An analysis of galaxial forms and motions.

Revolution Rates Within Galaxies 10/19/06

Why are constant rotation rates observed for galaxies when a slower revolution of outer vs inner planets occurs in the solar system? The bottom line of this extended explanation is that the revolution pattern of individual bodies has to do with relative size. In galaxies the orbitals are stars that are similar to each other while in the solar system we have the large central body sun and relatively tiny orbiting planets. There is much internal orbiting going on in Galaxies.

I personally view orbital systems from a perspective in which the central bodies net gravitational effect on it’s orbitals is to both attract and also to push orbiting bodies along in their orbits. I define pushing gravity particles which penetrate the central body, escape the opposite side of that gravitating body, incur angular motion from that body’s spin and apply that ‘now angular pressure’ to orbitals which the gravity subsequently encounters. So, if I reference bodies pushing each other it simply refers to the obvious requirement that adjacent bodies must be in motion relative to each other. However you view gravity, the underlying issue is that 2 adjacent bodies in space must move relative to each other or gravity will pull them together to collide/crash. Gravity likewise keeps them from departing each other, so the motions must be some form of orbiting.

Consider 2 equal sized bodies, call them stars. For them to coexist nearby they must be moving or revolving relative to each other. Revolution and rotation here will always be assumed counterclockwise. The bodies then orbit each other. An outside observer would observe their motion along the circumference of the circle of their joint orbiting as having a continuous velocity.

Next consider 3 equal sized bodies along a line with 1 and 3 equidistant from 2. So, 1 and 2 would try to orbit each other and while 1 would pretty much succeed, 2 would be affected by the outside influence of 3. In fact 2 and 3 try to orbit each other and while 3 pretty much succeeds, 2 is interfered with by 1. Essentially 1 and 3 motivate 2 to orbit in exactly opposite directions. So, 2 ends up being stationary while 1 and 3 revolve around it. The lesser influence of 1 and 3 on each other motivate them to revolve around each other essentially enhancing their joint revolutions around 2. This coincides with my model where bodies cause both revolution and rotation in others via gravitation. As such, body 2 gains rotation/spin, which now is double the rotation of the other two bodies. This rotation defines an increased density for body 2, so conveniently it acts a bit like a central body. The appearance of this system to an outside observer is very much the same as the 2 body system above.

As an aside, the galaxy picture is somewhat like the sun, earth. moon system where 2 bodies orbit the circumference in approximately equal periods due to mutual gravitation. At the same time the galaxy picture differs from the solar system which essentially pictures one central body causing the gravitating.

The four equal sized bodies system gets much more complex. With 2 bodies there was 1 interaction. With 3 bodies there are 3 interactions. With 4 bodies there are 6 interactions.
To picture this, place the 4 bodies along a line drawn vertically on a page, at distance marks 1,2,3, and 4 with 1 at the top end of the line. It isn’t clear which interaction to look at first, so analyze 1 vs 2 and 3 vs 4. Consider them to represent 2 clocks, where 1 is 12 o’clock and 2 is 6 o’clock on clock 1, while 3 is 12 o’clock and 4 is 6 o’clock on clock 2. Then 1 is being pushed left by 2 while 4 is pushed right by 3. Bodies 2 and 3 are influenced from both sides and their motion is less clear. When 1 reaches a point I’ll call 11 o’clock, 4 reaches 5 o’clock on his clock. Because 2 and 3 influence each other while being influenced by their clock mates, they move less than 1 digit on their clock. They move so little that now 2 might be at 5:50 while 3 is at 11:50. A complicating concern is that having moved so little from the line, their lack of revolution relative to each other might cause gravity to pull them together a bit. But we need not fear as somehow the original speeds, distances and sizes are just right to prohibit a catastrophic collapse.

Following the revolutions onward, I suggest next time locations for bodies 1,2,3,and4 might be 10 o’clock, 5:30, 11:30, and 4 o’clock. Then comes 9,5,11, and 3 o’clock. The bodies are far off the original line with the 1,2 clock to the left of the line while the 3,4 clock is right of the line. Note, there is always an equal balance relative to the original center point. Given approximately another time period and the 4 spheres now appear to serve as the corners of a rectangle. The distances and motions now cause the clocks to separate a bit.

This is incomplete because we have only inspected the originally stronger interactions. We will ignore1 acting with 3, 2 acting with 4 nor 1 acting with 4. Overall, the flow of separations should keep the average size of the system unchanged. Also the system shows a relatively consistent velocity along it’s circumference to outside observers. There are extra gravitation effects near the inner system which are conveniently absorbed by an increase in the spin/rotation of the inner spheres.

The 5 body system has 10 interactions. A quick inspection seems to imply it is similar to the 4 body system with body 3 now acquiring the features of a central body. Body 3 replaces the space that was between 2 and 4 and was at distance 2.5. It gains spin as did body 2 in the 3 body example. I conclude any odd number system has a central body around which all other bodies revolve.

The 6 body system presents complications similar to the 4 body system, but here, the 7 body problem is more interesting. In that system, body 2 acts partly as a center to 1 and 3 while 6 acts partly as a center to 5 and 7. We can denote them as subsystems and then analyze the other function of 2 and 6 which is to orbit around 4. In this process, body 2 brings 1 and 3 with it, however in inconsistent patterns of forward and backward motions relative to the central body.

As we add more bodies, the back and forth motions are less distinguishable than is the overall forward orbiting of all the bodies around the center. But, if we could look closely enough at galaxies we should detect second and maybe third levels of subordinate orbiting centers somewhat distant from the galaxy center.

In summary, the motivation for providing these constructions is the theoretical violation of Newton’s law by the orbiting in constellations. Newton said that bodies further from the central body will orbit more slowly than those closer to the center. The structure discussed above does not violate that law The law is visibly apparent in our solar system where planet 1 and planet 2 both orbit the sun and the more distant one takes longer to complete an orbit. These planets essentially do not coincidentally orbit each other.

Our galaxy example suggests that every body/star over the long term is the same ‘average’ distance from the galaxial center. Most will move in and out and back and forth in suborbits, but their average distance must all be the same. Thus over the long term they will all take the same average time to orbit the center. Newton’s law accepts that objects at the same ‘average’ distance take the same average time to orbit.

Our system must be orbiting around other star groups within the galaxy besides the center itself. We should maybe find those group centers. Since the environment within the galaxy may differ depending on distance from center, it is possible the most likely regions for other civilizations is out on galaxial arms the same distance from center as we are.


Paul Schroeder








paul schroeder

Revolution Rates Continued. 10/20/06

As a follow up to the ideas introduced in ‘Revolution Rates Within Galaxies”, I realized there are certain issues that need modification and others that should be expanded to fully explain galaxies. The following improvement issues are covered here:


1. The net motions of all stars which are revolving relative to each other are analyzed here leading to the creation of spiral arms, domes and other features.
2. Proximity concerns as the revolving stars approach other stars.
3. Minor open issues.


1. The first significant modification issue has to do with subsystems and net motions of suns. As my example expanded the number of bodies, to 7 for instance, the analysis led to thinking about 1 and 3 orbiting 2 and 5 and 7 orbiting 6. So then 2 and 6 were suborbital centers. But if you just consider bodies 2,3,and 4 for example then 3 looks like an orbital center. As you keep adding bodies, you can chose any one to view as a center. The better picture is that they are all orbital centers while all orbiting the galaxial center. Given 100 bodies in line on the north and on the south of center, something like body 7 from center on the north line has a line of bodies both to the north and to the south that wish to orbit it and also wish to push it into orbit. The pushes by the north line bodies on body 7 north, are in the opposite direction as the pushes by the southern line bodies. The difference is that there are more total bodies to the south so they will win in the long term. They will force 7 to revolve clockwise around center. By comparison, they will force body 14 north to revolve even faster because of the greater south vs north imbalance it experiences. Likewise body 1 north will revolve slower than any other northern body. So, the better overall picture is of a line revolving, rather than well placed suborbitals.

The actual rotation of the line depends on the separation of the bodies along the line. If we accept my original design with bodies equally spaced, then the farther out the body the more it wants to orbit around it’s neighbors. It’s proper motion will exceed the closer in bodies. The greater the proper motion the faster outer orbits will occur which causes the arms to wrap toward center like octopus arms. This suggests the idea that the outer bodies wrap towards the inside ultimately causing the inner bodies to wrap around them and the whole system warps internally. There is then a vortex, which is something like the suborbitals, but not focused on a particular body.

The proof of this rotating system, requires examples. Again consider a line of many star bodies numbered 1 - 100 equally spaced north of the center body as we move north. Let’s have body 1 caused to rotate 1 degree left from the line, and thus relative to the central body 0. It would take a long time for this to happen since there are almost as many bodies to body1's north as to it’s south. But, ultimately it will revolve this far, and bring with it to the new angle all other northern bodies. Now body 2 has been moved over by body 0 so that it is off the line by 1 degree. But we haven’t considered the revolution caused on body 2 by body 1. Body 1 is almost like body 0 and thus creates a revolution in body 2. Again the revolution forces are nearly offset, north to south, so the net revolution is small. However, body1 is more offset from center, so the revolution caused by body 1 on body 2 must be slightly more than the revolution caused on body 1 by body 0. Thus body 2 is now offset by 2 degrees, or slightly more, from straight north and from the new north point of body 1.

As we continue out the line of bodies, the degree of offset increases and soon reaches 90 degrees. Their motions have become perpendicular to the original line. By then we have something like the spiral arm of the galaxy. Note that the arm extends outward into the direction of motion of the galaxial rotation. This direction is an issue that Meta readers and others have been unable to fathom. It occurs naturally from the logical geometry of the system.

All of these reorientations have occurred within a single time unit. With more bodies originally located on the line, or upon considering more time units, we get even higher angles of the revolutions relative to the original line, such as 180 degrees to 270 degrees. So that the arm ultimately spirals in on itself. We must question whether a revolving sun crosses the connection between the two suns prior in the line or whether the whole spiral converges into a new center. I believe that outer stars such as star 100 will incline and cross the connection between stars 99 and 98. If they cross then each will intersect it’s next lower body in a cascading effect. The continuation of this pattern will allow a new line to be created in different sequence from the original.

In the example above I assumed a constant increase in the angle of displacement as we focus further outward. There may in fact be a more exponential increase since there is less resistance in the more distant regions of the original line. Then fewer stars would be required to produce spiral arms approaching the 90 degree angle.

2. The other important modification addresses my downplaying concern with stability of the system by saying the original speeds, distances, and sizes are just right to prohibit collapse. There is more to it. The issue is best seen in the 7 body construction where bodies 3 and 5 orbit body 4 and now approach something like their start position in line. The problem is that body 5 for example has more gravitating bodies to one side than to the opposite side. It might then tend to gravitate toward the ‘heavier’ side. My first thought was that on the original line there are so many bodies in both directions that these points are simply like their own centers and have essentially a balance to each side. That is not sufficient to avoid future collisions.

Now reconsider the 7 body example when body 5 (or 7) approaches the region between bodies 4 and 6. For ease of explanation, I refer back to my concept that central bodies ‘push’ orbitals along in their orbits via gravity which has been modified by central body spin/rotation. So, body 6 pushes body 5 counterclockwise but as body 5 encounters the system of body 4, it’s spin will tend to counter the motion of body 5. Body 4 spins counterclockwise relative to us outside observers, but when body 5 is nearby, body 4's spin theoretically acts to push body 5 backward in it’s orbit around body 6. Bodies 4 and 5 are now temporarily moving retrograde relative to each other. My model suggests tidal ripples form in the gravitation field between bodies 4 and 6. As such the ripples interfere with the passage of body 5. Body 5 must, and is forced to, travel above or below the tidal action, bringing the 3rd dimension into consideration for the motions within the galaxy.

In my model the gravitation of a central spinning body is partly caused by it’s spin. The gravitation is maximum along the extension of the central body’s equator and less as the latitude angle increases. So body 5 drifts up or down when passing near body 4, and does so sufficiently to decrease the gravitation from 4. It’s orbit around body 6 is therefore inclined. We see here a universal reason why orbitals follow paths inclined relative to the equatorial plane during their orbit. Similar reasoning extends to moons crossing equatorial planes as well as to planets crossing the ecliptic. To fully understand solar system cases we need to determine the location and motion of a secondary center of gravitation caused by the forces outside our solar system.

There is a region near the galaxy center where much activity occurs above and below the plane of the galaxy which appears as a dome to us. Essentially the inclination I have mentioned needs to be more extreme as bodies are closer to the extra high gravitating center. The higher the angle, relative to the center body, the less gravitation it exerts upon the body. In other words it is necessary for nearby bodies, ever closer to the central body, to travel into ever increasing latitudes of the central body. This follows my model of gravitation as presented for the sun. The sun’s rotation provides gravitational support to bodies along it’s equator more than it does in other directions, and the greater the latitude, the less the support.

In our example, as more and more bodies are visualized near the center of the galaxy, there is increasing inclination to the orbits to avoid the tidal action of many bodies passing through the region. More of their orbits must incline and the closer in toward the center the body, the greater the angle of inclination that is required. For this reason there is 3rd dimensional build up called a dome around the center, and to a lesser extent near other suborbital centers within the galaxy.

The passage of systems between adjacent systems and the inclination of systems near other systems suggests a period of difficult balancing of the overall system. The stars don’t collide but their appendages might. It is especially difficult in the outer regions of solar systems where suborbitals such as planets my incur masses from an encroaching system.

One can also view the ’near center’ situation in the other direction. Consider lines of bodies extending from the central body like we have been doing, however, now angling somewhat above or below the galactic plane. The same analysis given for planar bodies can be applied to bodies in these lines except that the length of the line must be less because the central body gravitation force is less in that direction. The length of the line is dependent upon the angle of inclination because the central body provides less gravitation as the latitude angle increases. Less spin is applied to the gravity particles.

3. Moving on to lesser issues, my construction was initiated with bodies in line, which is not necessarily an actual relationship between bodies. As the system progresses the bodies move offline, and there is no absolute reason to believe they will ever regain this initial relationship. It is only in theory that, by the impossible task of backing up the system that the linear relationship might ever be found.

My construction has bodies initially equally spaced. What happens if the separations vary? An example would be to assume bodies at locations 1, 2, and 4. Then you could picture 1 and 2 orbiting each other with center at location 1.5. But body 4 confuses the picture by orbiting 1, 2, and their center. The new center, if one exists must be outside of 1 and 2, such as at 2.1. But gravitationally the imbalance seems to make it impossible. However if we add a body at 5, then we have a balanced system centered at location 3. So occasional missing pieces is allowed without collapsing the system. Additionally my concept of gravitation as the medium provides the potential of system self adjustment to compensate for local disturbing events.

My original construction assumed all bodies being of the same size. In reality there are, and must be, variations due to the role spin plays in determining density and therefore in determining mass. Given there were one denser body, it would have some of the ‘regular’ bodies orbiting it and would carry them with it around the center. The only apparent requirement is that there be a similar such body on the other side of the galaxy to balance the system rotation.

As soon as we consider multiple subsystems, we have interference between them causing gravitational effects by “pulling’ on each other. While we try to discuss circular orbits within systems, the variations of pulling by a nearby system causes the internal orbits to become oblong/elliptical, rather than circular. Such interaction ultimately leads to the nature of the second focus of an ellipse as being a virtual center. Then the reason the orbital motion is slower in the vicinity of the second focus is that it provides none of the orbital push that the central body does.


Paul Schroeder




paul schroeder

The reason galatic motion does not conform to the model is because the model is wrong for the galatic structure. The model is based on an assumption that works well for structures like the solar system where nearly all the mass of the structure is at or near the center of the structure. The galatic disk has mass that is spread out all over the space within the disk. Its a totally different structure and needs a different model than what is being used to figure the motion.

Jim, 10-23-06

I very much appreciate getting your response to my submissions. Now to see if I can understand well enough to make a meaningful response.

1. When you refer to the model being wrong, I assume that is a mathematical model possibly one based on assuming the kinetic energy should be half the gravitational binding energy in galaxies. But the kinetic energy is found to be too high. You mention that the galactic disk has mass spread throughout making it a totally different structure than the solar system. Therefore the model is wrong and a new model is needed.

2. The difference between the galaxy and solar system you mention are main features of the geometric models I presented. I think I have accurately defined the motion causes and effects. However they are not in a mathematical model.

3. I read that galactic rotation curves showing velocity of rotation relative to the distance from galactic center cant be explained by visible matter. I assume this means a shortage of kinetic energy and will address it as so. There are 2 sources of kinetic energy, rotation and revolution.
Any time you add rotation to a system by adding another sun, it serves as the source of revolution motion for nearby existing suns. This should be understandable whether you have gravity particles participating in the rotations or in current theory with waves, possibly called density waves causing the angular motion and thus the kinetic energy. Essentially then adding mass adds kinetic energy, it doesn’t matter where the mass is added so distance from the galaxy center doesn’t matter .

4. An issue that stars far from the center of galaxies have much higher velocities than predicted indicates current theories depend on the center to provide the velocities and ignore the velocity sources spread across the galaxy.

5. Perhaps the real question is where does all the kinetic energy/velocity of motion come from in galaxies. The answer is available in my gravitation model and in all pushing gravity theories. There is an unlimited reservoir of potential energy within space itself. It consists of particles that move in all directions netting out to zero in any void place in space. Thus we don’t detect the potential energy. However when a mass is inserted it blocks some of the gravitation so for another mass nearby there is less pressure in one direction. Thus it creates a directional energy field in which any other local body will react with motion/kinetic energy. Overall it is simply the ‘net directional energy’ that has changed, not total energy. There is so much potential energy available in space that multiplying the number of bodies in a galaxy would hardly make a dent. The limiting component is being able to keep all motions from interacting with collisions.

6. A mathematical model to predict motions would tend to vary for each star and would require looking at all nearby gravitation sources as well as considering the galaxy center.

Paul Schroeder


paul schroeder

In point 3 above, I meant to say 'I assume this means a shortage of potential energy (and thus an excess of kinetic energy).

Paul

paul schroeder

The thing is Kepler's law is used by modelers for both the solar system and the galatic disk. The problem is Kepler's law requires the mass to be centered at a point. This works well for the solar system because most of the mass is centered at the sun which is a point more or less. In a galaxy the mass is not centered at the center of the galaxy but is distributed throughout the disk. So, you have a structure that does not behave in a manner that the solar system does. Using Kepler's law and assuming the galatic disk will move in the same way the solar system does(that is as if the center is the focus of motion)gets the wrong result. The motion of the galaxy is different than the motion of the solar system simply because the mass is not centered at a point in a galatic disk.