Wednesday, 23 March 2011

apples and culture _ some interesting stuff


Cultural aspects


"Brita as Iduna" (1901) by Carl Larsson

[edit]Germanic paganism

In Norse mythology, the goddess Iðunn is portrayed in the Prose Edda (written in the 13th century by Snorri Sturluson) as providing apples to the gods that give them eternal youthfulness. English scholar H. R. Ellis Davidson links apples to religious practices in Germanic paganism, from whichNorse paganism developed. She points out that buckets of apples were found in the Oseberg shipburial site in Norway, and that fruit and nuts (Iðunn having been described as being transformed into a nut in Skáldskaparmál) have been found in the early graves of the Germanic peoples inEngland and elsewhere on the continent of Europe, which may have had a symbolic meaning, and that nuts are still a recognized symbol of fertility in southwest England.[12]
Davidson notes a connection between apples and the Vanir, a tribe of gods associated withfertility in Norse mythology, citing an instance of eleven "golden apples" being given to woo the beautiful Gerðr by Skírnir, who was acting as messenger for the major Vanir god Freyr in stanzas 19 and 20 of Skírnismál. Davidson also notes a further connection between fertility and apples in Norse mythology in chapter 2 of the Völsunga saga when the major goddess Frigg sends KingRerir an apple after he prays to Odin for a child, Frigg's messenger (in the guise of a crow) drops the apple in his lap as he sits atop a mound.[13] Rerir's wife's consumption of the apple results in a six-year pregnancy and the Caesarean section birth of their son - the hero Völsung.[14]
Further, Davidson points out the "strange" phrase "Apples of Hel" used in an 11th-century poem by the skald Thorbiorn Brúnarson. She states this may imply that the apple was thought of by the skald as the food of the dead. Further, Davidson notes that the potentially Germanic goddess Nehalennia is sometimes depicted with apples and that parallels exist in early Irish stories. Davidson asserts that while cultivation of the apple in Northern Europe extends back to at least the time of the Roman Empire and came to Europe from the Near East, the native varieties of apple trees growing in Northern Europe are small and bitter. Davidson concludes that in the figure of Iðunn "we must have a dim reflection of an old symbol: that of the guardian goddess of the life-giving fruit of the other world."[12]

[edit]Greek mythology


Heracles with the apple ofHesperides
Apples appear in many religious traditions, often as a mystical or forbidden fruit. One of the problems identifying apples in religionmythology and folktales is that the word "apple" was used as a generic term for all (foreign) fruit, other than berries, but including nuts, as late as the 17th century.[15] For instance, inGreek mythology, the Greek hero Heracles, as a part of his Twelve Labours, was required to travel to the Garden of the Hesperides and pick the golden apples off the Tree of Life growing at its center.[16][17][18]
The Greek goddess of discord, Eris, became disgruntled after she was excluded from the wedding ofPeleus and Thetis.[19] In retaliation, she tossed a golden apple inscribed Καλλίστη (Kalliste, sometimes transliterated Kallisti, 'For the most beautiful one'), into the wedding party. Three goddesses claimed the apple: HeraAthena, and AphroditeParis of Troy was appointed to select the recipient. After being bribed by both Hera and Athena, Aphrodite tempted him with the most beautiful woman in the world, Helen ofSparta. He awarded the apple to Aphrodite, thus indirectly causing the Trojan War.
The apple was thus considered, in ancient Greece, to be sacred to Aphrodite, and to throw an apple at someone was to symbolically declare one's love; and similarly, to catch it was to symbolically show one's acceptance of that love.[20] An epigram claiming authorship by Plato states:
I throw the apple at you, and if you are willing to love me, take it and share your girlhood with me; but if your thoughts are what I pray they are not, even then take it, and consider how short-lived is beauty.
PlatoEpigram VII[21]

Adam and Eve
Showcasing the apple as a symbol of sin.
Albrecht Dürer, 1507
Atalanta, also of Greek mythology, raced all her suitors in an attempt to avoid marriage. She outran all but Hippomenes (a.k.a. Melanion, a name possibly derived from melon the Greek word for both "apple" and fruit in general),[17] who defeated her by cunning, not speed. Hippomenes knew that he could not win in a fair race, so he used three golden apples (gifts of Aphrodite, the goddess of love) to distract Atalanta. It took all three apples and all of his speed, but Hippomenes was finally successful, winning the race and Atalanta's hand.[16]

[edit]The Apple in the Garden of Eden

Though the forbidden fruit in the Book of Genesis is not identified, popular Christian tradition has held that it was an apple that Eve coaxed Adam to share with her.[22] This may have been the result of Renaissance painters adding elements of Greek mythology into biblical scenes (alternative interpretations also based on Greek mythology occasionally replace the apple with a pomegranate). In this case the unnamed fruit of Eden became an apple under the influence of story of the golden apples in the Garden of Hesperides. As a result, in the story of Adam and Eve, the apple became a symbol for knowledge, immortality, temptation, the fall of man into sin, and sin itself. In Latin, the words for "apple" and for "evil" are similar (mālum "an apple", mălum "an evil, a misfortune"). This may also have influenced the apple becoming interpreted as the biblical"forbidden fruit". The larynx in the human throat has been called Adam's apple because of a notion that it was caused by the forbidden fruit sticking in the throat of Adam.[22] The apple as symbol of sexual seduction has been used to imply sexuality between men, possibly in an ironic vein.[22]

apple _ botanical information - reference by wikipedia - will look into another source


Botanical information


Blossoms, fruits, and leaves of the apple tree (Malus domestica)

Wild Malus sieversii apple in Kazakhstan
The apple forms a tree that is small and deciduous, reaching 3 to 12 metres (9.8 to 39 ft) tall, with a broad, often densely twiggy crown.[4] The leaves are alternately arranged simple ovals 5 to 12 cm long and 3–6 centimetres (1.2–2.4 in) broad on a 2 to 5 centimetres (0.79 to 2.0 in) petiole with an acute tip, serrated margin and a slightly downy underside. Blossoms are produced in spring simultaneously with the budding of the leaves. The flowers are white with a pink tinge that gradually fades, five petaled, and 2.5 to 3.5 centimetres (0.98 to 1.4 in) in diameter. The fruit matures in autumn, and is typically 5 to 9 centimetres (2.0 to 3.5 in) in diameter. The center of the fruit contains five carpels arranged in a five-point star, each carpel containing one to three seeds.[4]

Tuesday, 22 March 2011

drawings (queen + pie)


Animation Test

This is a test of the intro, the faces on the apples and the leaves using the puppet tool. This is only at half resolution because the full res version was too big to upload.

Sunday, 20 March 2011

mass and weight - a little bit of physics might help make it more believable if we go with the fall scene :) read it! very interesting! _ reference by http://library.thinkquest.org/27585/

Page 3 - Mass vs. Weight


Every object in the universe has mass. It is the amount of matter an object contains and it never changes, no matter where that object happens to be. We often say that objects with a large mass are heavy and that objects with a small mass are light. This is true, at least in the situations we deal with here on Earth. However, mass and weight are not the same thing. Unlike mass, the weight of an object is simply a measure of how hard gravity happens to be pulling on that object. Because Newton's law says that the gravitational attraction between two objects is proportional to the product of their masses, the more mass an object has, the harder Earth's gravity will pull on it.

Another way in which weight differs from mass is that the weight of an object can actually change depending upon where it is. Because Newton's law says that the gravitational attraction between two objects decreases the greater the distance is between them, an object will get lighter the farther away it is from the Earth (or from any large body). This means that you will actually weigh less standing at the top of a high mountain than you will at sea level! Of course the difference is incredibly small but it is detectable.





For an object to really lose weight it must be far away from any large bodies like planets or stars (in deep space for example). When an object is far enough away from these bodies that it experiences practically no gravitational pull from them, it enters a state of zero gravity or weightlessness. As its name implies, an object in a weightless environment weighs nothing, no matter how large its mass.

For more on Newton's law of universal gravitation see What is Gravity Page 4.

The fall acceleration _ newton gravity - reference by http://library.thinkquest.org/27585/

Page 5 - Free Fall: An Accelerating Experience


Technically, an object is in free fall when gravity and only gravity is allowed to act on it. In other words, it is what you and I would generally refer to as falling. However, a ball thrown into the air, even though its initial motion is upward, is also said to be in free fall because the only force acting on it is that of gravity. Likewise, satellites in orbit around a planet or star are also considered to be in free fall. For more on orbits see Large Scale Effects Pages 45 and 6.

Now, if you are particularly on the ball today, you might have already come up with the argument that an object thrown or dropped in the air is not really in free fall because it is not just experiencing the force of gravity but air resistance as well. This is true. However, in most situations, air resistance has little effect on the motion of objects in free fall. And, because we are only trying to educate you on the effects of gravity and not those of air resistance, we are simply going to assume that it does not exist. Now that we’ve got that settled, let’s continue.

To really understand free fall you must also understand acceleration. Most people think acceleration is simply when an object increases speed. After all, the gas pedal in a car or truck which makes the vehicle move faster is called the accelerator. By its most exact definition however, acceleration is any change in an object's speed or direction. If an object is at rest or is traveling in a straight line at a constant speed we say it is moving uniformly. But if it is speeding up (positive), slowing down (negative), or even changing direction (angular), it is undergoing a type of acceleration.





When an object is in free fall near the Earth, it is being accelerated towards the center of the Earth at a constant rate. This rate is approximately 9.8 meters per second squared. This means that after being in free fall near Earth for one second an object will be traveling at a speed of 9.8 meters per second. After two seconds its speed will have doubled to 19.6 meters per second and after three seconds it will have tripled to 29.4 meters per second and so on. However, this is only near the surface of the Earth. If you dropped an object while standing on the Moon where gravity's pull is much weaker the object would accelerate much more slowly.

For more on gravity and acceleration see What is Gravity? Page 6.

more Newton

Newton, the Apple, and Gravity, Gravitation

Nearly everyone has heard about Newton and an apple. But few people seem to know the story behind it! Technically, there is no actual documentation for this story, so it might contain exaggerations. But it is relatively well accepted as having happened.Prior to this incident, Newton had invented something we now call the Calculus, and with it had mathematically proven that an "inverse square law" dependence, such as gravitation on distance, MUST act as though all the mass of an object (the Earth) is at the exact center of the Earth.

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Newton was trying to think of some way of experimentally confirming what he had already calculated, that inverse square dependence. He was sitting out in a field, looking at the Moon in the sky overhead. He believed that the Moon was orbiting the Earth because of the gravitation of the Earth. He believed that the Moon would normally have gone straight off into space, but the Earth's gravitation caused it to "constantly fall" toward the Earth, making its path curved rather than straight. But he hadn't thought of any way to experimentally prove that!By his time, science had fairly accurately calculated the radius of the Earth, just under 4,000 miles (6400 km). It was also known that the Moon orbited the Earth at an average distance of just under 240,000 miles (384,000 km), about 60 times as far from the center of the Earth as he was. These things were known.
When an apple fell from a tree near him, it suddenly dawned on him that the same Earth's gravitation that must be curving the Moon's path must also have made that apple accelerate toward the Earth in its fall!
His calculations had shown that the acceleration should NOT depend at all on the size or mass of the object. So, if that apple was out at the distance of the Moon, it should have the same acceleration as the Moon does, and would therefore also orbit the Earth.
He knew that an apple falls at "the acceleration due to gravity", 32 feet per second per second, what we call g. And that in the first second, that apple would fall very close to 16.1 feet (193") toward the Earth.
Then, if that apple was moved to a place 60 times as far away from the center of the Earth, and gravitation actually DID depend on an inverse square relationship, then the apple out there should fall 1/3600th as far as it did from the tree. So he multiplied 16.1 feet by 1/3600 and got an expected falling distance in one second to be 0.0535 inch.
That meant that the Moon must "fall" 0.0535" toward the Earth in a second (from an otherwise straight line. This is a REALLY small curvature (less than 1/16" over the 3,300 feet that the Moon moves every second!). But it turns out that it is still pretty easy to confirm. If you draw a really big circle that represents the orbit of the Moon, and then look at a small part of that circle, the part that the Moon moves through in one second, then simple geometry can determine that small curvature. (circle, chord, radius, etc.)
Interestingly, in this very simple calculation, the brilliant Newton apparently made a multiplication error regarding the radius of the Earth in inches! With this wrong value, there was no agreement in the results! Newton set aside this whole subject for six years! Around then, a new calculation of the radius of the Earth had been made (by Picard). Newton decided to try the calculation again, and he did it right this time, and the result was 0.0534", a virtually perfect match. The inverse square law of gravitation was therefore proven. Also proven was the fact that the mass of the object, whether apple or Moon, did not affect the acceleration results.
As to this last statement, Newton later calculated that there actually IS a tiny effect due to the mass. But it is an extremely tiny effect, for any practical sized objects, because the Earth is so big and massive!
There is also a tiny effect due to the differential gravitational effect of the Sun, which very slightly reduces the actual value for the Moon, which even explains that 0.0001" discrepancy!
Now you know about Newton and the Apple!


This presentation was first placed on the Internet in March 2003.This page - - Newton, the Apple, and Gravity, Gravitation - - is at http://mb-soft.com/public2/newton.htmlThis subject presentation was last updated on Sat, 30 Apr 2011 15:09:45 GMT


Link to the Index of these Public Service Pages( http://mb-soft.com/index.html )

apples and gravity _ reference by http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

Sir Isaac Newton: The
Universal Law of Gravitation 




There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation. As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened.

What Really Happened with the Apple?

Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "accleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree.

Sir Isaac's Most Excellent Idea

Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth.This can be illustrated with the thought experiment shown in the following figure. Suppose we fire a cannon horizontally from a high mountain; the projectile will eventually fall to earth, as indicated by the shortest trajectory in the figure, because of the gravitational force directed toward the center of the Earth and the associated acceleration. (Remember that an acceleration is a change in velocity and that velocity is a vector, so it has both a magnitude and a direction. Thus, an acceleration occurs if either or both the magnitude and the direction of the velocity change.)
But as we increase the muzzle velocity for our imaginary cannon, the projectile will travel further and further before returning to earth. Finally, Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls. That is,the cannon ball would have been put into orbit around the Earth. Newton concluded that the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit.By such reasoning, Newton came to the conclusion that any two objects in the Universe exert gravitational attraction on each other, with the force having a universal form:
The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally characterizes the intrinsic strength of the gravitational force.

The Center of Mass for a Binary System

If you think about it a moment, it may seem a little strange that in Kepler's Laws the Sun is fixed at a point in space and the planet revolves around it. Why is the Sun privileged? Kepler had rather mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place. However Newton, largely as a corollary of his 3rd Law, demonstrated that the situation actually was more symmetrical than Kepler imagined and that the Sun does not occupy a privileged postion; in the process he modified Kepler's 3rd Law.Consider the diagram shown to the right. We may define a point called the center of mass between two objects through the equations
where R is the total separation between the centers of the two objects. The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons sitting on the see-saw.Here is a Center of Mass Calculator that will help you make and visualize calculations concerning the center of mass. (Caution: this applet is written under Java 1.1, which is only supported by the most recent browsers. It should work on Windows systems under Netscape 4.06 or the most recent version of Internet Explorer 4.0, but may not yet work on Mac or Unix systems or earlier Windows browsers.)

Newton's Modification of Kepler's Third Law

Because for every action there is an equal and opposite reaction, Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun. Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system. He then modified Kepler's 3rd Law to read,
where P is the planetary orbital period and the other quantities have the meanings described above, with the Sun as one mass and the planet as the other mass. (As in the earlier discussion of Kepler's 3rd Law, this form of the equation assumes that masses are measured in solar masses, times in Earth years, and distances in astronomical units.) Notice the symmetry of this equation: since the masses are added on the left side and the distances are added on the right side, it doesn't matter whether the Sun is labeled with 1 and the planet with 2, or vice-versa. One obtains the same result in either case.Now notice what happens in Newton's new equation if one of the masses (either 1 or 2; remember the symmetry) is very large compared with the other. In particular, suppose the Sun is labeled as mass 1, and its mass is much larger than the mass for any of the planets. Then the sum of the two masses is always approximately equal to the mass of the Sun, and if we take ratios of Kepler's 3rd Law for two different planets the masses cancel from the ratio and we are left with the original form of Kepler's 3rd Law:
Thus Kepler's 3rd Law is approximately valid because the Sun is much more massive than any of the planets and therefore Newton's correction is small. The data Kepler had access to were not good enough to show this small effect. However, detailed observations made after Kepler show that Newton's modified form of Kepler's 3rd Law is in better accord with the data than Kepler's original form.

Two Limiting Cases

We can gain further insight by considering the position of the center of mass in two limits. First consider the example just addressed, where one mass is much larger than the other. Then, we see that the center of mass for the system essentially concides with the center of the massive object:
This is the situation in the Solar System: the Sun is so massive compared with any of the planets that the center of mass for a Sun-planet pair is always very near the center of the Sun. Thus, for all practical purposes the Sun IS almost (but not quite) motionless at the center of mass for the system, as Kepler originally thought.However, now consider the other limiting case where the two masses are equal to each other. Then it is easy to see that the center of mass lies equidistant from the two masses and if they are gravitationally bound to each other, each mass orbits the common center of mass for the system lying midway between them:
This situation occurs commonly with binary stars (two stars bound gravitationally to each other so that they revolve around their common center of mass). In many binary star systems the masses of the two stars are similar and Newton's correction to Kepler's 3rd Law is very large.Here is a Java applet that implements Newton's modified form of Kepler's 3rd law for two objects (planets or stars) revolving around their common center of mass. By making one mass much larger than the other in this interactive animation you can illustrate the ideas discussed above and recover Kepler's original form of his 3rd Law where a less massive object appears to revolve around a massive object fixed at one focus of an ellipse.
These limiting cases for the location of the center of mass are perhaps familiar from our afore-mentioned playground experience. If persons of equal weight are on a see-saw, the fulcrum must be placed in the middle to balance, but if one person weighs much more than the other person, the fulcrum must be placed close to the heavier person to achieve balance.
Here is a Kepler's Laws Calculator that allows you to make simple calculations for periods, separations, and masses for Keplers' laws as modified by Newton (see subsequent section) to include the effect of the center of mass. (Caution: this applet is written under Java 1.1, which is only supported by the most recent browsers. It should work on Windows systems under Netscape 4.06 or the most recent version of Internet Explorer 4.0, but may not yet work on Mac or Unix systems or earlier Windows browsers.)

Weight and the Gravitational Force

We have seen that in the Universal Law of Gravitation the crucial quantity is mass. In popular language mass and weight are often used to mean the same thing; in reality they are related but quite different things. What we commonly call weight is really just the gravitational force exerted on an object of a certain mass. We can illustrate by choosing the Earth as one of the two masses in the previous illustration of the Law of Gravitation:
Thus, the weight of an object of mass m at the surface of the Earth is obtained by multiplying the mass m by the acceleration due to gravity, g, at the surface of the Earth. The acceleration due to gravity is approximately the product of the universal gravitational constant G and the mass of the Earth M, divided by the radius of the Earth, r, squared. (We assume the Earth to be spherical and neglect the radius of the object relative to the radius of the Earth in this discussion.) The measured gravitational acceleration at the Earth's surface is found to be about 980 cm/second/second.

Mass and Weight

Mass is a measure of how much material is in an object, but weight is a measure of the gravitational force exerted on that material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant. It follows that mass is constant for an object (actually this is not quite true, but we will save that surprise for our later discussion of the Relativity Theory), but weight depends on the location of the object. For example, if we transported the preceding object of mass m to the surface of the Moon, the gravitational acceleration would change because the radius and mass of the Moon both differ from those of the Earth. Thus, our object has mass m both on the surface of the Earth and on the surface of the Moon, but it will weigh much less on the surface of the Moon because the gravitational acceleration there is a factor of 6 less than at the surface of the Earth.