Egypt's Pyramids, the Logarithmic Golden Mean Spiral, and Space Flight

[Tesla_WTC_Solution]

This special type of spiral is created in nature according to what is called the Golden Mean, Golden Section, or Divine Proportion, which is simply the ratio (phi) of 1 : 1.6180339... It is derived from Fibonacci's series, or a numerical list whereby each new number is the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... ad infinitum. Regardless of how large the spiral becomes, the ratio of its dimensions remains constant. For instance, the proportion AB to AC is the same as BC to BD or CD to CE.

The Golden Mean can also be applied geometrically to form the Golden Rectangle, the sides of which contain the phi ratio. The dimensions of the fabled Ark (spelled with a "k") of the Covenant is known to have conformed to Golden Mean proportions. This Hebrew artifact was 45 inches in length and 27 inches in both width and height. (2.5 cubits by 1.5 cubits by 1.5 cubits, with an ancient cubit equaling 18 inches.) 17 Although the sacred object was considered sacrosanct, it has apparently disappeared, and speculation on its whereabouts continues.

The growth of many objects in nature is determined by the Golden Mean, including the whorl pattern of sunflowers, pine cones, the distribution of leaves on a stem, fingerprints, and hurricanes.

The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant.

Logarithmic spirals are self-similar in that the result of applying any similarity transformation to the spiral is congruent to the original untransformed spiral. Scaling by a factor e^{2 \pi b}, for an integer b, with the center of scaling at the origin, gives the same curve as the original; other scale factors give a curve that is rotated from the original position of the spiral. Logarithmic spirals are also congruent to their own involutes, evolutes, and the pedal curves based on their centers.

"Were They Trying to Tell Us Something?"

Hello all. When I was a member on another website, my tag was KhufuKeplerTriangle. This was inspired by gawking at the Egyptian pyramids via Google, actually. But to continue the interest, I wanted to pose a rather strange theory (and I think maybe other people online have commented along the same lines) that the Pharaohs at some point in history were definitely aware of space flight and space travel.

I say this because today I was studying a webpage talking about the proposed NASA/ESA mission to Saturn and its moon Titan (TSSM): http://en.wikipedia.org/wiki/Titan_S...System_Mission

On the above page, it talks about a probe being launched from Earth and then using the gravity of Earth and Venus to enable it to reach Saturn and Titan:

The TSSM mission consists of an orbiter and two Titan exploration probes: a montgolfière (hot air balloon) that will float in Titan's clouds, and a lander that will splashdown on one of its methane seas.

Both probes’ data are to be relayed to a Titan orbiter. They will be equipped to study Titan’s features with instruments for imaging, radar profiling, and surface as well as atmospheric sampling, much more complete than done by the Cassini–Huygens mission.

The spacecraft will use several gravity assist flybys of other planets to enable it to reach Saturn. The baseline design envisaged a September 2020 launch, followed by four gravity assists (Earth-Venus-Earth-Earth), and arrival at Saturn 9 years later in October 2029. This is one of several available Earth-to-Saturn transfer options from the year 2018 through 2022. Current NASA plans do not give the TSSM a priority, however, and it is unlikely any of the proposed launch dates can be met.

Upon Saturn arrival, in October 2029, the orbiter’s chemical propulsion system would place the flight system into orbit around Saturn, followed by a two-year Saturn Tour Phase, characterized by the deployment of the in situ elements, and including a minimum of seven close Enceladus flybys and 16 Titan flybys. During this period, repeated satellite gravity assists and manoeuvres will reduce the energy needed to insert into Titan's orbit. As the craft completes its flyby by Enceladus, the orbiter will analyze the unusual cryovolcanic plumes at the moon's south pole.

The montgolfière, a hot air balloon, would be released on approach to the first Titan flyby for ballistic entry into Titan's atmosphere for its six Earth months’ mission from April 2030 to October 2030. Based on Cassini–Huygens discoveries, the montgolfière should be able to circumnavigate Titan at least once during its nominal lifetime at its deployment latitude of about 20°N, 10 kilometers above Titan's surface.

I was interested in the Saturn mission because of something I was reading about ELF waves occurring in nature: http://en.wikipedia.org/wiki/Extreme...atural_sources

Naturally occurring ELF waves are present on Earth, resonating in the region between ionosphere and surface. They are initiated by lightning strikes that make electrons in the atmosphere oscillate.[12] Though VLF signals were predominantly generated from lightning discharges, it was found that an observable ELF component (slow tail) followed the VLF component in almost all cases.[13] The fundamental mode of the Earth-ionosphere cavity has the wavelength equal to the circumference of the Earth, which gives a resonance frequency of 7.8 Hz. This frequency, and higher resonance modes of 14, 20, 26 and 32 Hz appear as peaks in the ELF spectrum and are called Schumann resonance.

They have also been tentatively identified on Saturn's moon Titan. Titan's surface is thought to be a poor reflector of ELF waves, so the waves may instead be reflecting off the liquid-ice boundary of a subsurface ocean of water and ammonia, the existence of which is predicted by some theoretical models. Titan's ionosphere is also more complex than Earth's, with the main ionosphere at an altitude of 1,200 km (750 mi) but with an additional layer of charged particles at 63 km (39 mi). This splits Titan's atmosphere into two separate resonating chambers. The source of natural ELF waves on Titan is unclear as there doesn't appear to be extensive lightning activity.[12]

Finally, huge ELF radiation power outputs of 100,000 times the Sun's output in visible light may be radiated by magnetars. The pulsar in the Crab nebula radiates powers of this order at the frequency 30 hertz.[14] Radiation of this frequency is below the plasma frequency of the interstellar medium, thus this medium is opaque to it, and it cannot be observed from Earth.

No wonder they want to look at Titan's atmosphere, right? It generates ELF waves somehow via a weird interaction between the upper and lower atmosphere, as stated above.

Anyhow, back to the pyramids. When I googled a picture of a "Gravity assisted flyby", it looked something like this:



Which caused me to remember this:



Which in turn caused me to wonder this: did Pharaoh somehow find out about gravity-assited flybys and other weird stunts of space travelers, and does the inclusion of a "fractal of the golden mean spiral" mean anything special to modern-day space travelers?

Many website authors (some kind of fringe, so beware, lol) seem to be asking (or claiming!) the same thing: that the golden mean spiral and fractals of said spiral represent crucial attributes of successful space-time navigation.

I am not sure what made me think about this, but about a year or so ago, I was wondering the same thing, about why the Pharaohs built the golden mean spiral into the pyramids. They wouldn't have done that for no reason, at least, I don't think they would have done that for no good reason.

There is usually a very good reason for long-term human efforts like that. People would have rioted otherwise -- if it was nothing more than the graveyard of a king.

I sincerely believe there is a message there and it's high-time someone addressed that, from an open-minded standpoint including the idea that Egyptians might have known more than NASA does about space travel.

I could be completely wrong, or assuming too much on the basis of too little, but it's definitely worth a thought or two.

here is the work of another culture who made a large earth sculpture depicting the Double Spiral of world-walking:



How could this be an accident?

Also look at the staff of Hermes as depicted by the Greeks:

The caduceus (☤; /kəˈduːsiːəs/ or /kəˈdjuːʃəs/; from Greek κηρύκειον kērukeion "herald's staff"[2] ) is the staff carried by Hermes in Greek mythology. The same staff was also borne by heralds in general, for example by Iris, the messenger of Hera. It is a short staff entwined by two serpents, sometimes surmounted by wings. In Roman iconography it was often depicted being carried in the left hand of Mercury, the messenger of the gods, guide of the dead and protector of merchants, shepherds, gamblers, liars, and thieves.[3]

As a symbolic object it represents Hermes (or the Roman Mercury), and by extension trades, occupations or undertakings associated with the god. In later Antiquity the caduceus provided the basis for the astrological symbol representing the planet Mercury. Thus, through its use in astrology and alchemy, it has come to denote the elemental metal of the same name.

By extension of its association with Mercury and Hermes, the caduceus is also a recognized symbol of commerce and negotiation, two realms in which balanced exchange and reciprocity are recognized as ideals.[4][5] This association is ancient, and consistent from the Classical period to modern times.[6] The caduceus is also used as a symbol representing printing, again by extension of the attributes of Mercury (in this case associated with writing and eloquence).

The caduceus is often used as a symbol of healthcare organisations and medical practice (especially in North America), due to confusion with the traditional medical symbol, the rod of Asclepius, although this has only one snake and is never depicted with wings.

It's hard to know exactly what that is referring to, but... could it be a symbol for the same thing? Contact? Where two worlds collide.

http://www.viewzone.com/carving_cosmos2.html



Echoing the hermetic maxim "As above, so below," this petroglyph grouping in Arizona includes not only the solar and the stellar but also the tellurian dimension. If we orient the elements of the Homolovi petroglyph to various geographical and human-made features on the landscape, a precise map of the southwestern edge of the Colorado Plateau begins to take shape. The center of the equilateral cross, for instance, corresponds to Tuuwanasavi, or the Hopi Mesas. On the upper end of the vertical axis is a natural hole in the rock over which a somewhat eroded but recognizable small equilateral cross has been abraded. This correlates to the ruins of Betatakin and Kiet Siel in Tsegi Canyon due north of the Hopi Mesas. Approximately the same number of inches below the intersection point, just to the right of the vertical axis, is a faint mark in the rock that represents Homolovi itself. If the Hopi Mesas were indeed first settled circa A.D. 1100 like archaeologists believe, then the Hisatsinom living at this spot where the petroglyph panel is located would certainly have recognized the well-established Center-place off to the north. After all, the first settlement at Homolovi came more than 150 years later. Significantly, Betatakin and Homolovi are equidistant on this north-south axis and were built at about the same time, viz., the latter half of the 13th century.

The plumed serpent petroglyph (the oblique axis of the large equilateral cross) may well represent water, specifically the Little Colorado River that snakes from the southeast to the northwest and joins the Colorado River at the Grand Canyon. To the right on the lower portion of the oblique axis is an incised mark in the rock just above the extended length of the serpent. This represents the Canyon de Chelly pueblo ruins. In addition, the tip of the serpent's tail might correspond to the Casa Malpais and Raven Site ruins in the southeast near the source of the Little Colorado. To the left on the upper portion of the oblique axis midway between the intersection and the serpent's head is a right angle turn that represents the Wupatki pueblo ruins. Moreover, the serpent's head itself could be linked with the smaller ruins in Glen Canyon along the Colorado River north of the Grand Canyon.

East of First Mesa nearly 140 miles are the vestiges of a grand ceremonial city in Chaco Canyon, which is represented in a proportional distance on the Homolovi petroglyph grouping by the antelope. If we look in the opposite direction at the extension of the spiral, we see that the trail roughly follows the geographic arcing of the Colorado River as it flows downstream, terminating at the clan petroglyphs mentioned above, in particular the Bear Clan and the Snake Clan. Some believe that the Hisatsinom traveled upstream and through the Grand Canyon to arrive at the "Sipapuni," where they emerged to seek their final destination upon the Colorado Plateau.

If we look closer at the earth/sky map, focusing on one constellation in particular, we are startled to find that a terrestrial Orion closely reflects its celestial counterpart, with prehistoric "cities" corresponding to every major star in the constellation. (See "Anasazi Star Cities" map.)

I think it's pretty clear, and I am a UFO skeptic (finally admitted it LOL), that Earthlings have been contacted by beings from space and other dimensions.

there are wayyyy too many similarities between these vastly-separated cultures and civilizations to ignore it any more.

[Tesla_WTC_Solution]

It's weird!

After I made this thread, the NASA auto-update shared a story about Cassini's view of Titan, one of Saturn's moons.

I am not sure what is going on with me tonight. I had a headache and don't feel very well.
I felt a bit better after writing about space...

but this update on Avalon above this thread, about Titan... makes me shiver.

NASA broadcast the Titan picture via the Avalon account at "Today 21:30" 10/23/2013.

I posted the above at 20:47 and edited it over the next few minutes.

http://solarsystem.nasa.gov/news/dis...?News_ID=45270

Cassini Gets New Views of Titan's Land of Lakes
23 Oct 2013
(Source: NASA/JPL)



PASADENA, Calif.-- With the sun now shining down over the north pole of Saturn's moon Titan, a little luck with the weather, and trajectories that put the spacecraft into optimal viewing positions, NASA's Cassini spacecraft has obtained new pictures of the liquid methane and ethane seas and lakes that reside near Titan's north pole. The images reveal new clues about how the lakes formed and about Titan's Earth-like "hydrologic" cycle, which involves hydrocarbons rather than water.

The new images are available online at: http://www.nasa.gov/mission_pages/ca...dia/index.html.

While there is one large lake and a few smaller ones near Titan's south pole, almost all of Titan's lakes appear near the moon's north pole. Cassini scientists have been able to study much of the terrain with radar, which can penetrate beneath Titan's clouds and thick haze. And until now, Cassini's visual and infrared mapping spectrometer and imaging science subsystem had only been able to capture distant, oblique or partial views of this area.

Several factors combined recently to give these instruments great observing opportunities. Two recent flybys provided better viewing geometry. Sunlight has begun to pierce the winter darkness that shrouded Titan's north pole at Cassini's arrival in the Saturn system nine years ago. A thick cap of haze that once hung over the north pole has also dissipated as northern summer approaches. And Titan's beautiful, nearly cloudless, rain-free weather continued during Cassini's flybys this past summer.

The images are mosaics in infrared light based on data obtained during flybys of Titan on July 10, July 26, and Sept. 12, 2013. The colorized mosaic from the visual and infrared mapping spectrometer, which maps infrared colors onto the visible-color spectrum, reveals differences in the composition of material around the lakes. The data suggest parts of Titan's lakes and seas may have evaporated and left behind the Titan equivalent of Earth's salt flats. Only at Titan, the evaporated material is thought to be organic chemicals originally from Titan's haze particles that once dissolved in liquid methane. They appear orange in this image against the greenish backdrop of Titan's typical bedrock of water ice.

"The view from Cassini's visual and infrared mapping spectrometer gives us a holistic view of an area that we'd only seen in bits and pieces before and at a lower resolution," said Jason Barnes, a participating scientist for the instrument at the University of Idaho, Moscow. "It turns out that Titan's north pole is even more interesting than we thought, with a complex interplay of liquids in lakes and seas and deposits left from the evaporation of past lakes and seas."

The near-infrared images from Cassini's imaging cameras show a bright unit of terrain in the northern land of lakes that had not previously been visible in the data. The bright area suggests that the surface here is unique from the rest of Titan, which might explain why almost all of the lakes are found in this region. Titan's lakes have very distinctive shapes -- rounded cookie-cutter silhouettes and steep sides -- and a variety of formation mechanisms have been proposed. The explanations range from the collapse of land after a volcanic eruption to karst terrain, where liquids dissolve soluble bedrock. Karst terrains on Earth can create spectacular topography such as the Carlsbad Caverns in New Mexico.

"Ever since the lakes and seas were discovered, we've been wondering why they're concentrated at high northern latitudes," said Elizabeth (Zibi) Turtle, a Cassini imaging team associate based at the Johns Hopkins Applied Physics Laboratory, Laurel, Md. "So, seeing that there's something special about the surface in this region is a big clue to help narrow down the possible explanations."

Launched in 1997, Cassini has been exploring the Saturn system since 2004. A full Saturn year is 30 years, and Cassini has been able to observe nearly a third of a Saturn year. In that time, Saturn and its moons have seen the seasons change from northern winter to northern summer.

"Titan's northern lakes region is one of the most Earth-like and intriguing in the solar system," said Linda Spilker, Cassini project scientist, based at NASA's Jet Propulsion Laboratory, Pasadena, Calif. "We know lakes here change with the seasons, and Cassini's long mission at Saturn gives us the opportunity to watch the seasons change at Titan, too. Now that the sun is shining in the north and we have these wonderful views, we can begin to compare the different data sets and tease out what Titan's lakes are doing near the north pole."

The Cassini-Huygens mission is a cooperative project of NASA, the European Space Agency and the Italian Space Agency. JPL manages the mission for NASA's Science Mission Directorate, Washington. The California Institute of Technology in Pasadena manages JPL for NASA. The VIMS team is based at the University of Arizona in Tucson. The imaging operations center is based at the Space Science Institute in Boulder, Colo.

For more information about the Cassini mission, visit: http://www.nasa.gov/cassini and http://saturn.jpl.nasa.gov .

[Tesla_WTC_Solution]

In case something happens to us, to me, I want you guys to know, I think ETs are out there.
Not all of them are bad. Some of them want to share with us.

But I don't know what they want to share. They are afraid too.

Edit: I think maybe what they want to share, is life. That is the number one prerogative. To be able to coexist.

I think maybe we are supposed to learn something from the events this week:
the fires in Australia because of military carelessness and the deaths of the two teachers in America within the same week.

How can we coexist with other species if our own species is not safe from itself? Not to mention our own planet's other intelligent species, who are not accorded "personhood" in the proper manner.

Perhaps it is true that should life on other worlds reveal itself, it would not assume a form to which we as humans would readily ascribe rights.

That would be very wrong -- we are not ready.

I hope we are not failing the test.

[Tesla_WTC_Solution]

http://en.wikipedia.org/wiki/Life_on_Titan

Whether there is life on Titan, the largest moon of Saturn, is at present an open question and a topic of scientific evaluation and research.

Titan is far colder than Earth, and its surface seems to lack liquid water; factors which have led some scientists to consider life there unlikely. On the other hand, the following points have been made in favor of Titan's suitability to sustain some form of life:

Titan appears to have lakes of liquid ethane and/or liquid methane on its surface, as well as rivers and seas, which some scientific models (still tentative and debated) suggest could support non-water-based life.[1][2][3]
It has also been suggested that life may exist in a sub-surface ocean consisting of water and ammonia.[4] Recent data from NASA's Cassini spacecraft have strengthened evidence that Titan likely harbors a layer of liquid water under its ice shell.[5]
Titan is the only known natural satellite (moon) in the Solar System that is known to have a fully developed atmosphere that consists of more than trace gases. Titan's atmosphere is thick, chemically active, and is known to be rich in organic compounds; this has led to speculation about whether chemical precursors of life may have been generated there.[1][2][3]
The atmosphere also contains hydrogen gas, which is cycling through the atmosphere and the surface environment, and which living things comparable to Earth methanogens could combine with some of the organic compounds (such as acetylene) to obtain energy.[1][2][3]
In June 2010, scientists analysing data from the Cassini–Huygens mission reported anomalies in the atmosphere near the surface which could be consistent with the presence of methane-producing organisms, but may alternatively be due to non-living chemical or meteorological processes.[6] The Cassini–Huygens mission was not equipped to provide direct evidence for biology or complex organics.

[ghostrider]

Everything we have now we have had all along , we are just re-living the same movie over and over , we've done it many times , it always ends the same ...

[Tesla_WTC_Solution]

Posted by ghostrider (here)
Everything we have now we have had all along , we are just re-living the same movie over and over , we've done it many times , it always ends the same ...

I wish someone in our lifetime would tell us the truth! Thank you for the visitor message, too. I don't know what accounts for these experiences.

Feel free to check out the following images:



http://www2.jpl.nasa.gov/basics/grav/primer.php

A Gravity Assist Primer

The "gravity assist" concept has proven fundamental to exploring our "back yard" — the solar system. The technique has even been employed at least once to rescue an Earth-orbiting communications satellite whose launch vehicle failed to place it in its intended geosynchronous orbit.

The Video
If you have a fast connection to the internet, be sure to watch this "Webcast" video of Charles White's interview with Mission Designer Charley Kohlhase, with questions and answers:
Trajectory Design and Gravity Assist.

Total running time: ~1.5 hours in 4 parts, plus downloadable accompanying charts. This webcast presents many of the basic concepts, quantities, and formulae important to understanding interplanetary space flight.

Some History Several robotic spacecraft have used the "gravity assist" technique to achieve their targets "high up" in the Sun's gravity well. Voyager 2 launched in August 1977 and flew by Jupiter for reconnaissance, and for a trajectory boost to Saturn. Voyager 1 launched the following month and did the same (reaching Jupiter before Voyager 2 did). Voyager 2 then obtained an assist from Saturn and another one later from Uranus, climbing all the way to Neptune and beyond. Galileo took one kick from Venus and two from Earth, while orbiting the Sun en route to its destination, Jupiter. Cassini took two boosts from Venus, one from Earth, and another from Jupiter to gain enough momentum to reach Saturn.

The "gravity assist" flyby technique can add or subtract momentum to increase or decrease the energy of a spacecraft's orbit. Generally it has been used in solar orbit, to increase a spacecraft's velocity and propel it outward in the solar system, much farther away from the Sun than its launch vehicle would have been capable of doing. Since a flyby can also decrease a spacecraft's orbital momentum, the Galileo spacecraft decreased its energy, relative to Jupiter, with a gravity assist flyby in front of the Jovian moon Io. In this way, it was possible to decrease the mass of rocket propellant needed for Jupiter orbit insertion. Comets and other bodies in solar orbit naturally experience changes in their orbits once in a while, as they happen to pass close by a planet or a moon.

The two Voyager spacecraft provide a classic example. They were launched aboard a Titan-III/Centaur, with destinations of Saturn and beyond. But their launch vehicles could provide only enough energy to get them to Jupiter (halfway out to Saturn). Had Jupiter not been there at the right time, the spacecraft would have reached aphelion near Jupiter's orbital distance (about 5 AU or 750,000,000 km from the Sun). Their perihelion would have been around Earth's orbital distance (1 AU or 150,000,000 km), and they would have remained in that orbit until a planet or something else caused it to change.

But of course their launch time was planned so that Jupiter coasted by at just the right time. The spacecraft felt Jupiter's gravity and started falling toward it. The spacecraft's velocity brought it close behind Jupiter in its solar orbit, but not close enough to impact. As Voyager climbed "up" away from Jupiter, it slowed down again with respect to Jupiter, eventually reaching the same speed it had on its way in.

How It Works From Jupiter's point of view, the situation is similar to a bicyclist speeding up going downhill into a valley, then slowing down again on the uphill part of the road.



In the vector diagram at left, the situation is simplified to two dimensions. You can see the magnitude and direction of the spacecraft's velocity on its way in towards Jupiter in the lower right. At the upper left, you can see that the accelerating force of Jupiter's gravitation has made a significant change in the direction of the spacecraft's velocity, but not in its magnitude. (These represent velocity at "infinity," from Jupiter, that is, before and after being noticeably changed by Jupiter's presence.) Near the middle of the diagram, the long arrow shows that there's a significant, but temporary, increase in the magnitude (speed). Note these speeds are all with respect to Jupiter.

To look at the same phenomenon in terms of a cyclist, VIN shows the cyclist approaching a downhill grade into a canyon. VOUT shows that the cyclist slowed down again at the top of the ensuing uphill grade (of course this cycling analogy asks us to ignore air friction and vehicle friction, etc., which are virtually absent in the spacecraft's case). Indeed, after negotiating the canyon, the cyclist's direction has changed, but in the end s/he has not made a lasting change in speed (unless you don't ignore all that friction etc.).

The planet's own motion is a key. A gravity assist with Jupiter involves not a stationary planet as considered above, but a planet with enormous angular momentum as it revolves around the Sun. In the diagram at right, Jupiter's motion along its solar orbit has been illustrated with a vector colored red (simplified, of course: Jupiter revolves along an arc, not a straight line. Imagine the Sun situated below the bottom of the diagram). The spacecraft acquires this Sun-relative vector, or a significant portion of it, during its interaction with Jupiter.



You can see how the red vector is added to VIN and VOUT. The resulting vector shows how the spacecraft's velocity, relative to the Sun, takes on a nice boost from Jupiter. Notice how rotation of the vector from VIN to VOUT (the bending of the spacecraft's path by the planet's gravity) helps increase the result. This trajectory bending is the other key.

The spacecraft is a physical mass, so it has its own gravitation. That's how the spacecraft can tug on Jupiter and actually decrease the planet's orbital momentum by a tiny amount. In the exchange, the spacecraft acquires momentum from Jupiter — a significant amount, compared to the momentum the spacecraft already had.

Some More Analogies
To help make a complicated-sounding concept easily understandable, consider the analogy in baseball. Picture a fast pitch coming toward the batter. The baseball represents a spacecraft. Now picture what the batter does, swinging a bat with all the force s/he can muster. The business end of the bat in motion represents a massive planet like Jupiter. The bat connects with the ball: wham! The ball receives momentum from the bat, and takes off in a different direction with a lot more speed as it soars out of the stadium. Of course in this analogy, the ball interacts with the bat mechanically, rather than by mutual gravitation. (Or you could look even closer and observe the ball's atoms interacting with repulsive electric force with the bat's atoms.) The results are similar: momentum taken from an object that has lots of it, and transferred into an object that makes use of its new-found momentum.



Another analogy, illustrated by the cartoon at right, involves a moving railroad train that represents Jupiter, moving along its track about the Sun. The kid in the propeller beanie throws a tennis ball that represents a spacecraft. It encounters the train, which transfers its momentum into the ball.

It's interesting to note the speeds in the cartoon. The propeller-beanie kid sees his tennis ball moving away from him at 30 miles per hour. So does the Sun, sitting on the stationary platform. The engineer driving the train sees the ball coming at about 80 MPH, since the train is moving 50 MPH with respect to the ground. The train and ball interact at 80 MPH. The ball rebounds from the front of the train at nearly the same 80 MPH, which can be added to the 50 MPH speed of the train, because it acquired it from the train. The result approaches a total of 130 MPH. This scenario is analogous the velocity of a spacecraft being added to the velocity of the massive speeding planet, and "rebounding" with a higher velocity still (although the spacecraft's "rebound" is a gravitational, rather than a mechanical, interaction, like in the baseball analogy).

_____________________________________________________

http://www.wired.com/wiredscience/20...ace-1961-1971/

Castles in Space: a 50-Year Survey of Gravity-Assist Space Travel
BY DAVID S. F. PORTREE12.01.127:23 PM



The last Mariner spacecraft to bear the series name was Mariner 10, which left Earth on 3 November 1973, on an Atlas-Centaur rocket (image at top of post). Mariner 10 was a flyby spacecraft, as were all but one of the Mariners before it, but with a difference: it would become the first spacecraft to use a planetary gravity-assist flyby to explore more than one planet.

The gravity-assist concept dates back at least to the early 1950s. Credit for the first rigorous analysis of the concept after the start of the Space Age probably belongs to Michael Minovitch. In a 1961 Jet Propulsion Laboratory internal document, he demonstrated mathematically that a spacecraft could decelerate or accelerate without using propellants as it flew past a planet. The planet would accelerate by a tiny amount if the spacecraft were decelerated or decelerate by a tiny amount if the spacecraft were accelerated.

Gravity-assists played no role in the many plans for piloted Mars and Venus flyby missions hatched in the 1960s. Planetary gravity was employed only to bend the flyby spacecraft’s course toward its next destination. It could, in fact, be a nuisance, for it could deflect the spacecraft from its free-return trajectory back to Earth. To compensate would require use of precious propellants.

Robert Sohn applied the gravity-assist concept to Mars exploration in 1963-1964, in a TRW study for NASA’s Ames Research Center. Sohn proposed using a Venus flyby to slow a spacecraft returning from Mars so that it could reenter Earth’s atmosphere at a safe speed. A ship returning from Mars in 1975 could, Sohn found, cut its Earth reentry speed from 66,500 feet per second to a more manageable 46,000 feet per second without using propellants by passing 3300 kilometers over Venus’s night side. Sohn found also that a Venus swing-by in 1973 would allow a spacecraft to gain speed without using propellants so that it could reach Mars in time to take advantage of a slow Earth-return opportunity. Sohn’s calculations indicated that Venus swing-by opportunities accompany every Mars transfer opportunity. Venus swing-bys with gravity-assists subsequently became a standard component of piloted Mars mission plans.

Walter Hollister of the Massachusetts Institute of Technology (MIT) looked into the gravity-assist concept at the same time as Sohn, but his work soon turned in a novel direction, Hollister became interested in Sun-centered “periodic orbits.” In such an orbit, a spacecraft could use gravity-assist flybys to cycle indefinitely between two or more planets with only modest course-correction propulsion requirements.



In January 1967, as a newly minted MIT professor, Hollister submitted a seminal paper to the journal Astronautica Acta. In it, he proposed “a bold concept of interplanetary exploration.” He explained that

the usual concept of manned interplanetary flight costs too much [and] takes too long. The cost is roughly proportionate to the initial mass [of the spacecraft] in Earth orbit. . .Any attempt to shorten the [trip] time appreciably [by expending additional propellant] causes the initial mass and total cost to go up exponentially. Both problems can be solved by providing an extremely luxurious spacecraft that can be used continuously for centuries. The initial cost is high, but the average cost is low because the spacecraft can be used over and over again. The travel time remains the same, but the unpleasantness is removed by providing an enjoyable place for the crew to live. Our own Earth is a large spaceship traveling through the interplanetary medium, and the usual complaint is that the trip is not long enough. . .The basic idea is to construct interplanetary spaceships as durable, luxurious shelters[:] literally, castles in space.

Determining periodic orbits for Mars was difficult, Hollister explained, because it has only 10% as much mass as Earth. This meant that a spacecraft had to pass very close to Mars to use its gravity to bend its course and change its speed. Hollister chose instead to determine periodic orbits for Venus, which has about 80% of Earth’s mass. This exercise would, he wrote, provide “evidence (but not proof)” that the periodic orbit concept might be extended to Mars.



Hollister proposed an “Earth-Venus Shuttle” system with two large periodic-orbit spacecraft. Each would complete 4.2 orbits of the Sun while Earth completed 3.2 orbits and Venus completed 5.2 orbits. Earth and Venus gravity-assist swing-bys would be spaced so that one spacecraft would be on its way to Venus while the other was on its way to Earth. Swing-by distance at Earth would be about 10,000 miles; the spacecraft would pass 5250 miles from Venus.

Hollister traced one periodic-orbit spacecraft’s course through a complete cycle. Following a Venus swing-by, the spacecraft would enter a Sun-centered orbit with Venus’s orbital period, but inclined relative to its orbital plane. The inclined orbit would keep the spacecraft close to Venus. Half a Venus orbit later, the spacecraft would swing past the planet a second time and use a gravity-assist to place itself into an elliptical orbit with Venus’s orbital period. It would encounter Venus a third time after the planet completed one orbit around the Sun and use a gravity-assist to again enter an inclined circular orbit with Venus’s orbital period. Half a Venus orbit later, the spacecraft would swing past the planet again. This time, Earth would be in position for a Venus-Earth transfer, so the spacecraft would use a Venus gravity-assist to place itself on course for Earth.

As the periodic-orbit spacecraft began the Venus-Earth leg, small crew shuttles would set out from Venus to rendezvous and dock with it for the trip to Earth. Hollister cited R. Titus’s seminal January 1966 Flyby-Landing Excursion Mode (FLEM) paper when he suggested this method of crew transfer. In his paper, Titus had proposed that a piloted Mars flyby spacecraft release a piloted Mars lander. The lander would set down on Mars ahead of the piloted flyby and astronauts would explore Mars for a few days. Then, as the piloted flyby spacecraft approached Mars, the lander would lift off in pursuit, catch up, and dock.

As Hollister’s Earth-Venus periodic-orbit spacecraft passed Earth, the crew shuttles would undock to deliver their passengers. The spacecraft, meanwhile, would use an Earth gravity-assist to enter an inclined circular orbit with the same period as Earth. Hollister proposed that automated electric-propulsion cargo ships be used to deliver supplies to the periodic-orbit spacecraft while it paced Earth in its inclined orbit.

Six months later, the spacecraft would encounter Earth again and use a gravity-assist to bend its course toward Venus. Crew transfer vehicles would rendezvous with it bearing passengers for the Earth-Venus trip, and the cycle of Venus and Earth encounters would begin again.



Hollister submitted his paper for publication in January 1967, but it did not appear in the pages of Astronautica Acta until April 1969. The delay meant that Minovitch became the first to publicly describe the concept, which he dubbed “Interplanetary Transportation Networks.” In May 1967, at a relatively obscure conference, he described “gigantic space liners” able to support “hundreds of people in complete safety and comfort for many months.”

Minovitch noted that, the more massive the space liner, the more effective would be the gravity-assist it received as it flew past a planet. His typical liner, a torus or sphere spun to provide its passengers with artificial gravity, would measure between 100 and 1000 meters across. Such spacecraft would, he wrote, “enable ordinary people to make trips from one celestial body to another on a scale adequate for colonization.”

The space liners would be assembled in “vast orbiting ‘ship yards’ equipped with all the facilities required to sustain hundreds of astronautical construction works.” “Gigantic nuclear injection engines” would launch each liner onto its “perpetual journey” among the planets, then would return to port for reuse. Fifty-person rendezvous modules would transport passengers to and from the liners as they passed planets.

Whereas Hollister sought out periodic short Venus-Earth and Earth-Venus transfers, Minovitch opted for a more brute-force approach. He provided several example trajectories for his liners, none of which included Hollister’s multiple encounters with a single planet between short interplanetary crossings. These encounters were a necessary feature of “phasing orbits” designed to keep a periodic-orbit spacecraft in motion while it awaited an opportunity to make a short interplanetary transfer.

Minovitch found that a liner leaving Earth on 14 May 1975 could perform a gravity-assist Venus swing-by on 23 October 1975 for a return to Earth on 26 July 1976. That Earth swing-by would put it on course for a Venus swing-by a year later, on 23 July 1977. That would in turn place the liner on course for Mars, which it would encounter after 14 months, on 30 November 1978. The Mars swing-by would place the liner on course for an Earth swing-by 20 months later, on 29 July 1980.



In many cases, Minovitch’s approach made for long voyages between planets; he noted, however, that liners in his vast network would follow many different paths, creating many opportunities to reduce the trip time. Passengers would merely need to disembark from the liner at a planet and wait a few weeks for a liner making a short trip to their destination planet to pass by.

Though Minovitch’s plan was grandiose, it had the advantage over Hollister’s plan in that it unquestionably permitted transfers between Earth and Mars. In 1969, Hollister’s doctoral student Charles Rall employed a new calculation method and improved computers to prove that Hollister’s approach also permitted such voyages.

Hollister and Rall reported their results in a January 1971 paper. In their four-spacecraft system, the individual periodic-orbit spacecraft would each repeat an identical sequence of Earth-Mars and Mars-Earth transfers and phasing orbits lasting approximately 3120 days (that is, about 8.5 years). To establish the system, the four spacecraft would depart Earth for Mars 26 months apart, when the two planets were positioned relative to each other to permit an initial short (about 148 days) Earth-Mars transfer.

For each spacecraft in their four-spacecraft system, short Earth-Mars crossings would occur about 8.5 years apart, as would short Mars-Earth crossings. After all four spacecraft were in motion, the system would permit 148-day trips from Earth to Mars and from Mars to Earth every 26 months. As one spacecraft crossed from Earth to Mars, another would cross from Mars to Earth, and two others would travel in phasing orbits.

The 3120-day cycle for each periodic-orbit spacecraft would occur as follows. After passing Earth and dropping off passengers from Mars, the it would enter a Sun-centered elliptical phasing orbit. After about 500 days, the spacecraft would swing past Earth again to take on passengers and begin a 148-day crossing to Mars.

After it dropped off its passengers at Mars, the periodic-orbit spacecraft would reach aphelion in the Asteroid Belt at slightly more than twice Earth’s distance from the Sun, then would return to Earth. The Mars-Asteroid Belt-Earth leg would need about 622 days.

The spacecraft would fly past Earth, where a gravity-assist would place it into an elliptical orbit with aphelion at Earth’s orbital distance. In this phasing orbit, it would perform four Earth flybys in about 1000 days. During the flybys, crews could rendezvous with the periodic-orbit spacecraft to perform maintenance and resupply.

The fourth Earth flyby would launch the periodic-orbit spacecraft on a 622-day journey to Mars via the Asteroid Belt, at the end of which it would pass Mars, pick up passengers, and begin a 148-day trip to Earth. As it flew by Earth and its passengers disembarked, it would end one 3120-day cycle and start another.

Mariner 10 flew past Venus on 5 February 1974. The spacecraft approached the planet’s night side and departed from its day side, passing about 3600 miles above its cloud tops. The maneuver slowed the spacecraft and bent its course without using propellants. Venus, for its part, accelerated by an infinitesimal amount. On 29 March 1974, Mariner 10 flew past Mercury, vindicating Minovitch, Sohn, Hollister, and their colleagues. As the spacecraft gathered data on the previously unexplored planet, it used its gravity to bend its course and accelerate toward a second Mercury encounter on 21 September 1974. The second Mercury flyby – the first instance of a single interplanetary spacecraft visiting the same world twice – put Mariner 10 on course for its third and final Mercury encounter on 16 March 1975.

In the years since, more robotic spacecraft have reached their planetary destinations via gravity-assist maneuvers than have not. What follows are only a few examples.


The Mariner-derived Voyager 2 spacecraft left Earth 20 August 1977, and received gravity-assist boosts from Jupiter, Saturn, Uranus, and Neptune. At launch the spacecraft was officially targeted only to Jupiter and Saturn; scientists made no secret, however, of their desire to take advantage of a once-in-175-years planetary line-up to direct it onward to Uranus and Neptune, thus accomplishing one of the many possible flight plans of the proposed “Grand Tour” mission scrapped in 1972. Voyager 2 is now at the heliopause, on the border of interstellar space, more than 100 times Earth’s distance from the Sun. It continues to return data as it moves outward a rate of 3.26 times the Earth-Sun distance per year.

The Galileo Jupiter Orbiter left Earth on 18 October 1989, bound for Venus; following the Venus gravity-assist, it gained enough velocity to perform a gravity-assist Earth flyby that took it out into the Main Asteroid Belt. It performed a second Earth flyby on 8 December 1992, at last gaining enough speed to reach Jupiter on 8 December 1995. Galileo then performed repeated gravity-assist flybys of the large Jovian satellites, caroming around the Jupiter system and returning data to Earth until 21 September 2003, when NASA disposed of it in Jupiter’s atmosphere.

The Mercury-bound MESSENGER spacecraft, launched on 3 August 2004, performed an Earth flyby about a year later, then flew past Venus twice and Mercury three times before capturing into Mercury orbit on 18 March 2011. The complex series of gravity-assist flybys was necessary because a spacecraft launched directly to Mercury, deep in the Sun’s gravity well, arrives too fast to capture into Mercury orbit without an excessive expenditure of propellants. The six gravity-assist maneuvers helped the spacecraft to nearly match orbits with Mercury; then, as it neared the planet, the spacecraft’s rocket engine ignited to slow it so Mercury’s gravity could capture it into an elliptical orbit. MESSENGER’s Mercury exploration mission is on-going at this writing.

(sorry had to cut out the nice pic to fit this in)

Piloted cycling spacecraft akin to the Hollister and Minovitch concepts enjoyed unprecedented prominence in the mid-to-late 1980s after they appeared in the report of the U.S. Congress-mandated National Commission on Space. At about the same time, the Case for Mars Conferences in Boulder, Colorado, Science Applications International Corporation (SAIC) engineers, and Apollo 11 astronaut Buzz Aldrin promoted the concept of multi-cycler networks. Interest in the concept flagged in the 1990s, but at the beginning of the 2000s, a team led by retired JPL engineer Kerry Nock conducted a NASA Institute for Advanced Concepts study which examined a low-cost Earth-Mars cycler system in considerable detail. Nock called his cycling spacecraft “astronaut hotels.”

More recently, a concept that puts Minovitch’s “gigantic spaceliners” to shame appeared in the realistic science fiction of Kim Stanley Robinson, whose award-winning Mars trilogy catapulted him to prominence in the first half of the 1990s. In his 2012 novel 2312, Robinson describes an extensive network of hollowed-out asteroids that cycle continually among the inhabited worlds of the Solar System three centuries hence. The asteroids, which number in the hundreds or thousands, have different themes; for example, some are “terraria” that reproduce ecosystems long defunct on Earth.

References:

“Venus Swingby Mode for Manned Mars Missions,” Robert Sohn, Journal of Spacecraft and Rockets, Vol. 1, No. 6, September-October 1964, pp. 565-567.

“Manned Mars Trips Using Venus Swingby Modes,” Robert Sohn, AIAA/NASA Third Manned Space Flight Meeting, 4-6 November 1964.

“A Chance for an Early Manned Mars Mission,” Robert Sohn, Astronautics & Aeronautics, May 1965, pp. 28-33.

“FLEM – Flyby-Landing Excursion Mode,” AIAA Paper No. 66-36, R. R. Titus; paper presented at the 3rd AIAA Aerospace Sciences Meeting, New York, New York, 24-26 January 1966.

“Manned Mars Trips Using Venus Swingby Modes,” Robert Sohn, Journal of Spacecraft and Rockets, Vol. 3, No. 2, February 1966, pp. 161-169.

“Gravity Thrust and Interplanetary Transportation Networks,” Michael Minovitch; paper presented at the AAS Symposium on Use of Space Systems for Planetary Geology and Geophysics in Boston, Massachusetts, 25-27 May 1967.

“Castles in Space,” Walter M. Hollister, Astronautica Acta, Vol. 14, April 1969, pp. 311-316.

“Free-Fall Periodic Orbits Connecting Earth and Mars,” AIAA Paper No. 71-92, Charles S. Rall and Walter M. Hollister; paper presented at the AIAA 9th Aerospace Sciences Meeting in New York, New York, 25-27 January 1971.

Pioneering the Space Frontier: An Exciting Vision of Our Next Fifty Years in Space, The Report of the National Commission on Space, Bantam Books, 1986.

The Case for Mars: Concept Development for a Mars Research Station, NASA-CR-179753/JPL-PUB-86-28, Jet Propulsion Laboratory, 15 April 1986.

Cyclical Visits to Mars via Astronaut Hotels, Phase II Final Report, Global Aerospace Corporation, NASA Institute for Advanced Concepts, 9 April 2003.

2312, Kim Stanley Robinson, Orbit Books, 2012.

[Tesla_WTC_Solution]

http://www.esa.int/Our_Activities/Sp...ity_assist_you

LET GRAVITY ASSIST YOU

21 June 2013

When a spacecraft launches on a mission to another planet it must first break free of the Earth’s gravitational field. Once it has done that, it enters interplanetary space, where the dominant force is the gravitational field of the Sun.

The spacecraft begins to follow a curving orbit, around the Sun, which is similar to the orbit of a comet. When this orbit brings it close to its target destination the spacecraft must fire a retrorocket to slow down and allow itself to be captured by the gravitational field of its target. The smaller the target, the more the spacecraft must slow down.

Sometimes passing a planet can result in the spacecraft being accelerated, even without the spacecraft firing any of its thrusters. This is known as the 'slingshot' effect. Such 'gravity assist' manoeuvres are now a standard part of spaceflight and are used by almost all ESA interplanetary missions. They take advantage of the fact that the gravitational attraction of the planets can be used to change the trajectory and speed of a spacecraft.

The amount by which the spacecraft speeds up or slows down is determined by whether it is passing behind or in front of the planet as the planet follows its orbit. When the spacecraft leaves the influence of the planet, it follows an orbit on a different course than before.

ESA’s comet-chasing Rosetta mission launched in 2004 and is using slingshot manoeuvres to reach its destination, Comet 67P/Churyumov-Gerasimenko, in 2014. It has received gravitational ‘kicks’ from close flybys of Mars (2007) and Earth (2005, 2007 and 2009). Rosetta has also made close flybys of two asteroids.

[Tesla_WTC_Solution]

Excellent news: https://projectavalon.net/forum4/show...395#post753395

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Default India's space-based 'revolution' Sending Mars Orbitor...


India's space-based 'revolution'K Radhakrishnan



Mr Radhakrishnan defended the money spent on India's Mars orbiter

India's space ambition takes off

Q: So, when the spacecraft takes off from the east coast of India, what exactly will it do
and how long is it expected to take?

A: Any mission to Mars has to be done in an opportune window and the imminent
window is November 2013, that is we need to get out of this sphere of influence of
earth by 30 November to ensure that we have the minimum distance between Earth
and Mars.

Now we are launching this Mars orbiter from Sriharikota in the east coast of India in the
first week of November and then the PSLV-XL (Polar Satellite Launch Vehicle) is used
for the launch which will put this orbiter into an elliptical orbit around the Earth... then
around the last week of November, we have a crucial operation, it's called the "trans-
Martian injection" where the spacecraft is directed towards Mars.

Then it is a long voyage of 300 days where the orbiter spacecraft passes through the
sphere of influence of the Earth... Then it goes through a long phase of heliocentric
flight where the orbiter spacecraft will be influenced not only by the Sun but by the
other planets too. Then as it approaches Mars... we have another major action:
capturing the orbit of Mars, which is on 21st of September 2014.

Q: After that how long will it take to get the readings or get the data that you are
hoping to get from there? How long will it take after September 2014?

A: Soon after the orbiter is put into the orbit of Mars, we would start the
experimentation and even before this orbiter reaches the Martian environment we would
be calibrating these instruments as it travels from Earth to Mars. But the most
important part of it is looking at the distances involved. It takes at least 20 minutes for
any signal to come from the Mars orbiter to Earth in some phases. It could be anything
between four to 20 minutes one-way.