planet-moon relationships. Darin Ragozzine has investigated recession in the tiny and unusual moons of Mars -- Deimos and Phobos [F26].

Deimos has an orbital period of 30.3 hours, Phobos 7.6 hours, while Mars itself rotates in 24.63 hours, so Phobos's orbit round Mars is completed more quickly than the planet itself rotates. As Mars has a similar orientation in space as the Earth, this means that Phobos rises in the West and sets in the East, while Deimos follows the normal pattern.

Among the results of this analysis, it states "Because tides dissipate energy and conserve angular momentum, it can be shown that they transfer angular momentum from faster spinning objects to slower spinning objects. This results in the decay of subsynchronous orbits (like Phobos) and growth of supersynchronous orbits (like Deimos), while all retrograde orbits decay. Phobos is decaying by roughly 2 cm/year, while Deimos hardly changes position over the age of the solar system" [F26].

The decay of retrograde orbits (ones which turn in the opposite sense to the norm) may have relevance to the fact that the innermost Planets, Mercury and Venus, have no moons and turn very slowly, while Earth and Mars rotate briskly in the standard direction, and each has moons. If Mercury and Venus had retrograde motion when coming under the Sun's influence, Spin Gravity would soon counter their innate rotation, while any satellites they had captured would quickly fall to their surface.

The Final Puzzle
The two natural satellites of Mars are the subject of one of the strangest puzzles in scientific history. Small, irregular lumps of rock -- even the biggest, Phobos, is less than 14 km long on its largest axis -- both of them are smaller than Rottnest. Both are close in to the planet, Phobos so close that it goes round Mars in under 8 hours, less than Mars' 25-hour day, and so it rises in the West and sets in the East. These are very unusual objects [F28].

These tiny, close-in moons were not discovered till 1877, when they were picked up by the American astronomer Asaph Hall. Such a late discovery can be understood, the satellites' small size and closeness to the planet making them undetectable until telescopes were improved enough. How, then, can we explain the relatively accurate description of these two satellites, given in Jonathon Swift's "Gulliver's Travels", published more than 150 years previously, in 1726?

Although nowadays regarded as a children's book, "Gulliver's Travels" was, in fact, a bitter political satire on the society of Swift's times. In the third voyage, Gulliver describes the island of Laputa, inhabited by scientists and able to float in the air, its position controlled by a giant natural magnet. The island is described in some detail -- its thickness (300 yards), its area (10,000 acres).

Fig. OC406-F22. Early "Laputa: Castle in the Sky" concept art, inspired by "The Tower of Babel" by Pieter Brueghel the Elder. From [F29].

Gulliver notes that the astronomers of Laputa had much better telescopes than those known in Swift's day, and that "they have likewise discovered two lesser stars, or satellites, which revolve about Mars; whereof the innermost is distant from the centre of the primary planet exactly three of his diameters, and the outermost, five; the former revolves in the space of ten hours, and the latter in twenty-one and a half".

It seems quite beyond the bounds of chance for these very unusual objects to have been predicted, so accurately and so far ahead of time, almost as an aside in a satirical novel. If Isaac Newton was unable to solve the puzzle about comet orbits, the puzzle about Gulliver and the Moons of Mars is one which, so far, has proved beyond me.

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References and Links

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[F5]. Preparations underway as cyclone Rusty intensifies. https://www.abc.net.au/news/2013-02-25/preparations-underway-as-cyclone-intensifies/4537702 .
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[F16]. René Descartes. https://en.wikipedia.org/wiki/René_Descartes .
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[F19] A schematic tokamak. https://www.researchgate.net/publication/262364216 .
[F20] Flywheel. https://en.wikipedia.org/wiki/Flywheel .
[F21] David Noel. P3: Living In The Universe. http://aoi.com.au/Living/ .
[F22]. Sir Isaac Newton. https://www.youtube.com/watch?v=UjUxRE_TiZc .
[F23]. Newton's Law of Universal Gravitation Poster). https://www.redbubble.com/people/allhistory/works/23180049-newtons-law-of-universal-gravitation?p=poster .
[F24]. David Noel. P1: The Cosmic Smog model for solar system formation, and the nature of 'Dark Matter'. http://aoi.com.au/bcw1/Cosmic/index.htm .
[F25]. Isaac Newton. Opticks. Fourth edition, 1730. Facsimile edition, Dover Books, 1952.
[F26]. Darin Ragozzine. Why do moons move away from or approach their primaries?. http://assets.zombal.com/7f59e7d3/TidalEquations.pdf .
[F27]. Orbital resonance. https://en.wikipedia.org/wiki/Orbital_resonance .
[F28]. David Noel. The Moon and the Planets [NU015]. http://aoi.com.au/NUSite/NU015.htm .
[F29]. Laputa: Castle in the Sky. https://www.reddit.com/r/ghibli/comments/b7mfdn/early_laputa_castle_in_the_sky_concept_art_this/ .

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Version 1.0 published November 2019 as Segment F of the book "The Oort Cloud: Almost all the Universe". AOI Press, ISBN 9798614884314.
Version 2.0 placed on web at "AOI.com.au", 2022 Jun 28.