Three-body problem and WMAP

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

See:The Gravity Landscape and Lagrange Points



Now there is a reason that I am showing "this connection" so that the jokes that go around at the PI institute in regards to Tegmark( not that I am speaking for him and have absolutely no affiliation of any kind) and the "mathematical constructs are recognized" beyond just the jeering section, that while not being a party too, will and can be shown some light.

Three-body problem

For n ≥ 3 very little is known about the n-body problem. The case n = 3 was most studied, for many results can be generalised to larger n. The first attempts to understand the 3-body problem were quantitative, aiming at finding explicit solutions.

* In 1767 Euler found the collinear periodic orbits, in which three bodies of any masses move such that they oscillate along a rotation line.
* In 1772 Lagrange discovered some periodic solutions which lie at the vertices of a rotating equilateral triangle that shrinks and expands periodically. Those solutions led to the study of central configurations , for which \ddot q=kq for some constant k>0 .

The three-body problem is much more complicated; its solution can be chaotic. A major study of the Earth-Moon-Sun system was undertaken by Charles-Eugène Delaunay, who published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. Among many other accomplishments, the work already hints at chaos, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory.
The chaotic movement of 3 interacting particles
The chaotic movement of 3 interacting particles

The restricted three-body problem assumes that the mass of one of the bodies is negligible; the circular restricted three-body problem is the special case in which two of the bodies are in circular orbits (approximated by the Sun-Earth-Moon system and many others). For a discussion of the case where the negligible body is a satellite of the body of lesser mass, see Hill sphere; for binary systems, see Roche lobe; for another stable system, see Lagrangian point.

The restricted problem (both circular and elliptical) was worked on extensively by many famous mathematicians and physicists, notably Lagrange in the 18th century and Poincaré at the end of the 19th century. Poincaré's work on the restricted three-body problem was the foundation of deterministic chaos theory. In the circular problem, there exist five equilibrium points. Three are collinear with the masses (in the rotating frame) and are unstable. The remaining two are located on the third vertex of both equilateral triangles of which the two bodies are the first and second vertices. This may be easier to visualize if one considers the more massive body (e.g., Sun) to be "stationary" in space, and the less massive body (e.g., Jupiter) to orbit around it, with the equilibrium points maintaining the 60 degree-spacing ahead of and behind the less massive body in its orbit (although in reality neither of the bodies is truly stationary; they both orbit the center of mass of the whole system). For sufficiently small mass ratio of the primaries, these triangular equilibrium points are stable, such that (nearly) massless particles will orbit about these points as they orbit around the larger primary (Sun). The five equilibrium points of the circular problem are known as the Lagrange points.

So the thing is, that while one may not of found an anomalousness version of what is written into the pattern of WMAP( some Alien signal perhaps in a dimension of space that results in star manipulation), and what comes out, or how string theory plays this idea that some formulation exists in it's over calculated version of mathematical decor.

String Theory

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.

Bold was added by me for emphasis. See also:Angels and Demons on a Pinhead

This is/was to be part of the hopes of people in research for a long time. I have seen it before, in terms of orbitals(the analogical version of the event in the cosmos) and how such events could gave been portrayed in those same locations in space. Contribute, to the larger and global distinction of what the universe is actually doing. If it's speeding up, what exactly does this mean, and what should we be looking for from what is being contributed to the "global perspective" of WMAP from these locations??

But lets move on here okay.

If you understand the "three body problem" and being on my own, and seeing things other then what people reveal in the reports that they write, how it is possible for a lone researcher like me to come up with the same ideas about the universe having some kind of geometrical inclination?

You would have to know that "such accidents while in privy to data before us all", and what is written into the calculations by hand would reveal? Well, I never did have that information. What I did know is what Sean Carroll presented of the Lopsided Universe for consideration. This coincided nicely with my work to comprehend Poincaré in a historical sense. The relationship with Klein.

As mentioned before, at the time, I was doing my own reading on Poincaré and of course I had followed the work of Tegmark and John Baez's expose' on what the shape of the universe shall look like. This is recorded throughout my bloggery here for the checking.

What I want to say.

Given the mathematics with which one sees the universe and however this mathematical constructs reveals of nature, nature always existed. What was shown is that the discovery of the mathematics made it possible to understand something beautiful about nature. So in a sense the mathematics was always there, we just did not recognize it.:)

Levitation Energy: What is it?

You must know, that contrary to what is understood of levitation, I have a view on this that cannot be said less then in complete wonderment, knowing full well the aspects of what science is stating. "I know" with all of sciences tools, there "is" something we do not understand. It would then be assigned to a Metaphysical description here falls short of the scientific definition.

I preserver still, given the circumstance of my youth, and the direction it pushed my life in terms of scientific study and philosophical determinations. What are one's motivation underpinnings with self and we find the course of life can be set to a degree?

ASSESSING POTENTIAL PROPULSION BREAKTHROUGHS
Marc G. Millis
NASA John H. Glenn Research Center at Lewis Field
21000 Brookpark Rd., MS 86-2
Cleveland, OH 44135-3191

Levitation is an excellent challenge to illustrate how contemplating breakthrough propulsion is different from contemplating rocketry. Rockets can hover, but not for very long before they run out of propellant. For an ideal breakthrough, some form of indefinite levitation is desirable, but there is no clear way how to represent the energy or power to perform this feat. Since physics defines work (energy) as the product of force acting over distance, no work is performed if there is no change in distance. Levitation means hovering with no change in height. Regardless, there are a variety of ways to toy with the notion of energy and power for indefinite levitation. A few of these approaches are listed in the next session. For now, only one approach is illustrated, specifically the nullification of gravitational potential.

An object in a gravitational field has the following defined value for its gravitational potential energy:



Equation 11

(11)

Usually this definition is used to compare energy differences between two relatively short differences in height ( r) but in our situation we are considering this potential energy in the more absolute sense. This same equation for potential energy can also be derived by calculating how much energy it would take to completely remove the object from the gravitational field, as if moving it to infinity. This is more in line with the analogy to nullify the effect of gravitational energy. This is also the same amount of energy that is required to stop an object at the levitation height ( r) if it were falling in from infinity with an initial velocity of zero.

Using this equation, it could conceivably require 62 mega-Joules to levitate 1-kg near the Earth's surface. This is roughly twice as much as putting 1-kg into low Earth orbit. Again, these assessments are strictly for illustrative purposes rather than suggesting that such breakthroughs are achievable or if they would even take this form if achievable. Some starting point for comparisons is needed, and this is just one version.

See: Breakthrough Propulsion Physics?

The elephant and the event horizon by Amanda Gefter

Hawking radiation owes its existence to the weirdness of the quantum world, in which pairs of virtual particles pop up out of empty space, annihilate each other and disappear. Around a black hole, virtual particles and anti-particles can be separated by the event horizon. Unable to annihilate, they become real. The properties of each pair are linked, or entangled. What happens to one affects the other, even if one is inside the black hole.

See here for article.



Given "thought experiments" sometimes it is necessary to understand the close relation with which entanglement issue, an elephant that falls into a blackhole, and a elephant that resides on the horizon, we look to explain what "measurement may mean" as we look at the entanglement.

All of physics as we know it is conditioned on the fact that information is conserved, even if it's badly scrambled," Susskind says.

So I ask, is there a way to see "mirror symmetry" as a viable aspect of the entanglement, while we look ever deeper into the blackhole for what can be expected/measured? Information, never lost?

How can one not look at space with such regard and understand that the geometrical tendencies while presenting them in coordinated space, can give a dynamical quality to what was never apparent before. Spacetime, takes on a whole new meaning. Moves the Gaussian coordinates to the realm of "abstract thinking in non euclidean , and presents new aspects for consideration that was previously dismissed and thought arrogant in relation to string theory.

Now, I am no way saying that what is being written here is to be compared, on the basis of the many mathematical insights portrayed in the development of string theory. I have hoped to touch this aspect of "dynamical thinking" at the microscopic level and at the same time, spoken to a macroscopic understandings well.

The Future of the Quantum Mechanical View


Gerard 't Hooft-Professor Theoretical Physics

Quantum gravity and black holes. Whenever particles are separated further than 10-^33cm, the gravitational force between them is very adequately described by Einstein's theory of general relativity. But when they come closer, the gravitational force becomes strong, whereas gravity is more complicated than gauge theories. Finding a logically coherent theory telling us how particles behave at such small distance scales is a fundamental problem. The most dazzling problem is the question whether these particles will make microscopic black holes. Predicting the behavior of such tiny black holes is a deep theoretical challenge. Or maybe they can't form black holes? Formulating laws of physics that avoid black hole formation is even more difficult.

How fit and comparative the mind to think that it's journey in the imaginations could travel space as we know it on so many levels? Microscopic tendencies to see reality in it's makeup could have been compared to the "powers of ten."

Gravitational Mass for a Photon

The relativistic energy expression attributes a mass to any energetic particle, and for the photon



The gravitational potential energy is then



When the photon escapes the gravity field, it will have a different frequency




Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.

Escape Energy for Photon

If the gravitational potential energy of the photon is exactly equal to the photon energy then



Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole."

For more see "Time as a measure.


Special Lagrangian geometry

Dr. Mark Haskins

Special Lagrangian geometry in particular was seen to be related to another String Theory inspired phenomenon, "Mirror Symmetry". Strominger, Yau and Zaslow conjectured that mirror symmetry could be explained by studying moduli spaces arising from special Lagrangian geometry.

How many of the good scientists can say this themself, that no matter what, with all the avenues of propulsion systems talked about, all the aspects of satellite deployment, where are there such places, that we set our sight on with the habitation of space(L5)? Does it hold to the thinking mind, that we would talk about such comparisons for consideration first? How is it then we should look at space?



So we understand not only the travels of satellites, but the place and tunnels through which they travel through in that space.

See:

Entanglement and the New Physics

LTool

A "freeway" through the solar system resembling a vast array of virtual winding tunnels and conduits around the Sun and planets, as envisioned by an engineer at NASA's Jet Propulsion Laboratory (JPL), Pasadena, Calif., can slash the amount of fuel needed for future space missions. Called the Interplanetary Superhighway, the system was conceived by Martin Lo, whose software was used to help design the flight path for NASA's Genesis mission, which is currently using this "freeway in space" on its mission to collect solar wind particles for return to Earth. Most missions are designed to take advantage of the way gravity pulls on a spacecraft when it swings by a body such as a planet or moon. Lo's concept takes advantage of another factor, the Sun's pull on the planets or a planet's pull on its nearby moons. Forces from many directions nearly cancel each other out, leaving paths through the gravity fields in which spacecraft can travel.

Minature Satellites in Space

KC-135 Flight Experiments

The Reduced Gravity Program at NASA's Johnson Space Center provides the unique "weightless" or "zero-g" environment of space flight using a specially modified KC-135A. The KC flies parabolic arcs to produce weightless periods of 20 to 25 seconds. This capability is ideal for the development and verification of space hardware, experiments, crew training and basic research.

Flight tests of the SPHERES testbed onboard NASA's KC-135 accomplished two objectives: (1) establish the functionality of testbed systems and subsystems and (2) perform limited formation flight experiments. Flight experiments were conducted over two separate weeks in early 2000, once in mid-February and again in late March. The time between flights was used to refine operations protocols, improve testbed systems, and develop more complicated experiments using lessons learned from the first week of flights.

There is a always a history to such developments and to me not ever knowing of this process about the spheres, I find it very satisfying to have some "correlation of cognition."

Synchronized Position Hold, Engage, Reorient Experimental Satellites


The MIT Space Systems Laboratory developed the SPHERES (Synchronized Position Hold Engage and Reorient Experimental Satellites) laboratory environment to provide DARPA, NASA, and other researchers with a long term, replenishable, and upgradable testbed for the validation of high risk metrology, control, and autonomy technologies for use in formation flight and autnomous docking, rendezvous and reconfiguration algorithms. These technologies are critical to the operation of distributed satellite and docking missions such as Terrestrial Planet Finder and Orbital Express.



Most would not understand the significance of this posting.

For me it is the correlation of insight that I had in a dream sometime ago, about my future. Most would not of thought that we would be capable as human beings to have this ability, to be able to project people we will become, to a people who are working in relation to what is developing and was developed in this post.

In my dream I am releasing a satellite, a Christmas tree design one without all the bells and lights.

The Gravity Landscape and Lagrange Points

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

There is a deep seated need to look beyond ourselves. We tend to look up in space, while there is this greater vision that lies even beyond what we are so used to in our everyday lives.


(Larry Niven's Ringworld, seen from space. Artwork by Harry Frank

Ringworld is a Hugo and Nebula award-winning 1970 science fiction novel by Larry Niven, set in his Known Space universe. The work is widely considered one of the classics of science fiction literature. It is followed by three sequels, and it ties in to numerous other books in the Known Space universe.

.

Our view of space and living beyond the confines of Earth, is lived over in the minds of those who have struggled within science to make these travels possible.

Imagine that first look at the blue planet. How glorious this view, while here we mere mortals look at what those take for granted as they now use the machines they created to visit new planets.

L4 and L5

The L4 and L5 points lie at 60 degrees ahead of and behind Earth in its orbit as seen from the Sun. Unlike the other Lagrange points, L4 and L5 are resistant to gravitational perturbations. Because of this stability, objects tend to accumulate in these points, such as dust and some asteroid-type objects.

A spacecraft at L1, L2, or L3 is ‘meta-stable’, like a ball sitting on top of a hill. A little push or bump and it starts moving away. A spacecraft at one of these points has to use frequent rocket firings or other means to remain in the same place. Orbits around these points are called 'halo orbits'.

But at L4 or L5, a spacecraft is truly stable, like a ball in a bowl: when gently pushed away, it orbits the Lagrange point without drifting farther and farther, and without the need of frequent rocket firings. The Sun's pull causes any object in the L4 and L5 locations to ‘orbit’ the Lagrange point in an 89-day cycle. These positions have been studied as possible sites for artificial space stations in the distant future.

I draw you attention too,"ball sitting on top of a hill" in the previous article. One should get the idea right away, that what was revealed in the possibilities of the landscape, could have correspondences in how we look at the universe in it's gravitational considerations.



Who would have known that such "orbital tendencies" which would have seem so chaotic, could have let one seen Lissajous's by design. You might think of Lorentz's butterfly flapping it's wings, yet such probabilities are held "to a spot" that is a result of placement within the very nature of the landscape of the gravitational cosmos.

So would you have wondered, "if we considered "E8" as a dimensional attribute of such probabilities "by design in such a place" what would this place look like? Would you have selecedt the probability of this resulting ball to falling in the respective valley as a, moduli form?

Home on Lagrange (The L5 Song)

Oh, give me a locus where the gravitons focus
Where the three-body problem is solved,
Where the microwaves play down at three degrees K,
And the cold virus never evolved. (chorus)
We eat algea pie, our vacuum is high,
Our ball bearings are perfectly round.
Our horizon is curved, our warheads are MIRVed,
And a kilogram weighs half a pound. (chorus)
If we run out of space for our burgeoning race
No more Lebensraum left for the Mensch
When we're ready to start, we can take Mars apart,
If we just find a big enough wrench. (chorus)
I'm sick of this place, it's just McDonald's in space,
And living up here is a bore.
Tell the shiggies, "Don't cry," they can kiss me goodbye
'Cause I'm moving next week to L4! (chorus)

CHORUS: Home, home on LaGrange,
Where the space debris always collects,
We possess, so it seems, two of Man's greatest dreams:
Solar power and zero-gee sex.
--Home on Lagrange (The L5 Song) © 1978 by William S. Higgins and Barry D. Gehm

Lagrange points

As always, the pictures serve as links, as well as highlighted paragraphs in blue, and having once visited, purple. Pictures and paragraphs that are highlighted in gold are in conjunction and are direct links to sites, as well as fawcetts, within this blog. The neurolgical funcxtion of imagery was designed this way and I would encurgae wikipedia to use this idea in the images that they use. I suspect server updates reduce links back to them, which is retarded since all apragraph staements can be assigned to them quite easily.

This is the advancement in imagery use that mental powers had to keep pace with in computer developement. We know streaming video is quite useful, so why not the neurological fucntioning of "the image" that your minds can produce, that connect as these highlighted paragraphs can do?



These ideas make sense when you understand the effects of gravitational variances, and can see, what the effect of a fifth dimensional perspective can do. I think the writer understood what I was saying in article that follows?

Figure 2 shows a map of the gravity field of the Sun-Earth restricted three body problem. The contours show that the steepest gradients surround the Earth and Sun, with the five Earth Lagrange Points located in equilibrium regions with relatively gentle gradient. L1-L3 are unstable saddle points, and spacecraft positioned here will always drift away from the equilibrium. L4 and L5 are stable equilibria, and objects can orbit here indefinitely. The blue arrows show that L4 and L5 are actually atop a potential hill - it is the additional effect of the "Coriolis force" that makes them stable.
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This newly found Interplanetary Superhighway is a perfect example of the overlap between classic analysis and modern numerical techniques. The genius minds of Euler and Lagrange used the new technique of calculus to solve the restricted three body problem and show the existence of these intriguing equilibrium points in space. Now, 200 years later, we are employing our own ground-breaking methods using dynamical systems theory and supercomputers, and taking our first steps along the invisible tunnels stretching through the solar system

If one didn't understand this application from a fifth dimensional perspective how would "this viewer" made any sense?



Such develoepments and perspective allow other views to develope in relation to how we see this planet, beyond the bubble enclosures one might have developed and culminates in this Thalean view.:)

This all leads to the developement of the Thalean view It is mathematically orientated although I have much to learn, I made use of a developing perspective that few would have realized, had they not put these things together. That's what I try to do, anyway.

Genesis Spacecraft uses Tubes as Freeways

Without someview that would be consistent through out the cosmo, how would such points be of value? Did we not see this variation could exist when you travelled to another location, given higher dimensional comprehenisons? In order for this view to be scalable it had to have begun in some other way, that we could sufficely say that it was strong once and all pervasive, but now?

There are reasons for this story to be thought abou,t and here after seeing the greater challenge of gravitational consideration in terms of how we percieve Earth's relationship with the sun and moon. Now why did we not see the significance of gravitational considerations bring to us views of the cosmos before now? Consider space travel in light of these tubes?


LOOP-DE-LOOP. The Genesis spacecraft's superhighway path took it to the Earth-sun gravitational-equilibrium point L1, where it made five "halo" orbits before swinging around L2 and heading home.Ross

In the 18th century, European mathematicians Leonhard Euler and Joseph-Louis Lagrange discovered that in this rotating frame there are five gravitational sweet spots, now called Lagrange points. At these equilibrium points, the competing pulls on the third body balance each other, and the body remains motionless.

by Douglas L. Smith

A set of five of these balance points, called Lagrange or libration points, exist between every pair of massive bodies—the sun and its planets, the planets and their moons, and so on. Joseph-Louis Lagrange (1736–1813) discovered the existence of the two points now known as L4 and L5, each of which is located in the orbital plane at the third vertex of an equilateral triangle with, say, Earth at one vertex and the moon at the other. So L4 is 60° in advance of the moon, and L5 60° behind it. Ideally, a spacecraft at L4 or L5 will remain there indefinitely because when it falls off the cusp, the Coriolis effect—which makes it hard for you to walk on a moving merry-go-round—will swirl it into a long-lived orbit around that point. Comet debris and other space junk tends to collect there, and Jupiter has accumulated an impressive set of asteroids that way.