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Showing posts with label lagrangian. Show all posts
Showing posts with label lagrangian. Show all posts

Tuesday, February 19, 2013

Nightlights from Coast of Eastern US

ISS030-E-078095 (6 Feb. 2012) --- One of the Expedition 30 crew members aboard the International Space Station took this nighttime photograph of much of the eastern (Atlantic) coast of the United States. Large metropolitan areas and other easily recognizable sites from the Virginia/Maryland/Washington, D.C. area spanning almost to Rhode Island are visible in the scene. Boston is just out of frame at right. Long Island and the Greater Metropolitan area of New York City are visible in the lower right quadrant. Large cities in Pennsylvania (Philadelphia and Pittsburgh) are near center. Parts of two Russian vehicles parked at the orbital outpost are seen in left foreground.

Saturday, November 10, 2012

Artemis

Illustration of Artemis-P1 liberations orbits. Credit: NASA/Goddard

ARTEMIS-P1 is the first spacecraft to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. There are five Lagrangian points associated with the Earth-Moon system. The two points nearest the moon are of great interest for lunar exploration. These points are called L1 (located between the Earth and Moon) and L2 (located on the far side of the Moon from Earth), each about 61,300 km (38,100 miles) above the lunar surface. It takes about 14 to 15 days to complete one revolution about either the L1 or L2 point. These distinctive kidney-shaped orbits are dynamically unstable and require weekly monitoring from ground personnel. Orbit corrections to maintain stability are regularly performed using onboard thrusters.



Saturday, October 13, 2012

When You Look at the Cosmos......?


Scientists have turned up rare evidence that space-time is smooth as Einstein predicted, while pushing closer to a complete theory of gravity. From NASA Goddard Space Flight Center, Fermi Gamma Ray Space Telescope. See: SpaceRip.com




.....you might be enamored with how you might see the cosmos as I am.

The question of continuity of expression as some mathematical construct with out seeing the uniqueness of  lets say lensing....how might we associate with such dynamics of that continuity?

According to Einstein's theory of general relativity, the sun's gravity causes starlight to bend, shifting the apparent position of stars in the sky.


It's the way in which the Lagrangian expressions are understood or how satellite travel helps to denote the pathways throughout our universe. Are traverse pathways being suggested as we might see the holes in the cosmos as unique just to satellite travel alone? Ask yourself how the photon is influenced then? What pathways are traveled that we may see the evidence on the screen that such association measure in the spectrum are revealing of events across space and time.

Astronomers use the light-bending properties of gravity to view very distant galaxies--such as the arc shapes in this image--in a technique called "gravitational lensing.





This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel.




See Also:

Tuesday, June 26, 2012

Core Optics

A pair of polished Advanced LIGO end mirrors (ETM's)
Core optics are the 40-kg masses that form the heart of a LIGO detector. A core optic is manufactured from fused silica, polished to a few nanometers of smoothness and coated with dozens of layers of optical coatings. The result is a tuning of the balance of reflection and transmission of the mirror at the parts per million level. See: Advanced LIGO

Tuesday, March 06, 2012

Geodesy and geophysics


Mean Gravity Field



Anomalies by definition would require that we understand something about our selves that we did not know before, in that the whole history of you, is a large synopsis of everything that thinks and breath? Imagine indeed that such a vast resource could defined you as in some book to know that what would come next would be the unfolding of what you have been to what you shall become.

So I veered away from this act of who you are, toward a question of our relationship with understanding the world around us. What can exist in nature as some anomaly is really our inability to describe something in nature that awes us and had never gone deeper then then on the surface observance of who we are and where we live.


Map of free-air gravity anomalies around Britain and Ireland
Variations in the strength of gravity occur from place to place according to the density distribution of the rocks beneath the surface. Such gravity anomalies have been mapped across the British Isles and the surrounding seas and they reveal aspects of these islands’ geological structure.

(Bouguer) gravity anomaly map of the state of New Jersey (USGS)
 The Bouguer anomalies usually are negative in the mountains because of isostasy: the rock density of their roots is lower, compared with the surrounding earth's mantle. Typical anomalies in the Central Alps are −150 milligals (−1.5 mm/s²). Rather local anomalies are used in applied geophysics: if they are positive, this may indicate metallic ores. At scales between entire mountain ranges and ore bodies, Bouguer anomalies may indicate rock types. For example, the northeast-southwest trending high across central New Jersey (see figure) represents a graben of Triassic age largely filled with dense basalts. Salt domes are typically expressed in gravity maps as lows, because salt has a low density compared to the rocks the dome intrudes. Anomalies can help to distinguish sedimentary basins whose fill differs in density from that of the surrounding region - see Gravity Anomalies of Britain and Ireland for example.

Bouguer Anomaly Map of Belgium and Surrounding areas

The anomalies are calculated using a uniform Bouguer reduction density of 2.67 gr/cm3 the grid was obtained by Krigging, cell size : 5 km, search radius : 30 km. The French data are copyrighted by BRGM (France).

While the examples above help to shed light on how we can perceive earth in a way that we are not accustomed too, this idea of gravity is important to understand the way in which gravitationally we my look at the world/earth. In our early years abstractly the idea of curvature was something that did not make sense until one moved beyond the Euclidean lines of understanding to a Non Euclidean view?

To that point we did not understand what the earth look like in its pearl form in space without having left the confines of earth?

I want you too look at space as well to understand what may be conceivable even though we may talk about an anomaly in nature that to this point we did not necessarily understand until we were presented with the examples as to confront and require an explanation. So you have the earth and space to contend with here.

LTool


So we graduate with the understanding with how we have seen the earth in observatory implicitness to have it detailed in a more "ugly definition of its composed parts?" To me it's not really that ugly at all,  although as you venture to take in the color representation of the component parts of our earth's geological structure,  you learn to understand the concreteness of our definitions.

Sunday, January 24, 2010

Interplanetary Transport Network




This stylized depiction of the ITN is designed to show its (often convoluted) path through the solar system. The green ribbon represents one path from among the many that are mathematically possible along the surface of the darker green bounding tube. Locations where the ribbon changes direction abruptly represent trajectory changes at Lagrange points, while constricted areas represent locations where objects linger in temporary orbit around a point before continuing on




This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel.

Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions.

Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.


See:Interplanetary Superhighway Makes Space Travel Simpler
July 17 2002

Sunday, March 01, 2009

Gravity Wave Spectrum

PURPOSE: To show the two-dimensional standing waves on the surface of a square or circular plate.


Early perception of sound as analogy to the ideas of the WMAP background were forming in my mind when Wayne HU was demonstrating the image of polarizations in B mode. To me its as if one puts on a pair of glasses and based on an assumption of the gravitational waves, then one tends to see "all of it" in this Lagrangian way.



With the discovery of sound waves in the CMB, we have entered a new era of precision cosmology in which we can begin to talk with certainty about the origin of structure and the content of matter and energy in the universe.Polarization


This was the basis of how I was seeing the progression of Webber's experiments in using the aluminum bars in gravitational wave detection. It was also more then this that I came to the conclusion I did.

***


Sounding out the Big BangJun 1, 2007 by Craig J Hogan is in the departments of physics and astronomy at the University of Washington, Seattle, US.

Our view of the universe is about to change forever. Since science began, all our knowledge of what lies above, below and around us has come from long-familiar forms of energy: light, produced by distant astrophysical objects; and matter, in the form of particles such as cosmic rays. But we are now in a position to study the universe using an entirely different form of energy that until now has never been directly detected – gravitational waves.





Gravitational waves open up a new window on the universe that will allow us to probe events for which no electromagnetic signature exists. In the next few years, the ground-based interferometers GEO-600, LIGO, VIRGO and TAMA should be able to detect the high-frequency gravitational waves produced by extreme astrophysical objects, providing the first direct detection of these disturbances in space–time. With its much longer arm lengths, the space-based interferometer LISA will, if launched, be able to detect lower-frequency gravitational waves, possibly those generated by phase transitions in the early universe. At even lower frequencies, other experiments will look for tiny signatures of gravitational waves in the cosmic microwave background. Source: NASA.


The flow of energy in a cosmic phase transition is similar to that in a waterfall, with turbulence in the cosmic fluid generating a gravitational-wave background today.

***


Sound and fluidized interpretation seemed very close to me of the way in which such analogy would help us to look at the universe and the spaces in between cosmological locations, as if, in a three body problem relation.

The Origin of the Universe as Revealed Through the Polarization of the Cosmic Microwave Background submitted by Scott Dodelson Sun, 22 Feb 2009 14:27:37 GMT

Modern cosmology has sharpened questions posed for millennia about the origin of our cosmic habitat. The age-old questions have been transformed into two pressing issues primed for attack in the coming decade: How did the Universe begin? and What physical laws govern the Universe at the highest energies? The clearest window onto these questions is the pattern of polarization in the Cosmic Microwave Background (CMB), which is uniquely sensitive to primordial gravity waves. A detection of the special pattern produced by gravity waves would be not only an unprecedented discovery, but also a direct probe of physics at the earliest observable instants of our Universe. Experiments which map CMB polarization over the coming decade will lead us on our first steps towards answering these age-old questions.


***


See:
  • Sound Waves in the CMB
  • The Sound of the Landscape
  • Distinctions of Holographical Sound
  • B Field Manifestations
  • Friday, October 03, 2008

    Centroids

    Conclusion:The state of mind of the observer plays a crucial role in the perception of time.Einstein


    It is often I consider the Center of Gravity(Mass) as an illustration of the perspective that exists "around and within us" as a product of the natural world. We are limited by our own knowledge, yet when given, and lead to observation of what is natural in our world, we see where we had not seen before.

    \bar z = \frac{\int z dm}{m}The center of gravity (or mass), abbreviated as COM, of any object is that point within the object upon which gravity (or any body force) acts, regardless of the orientation of the object. The COM of an object may be calculated by using the principle of equilibrium.


    First off you must know that I work according to a set of principles that were discovered after a time through "subjective reflection" on the nature of mind and how it works. Of course I am no expert here, but the principles themself are realizable as an active function in the recognition of how one might interpret the world.

    \bar y = \frac{\int y \rho dV}{\int \rho dV}In the event that the density ρ of an object is not uniform throughout, the calculation of COM may be done by a similar set of equations involving the addition of density to the analysis.


    It is by taking one to recognisance of the title of this blog entry that I wanted to discuss the "subjective part" and the understanding of the "mathematical construct" that one, in my opinion exists. Just as we progress to understand the natural world around us, I believe these are synonymous with each other.

    \bar Y = \frac{\sum m \bar y}{\sum m}If a body is made up of multiple sections, each of which has a unique mass, the method for evaluating the centroid of that body is to evaluate the composite body by finite element analysis of each of the sections through the use of moment balancing, as above.



    Liminocentric structures




    You can find much on this site in regards to this issue, and I now relate centroid for consideration in the case of this topic. I presented it at the Backreaction site today to show an advancement in the thinking as we move to incorporate the knowledge. As we come to understand the natural world around us.

    Giving earth a new understanding in terms of its densities and it's relation to the gravitational contribution, it has in our new views of the globe, helped me learn and understand the feature of gravity as it extends to the cosmos.

    I have taken it a step further as many of you know to include the emotive states as valued physiological relations to what manifests in the immediate environs of the body home. While this is a far cry from the understanding of gravitational research it was inevitable for me to see an extension of how one can topological relate to the world, in this inductive/deductive mode to reason.

    While living on this earth, we always come home for reflection, and if any have not taken stock of what has accumulated during the day, then it is inevitable that is will come to reside very close to home as one sleeps through the nocturnality night. This research of subjectivity and mind had to entail "all of our activities." It had to include an understanding of the "mathematical constructs" that we observe, in order to relate to nature.

    List of Centroids




































































































    ShapeFigure\bar x\bar yArea
    Triangular areaImage:Triangle_centroid_2.svg\frac{b}{3}\frac{h}{3}\frac{bh}{2}
    Quarter-circular areaImage:Quarter_circle_centroid.svg\frac{4r}{3\pi}\frac{4r}{3\pi}\frac{\pi r^2}{4}
    Semicircular areaImage:Semicircle_centroid.svg\,\!0\frac{4r}{3\pi}\frac{\pi r^2}{2}
    Quarter-elliptical areaImage:Elliptical_quarter.svg\frac{4a}{3\pi}\frac{4b}{3\pi}\frac{\pi a b}{4}
    Semielliptical areaThe area inside the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 and above the \,\!x axis\,\!0\frac{4b}{3\pi}\frac{\pi a b}{2}
    Semiparabolic areaThe area between the curve y = \frac{h}{b^2} x^2 and the \,\!y axis, from \,\!x = 0 to \,\!x = b\frac{3b}{8}\frac{3h}{5}\frac{2bh}{3}
    Parabolic areaThe area between the curve \,\!y = \frac{h}{b^2} x^2 and the line \,\!y = h\,\!0\frac{3h}{5}\frac{4bh}{3}
    Parabolic spandrelThe area between the curve \,\!y = \frac{h}{b^2} x^2 and the \,\!x axis, from \,\!x = 0 to \,\!x = b\frac{3b}{4}\frac{3h}{10}\frac{bh}{3}
    General spandrelThe area between the curve y = \frac{h}{b^n} x^n and the \,\!x axis, from \,\!x = 0 to \,\!x = b\frac{n + 1}{n + 2} b\frac{n + 1}{4n + 2} h\frac{bh}{n + 1}
    Circular sectorThe area between the curve (in polar coordinates) \,\!r = \rho and the pole, from \,\!\theta = -\alpha to \,\!\theta = \alpha\frac{2\rho\sin(\alpha)}{3\alpha}\,\!0\,\!\alpha \rho^2
    Quarter-circular arcThe points on the circle \,\!x^2 + y^2 = r^2 and in the first quadrant\frac{2r}{\pi}\frac{2r}{\pi}\frac{\pi r}{2}
    Semicircular arcThe points on the circle \,\!x^2 + y^2 = r^2 and above the \,\!x axis\,\!0\frac{2r}{\pi}\,\!\pi r
    Arc of circleThe points on the curve (in polar coordinates) \,\!r = \rho, from \,\!\theta = -\alpha to \,\!\theta = \alpha\frac{\rho\sin(\alpha)}{\alpha}\,\!0\,\!2\alpha \rho


    Why are Planets Round?

    It is always interesting to see water in space.

    Image: NASA/JPL-
    Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

    With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.


    See:Isostatic Adjustment is Why Planets are Round?