Harmony…

Notes written by Johannes Kepler, representing the music “sung” by the planets.

Up and Running… It is altogether absurd that a heavenly body should not always move

with uniform velocity in a perfect circle.

Copernicus

Perhaps it is our fondness for beauty…Maybe we are motivated by simplicity…our admiration for the circle has always drawn us to make it our natural geometric choice to represent the paths that celestial bodies glide upon. Why should Nature be confined by our wishes? Can the planets not pursue their own pleasure unbounded by our whims and desires? Could they not direct their own destiny?Indeed…It is absurd not to think otherwise…

Up…

Think of your experience watching a jet airliner flying gracefully high above the ground. Although it seems only to creep along among the clouds, in reality it is traveling at a very fast speed. No one will ever stand at some distant point in space and see the earth orbit around the sun. Think about how far away you would have to be to see this pair together in space. At such a distance, all would seem motionless…

So when it comes to planetary behavior dynamics, how do we know what’s up? The resolution of planetary orbital geometry required the work of two opposite personalities. One,Tycho Brahe, was jovial, a practical, concrete collector while the other, Johannes Kepler, was reclusive, an attentive to detail, abstract mathematical type thinker. Through their mutual distrust for one another they managed a very fragile bond that was resilient enough to allow for the merger of the necessary observational science with the necessary theoretical science to form an enduring, precise geometric model of how the heavens go.

Kepler mathematically mines from Tycho’s observational data three conclusions:

• Planets orbit in nearly circular orbits about the sun. The true geometric nature of their orbital path is an ellipse.

• Assume in the above orbital diagram that it takes the same amount of time to go from one end of the green portion of the orbital track as it does to go across the purple side. This would than imply that the orbital speed of a planet around the sun varies. The speed of a planet is fastest when it is closest to the sun. It should also be noted that the areas shaded in the above diagram are equal.

• Imagine two runners set to race around the tracks shown in the upper left diagram. Although the inner “blue” course is a shorter distance to run, it is possible for a very fast runner who goes along the outside “black” length to still win the race. Nature could have it any way with the planets as they “run” around the sun. Such is not the case. As shown in the graph in the upper right there is a rigidity that rules over the behavior of the system. From the graph it is seen that a planet close to the sun requires a shorter amount of time to complete a lap around the sun. This implies that a planet close to the sun not only “runs” a shorter course but it must also go at a higher speed. There is an unseen control that defines a relationship between the planets and the sun.

Kepler extracted from the data a vision that required an abandonment of our cherished circular bias. The geometric conundrum of how the planets are up in space was answered. The why they run this way eluded him. In his three laws of planetary behavior it is obvious that the the sun plays a crucial role in creating the background music for this dance of the planets. The insightful Kepler speculated that it was an unseen magnetic power emanating from the sun that kept such heavenly harmony…

Running…

In Powers of Ten, Philip Morrison tells us, “It reaches inside every candy box, no matter what the wrapping, to distinguish the full pound from the empty container.” Think more carefully about…It. Take a piece of paper and hold it above the floor away from your body. Do not let the page touch the floor. Observe the result. Now, tear the paper so that it just hangs by the flimsiest shred. Carefully move it again away from your body. Do not let the page touch the floor. Observe the result. It is pretty amazing! It is strong enough to keep the moon in tow yet so feeble that all of it the earth can muster is kept in balance by the muscle fibers in our bodies and the molecular fibers between a shredded page. It is the unseen control that defines the relationship between the planets and the sun. So familiar…So mysterious…Mark Twain observes, “Why shouldn’t truth be stranger than fiction? Fiction after all, has to make sense…”

Newton’s ReachWatch the stars, and from them learn.

To the Master’s honor all must turn,each in its track, without a sound,forever tracing Newton’s ground.

---- Einstein

In Coming of Age in the Milky Way, Timothy Ferris relays this about Newton, “…was himself one of the strangest and most remotely inaccessible individuals who ever lived. Richard Westfall spent twenty years writing a highly perceptive scholarly biography of Newton, yet confessed, in the first paragraph of its preface, that

The more I studied him, the more Newton has receded from me.It has been my privilege at various times to know a number ofdifferent men, men whom I acknowledge without hesitation to bemy intellectual superiors. I have never, however, met one againstwhom I unwilling to measure myself, so that it seemed reasonableto say that I was half as able as the person in question, or a thirdor a fourth, but in every case a finite fraction. The end result of mystudy of Newton has served to convince me that with him thereis no measure. He has become for me wholly other, one of the tinyhandful of supreme geniuses who have shaped the categories ofthe human intellect, a man not finally reducible to the criteria bywhich we comprehend our fellow beings.”

Newton and Gravity

Cambridge was closed because of the Plague. As the story goes, Newton was sitting under the apple tree outside his farmhouse (shown above) and while watching the apples fall he realized that the force that made the apples fall also made the planets orbit the sun. Using his newly invented Calculus, Newton was able to show that Kepler’s 3 laws of planetary motion followed directly from this hypothesis.

You’re traveling through another dimension. A dimension,not only of sight and sound, but of mind.

A journey into the wondrous land whose boundaries are that of imagination.

Next stop, the TWILIGHT ZONE1Rod Serling

A strange idea required a strange genius…In the gravitational simulation of the attractive behavior between the two bodies shown in the following hyperlink, notice that a changing message must be “communicated” instantaneously between the two participants. The “conversation” never stops…keep coming…sure...nice and easy…alright…now,faster…okay…FASTER!….OKAY,OKAY!

http://www.colorado.edu/physics/2000/applets/orbits.html

In Coming of Age in the Milky Way, Timothy Ferris comments, “… that the Principia left many questions unanswered, and he was forthright in confronting them. Of these, none was more puzzling than the mystery of gravitation itself. If nature operated according to cause and effect, its paradigm the cue ball that scatters the billiard balls, then how did the force of gravitation manage to make itself felt across gulfs of empty space, without benefit of any medium of contact between the planets involved? This absence of a casual explanation for gravity in Newton’s theory prompted sharp criticism: Leibniz branded Newton’s conception of gravity “occult,” and Huygens called it “absurd.” Newton agreed, calling the idea of gravity acting at a distance “so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it,” and conceding that he had no solution to the riddle: “The Cause of Gravity is what I do not pretend to know.”

Toto, I have a feeling we’re not in Kansas anymore…

Dorothy

Action at a distance is a difficulty that needs resolution. I can not do something over in this part of the universe and have an immediate effect in another more distant location. I can not wave my hand here where I sit and expect to have you turn your cheek aside in anticipation of my pate upon it. The message of my intention needs time for it to be delivered across the separation distance between you and I. As the two bodies of the previous hyperlink showed, as one moved the “force” on it changed instantaneously. The message of the gravitational effect traveled with infinite velocity instead of being finite and below the speed of light.

Did you notice at the hyperlink site how this “effect” was present in all directions (both in and out of the demonstration page as well). The mathematical relationship also works regardless of the type of masses involved. A pound of air has the same gravitational effect as a pound of lead. In spite of all of its limitations Newton ideas as expressed in the above simple mathematical terms, allows us to make sense of the world around us. IT WORKS!

Science…Make the metaphors transparent not invisible.

Roger Jones

What is gravity? Its reality is difficult to describe and comprehend. Someone has said the map is not the territory. For our survival and security purposes we map gravity as a “force of attraction” that mutually exerts itself between bodies. We make it tangible by imagining a “gravitational hand” reaching out and pulling upon another object. It is hard to remember that this “hand”, this “force” is not the territory. Albert Einstein problems required a different metaphor for gravity.

Imagine that a bowling ball is placed at the center of a trampoline. The mass of the bowling ball will stretch the fabric and distort the shape of its flat geometry. If conditions are right, it is easy to imagine a tennis ball that is launched in the direction of the bowling ball to become captured by the bigger ball and to orbit the bowling ball on the warped induced trampoline fabric. In this view the invisible “hand” or force of gravity that reaches out is replaced by geometry, a distortion of space-time. It is common to use the above analogy to map this territory. This seems to be an acceptable way for us to wrap our brains around this problem but remember that this analogy is still incomplete…

… gravity extends it “reach” in all directions! Length…Width…Height…Time

Newton’s LawsNewton devised a uniform and systematic method for

describing motion, which we today refer to as the Science of Mechanics. It remains the basic description of motion, requiring correction only at very high velocities and very small distances.

Newton summarized his theory in 3 laws:

1. An object remains at rest or continues in uniform motion unless acted upon by a force.

2. Force is equal to mass x acceleration (F=ma)

3. For every action there is an equal and opposite reaction.

1. An object remains at rest or in constant velocity unless acted on

by a force

2. Force equals mass times acceleration

F = ma

Mass is intrinsic to an object (according to Newton). It’s the object’s budgability.

Acceleration:

Any change in speed and/or direction of motion.

For circular motion:

a = v2/r

Newton’s view of gravity, the “force” metaphor, combined with his formulations about the nature of motion serves us well in providing a way for us to understand why the planets behave in the three ways Kepler described. It now becomes obvious that a planet further removed from the sun than earth should be traveling slower in its orbit than us. As the distance increases the impact of the gravity of the sun will diminishes as shown from the formula in the upper left. If the strength of the unbalanced force upon a planet decreases than the resulting acceleration on the mass will lessen as expressed in Newton’s Second Law displayed in the upper right. Thus the nature of gravity, guarantees that this outer planet will need a longer time to complete its orbit. Newton explains the why behind the how of Kepler’s Third Law.

F = m1·a

To understand the interplay between orbital speed and the achievement of a stable planetary orbit please refer to the Projectiles and Planets section of the hyperlink below.

http://galileoandeinstein.physics.virginia.edu/lectures/newton.html

A planet in circular orbit

Cancel out m1: v2/r = Gm2/r

2

Multiply both sides by r: v2 = Gm2/r

The speed of the planet depends on the mass of the Sun and the planet-Sun distance in a precise way.

m1 = planet’s mass, m2 = Sun’s mass, r = planet-Sun distance, v = speed of planet

Reflections…

The great theories have all been marked by a kind of inevitability. One finds it in great paintings or great poems in which not a single stroke or word can be changed without damaging the whole. This

quality is beauty.

Steven Weinberg

This may have been one small step for a man but what a giant leap for mankind. Rosemary Sullivant captures the impact of this work with these words, “…For centuries before Isaac Newton was born, stargazers saw light but could not understand it…they observed heavenly bodies but could not explain their movements…they felt gravity but could not comprehend it…after Newton they could.”

Imagine the clearest and darkest night sky you have ever seen. It is a glorious sight! Pause for a moment. In the rich blackness that overwhelms the feeble pin points of light, did you detect a flaw in this view? A defect in nature unlike any other experience familiar to us down on the surface. Nothing up there…none of it… falls down…… to here!

That very law which moulds a tearAnd bids it trickle from its source,

That law preserves the earth a sphereAnd guides the planets in their course.

Samuel Rogers, “On a Tear”

The later discoveries of the unknown outer planets confirmed the validity of these theoretically derived truths of Kepler and Newton. How beautiful is this all wonders Timothy Ferris,”Why this should be possible-Why we should be able to find rational laws operating in nature at large, and make some sense of it all-remains a mystery.” No longer does there exist a separation between earth and heaven. Now all is one…Universe…

Nearer the gods no mortal may approach.---Edmond Halley, on Newton’s Principia

The idea of eternal laws of nature is a theological- mechanistic-scientific seventeenth-century mixture. Until you were prepared to believe that the universe was capable of going on for thousands of millions of years in the future, you were open to these kinds of apocalyptic ideas that it was all going to fall apart, because there wasn't anything like laws of nature to sustain our conviction that the thing would keep going.

 

Source: Rupert Sheldrake and Stephen Toulmin

Physics Continuum…Newton’s work is easy to embrace and its clarity is so appealing. It is easy to become infatuated with its grandness as it encompasses so much of the universe. But it is far from being the last word on how it all works. Scientist still are searching for the ultimate language that expresses elegantly the oneness of the universe. Our general day-to-day experience on earth is nicely understood by applying Newtonian Physics. Although it is the physics of daily survival it is not the physics of the micro/macro universe. Here we find that force is external to matter. There is a subject and object. It features a detached,separate and distinct observer. It results in a worldview that is deterministic, mechanistic and it generates a reductionism viewpoint Einstein’s rules derived from relativity for understanding the large scale universe show that space-time is not absolute. Quantum rules that apply to the micro verse attempt to interconnect the dynamic whole. Particles are not seen as isolated entities; rather they are condensations of a continuous field,which is presented throughout space. The whole determines the behavior of the parts. The observer is integrated with the observation. Statistical causality describes behaviors. Thankfully the universe is not easy to comprehend…would we want it any other way?…A universe that was easy to understand would bore us…The bases of these ideas were found in THE TAO OF PHYSICS By Fritjof Capra

Harmony…

Up and Running…

The force is love…may the force be with you…

Credits:Larry Mascotti

Special Assistance:Nancy PoeschelMegan Whaley