A FUNDAMENTAL SYMMETRY PRINCPLE ABSTRACT The mechanics of a TELESCOPE vrs the mechanics of a MICROSCOPE are simple enough, both are similar, though not the same. When applied to a system of bodies in a straight line the mechanics become definative, and a surprise occurs in realizing that the mathematics for the bodies cannot of their own distinquish between the two different mechanical embodiments. FOOTNOTE See after SYSTEM 4 further below, for mathematical examples. ---------------------------------------------- SYMMETRY 1 - A TELESCOPE ARRAY ---------------------------------------------- SYSTEM 1 Imagine a transparent massless Sun moved out to the orbit of Venus, then 3 Sun duplicates positioned in 3 places; at the Venus Perihelion position in orbit (Venus' averaged yearly closest approach to the real Sun), at the Mean of Venus orbit, and at the Aphelion of Venus' orbit (the averaged yearly farthest away from the Sun). Next imagine yourself at the Mean of Earth's orbit (mid distance between Earth's Aphelion and Perihelion), looking at a transparent object at the orbit of the Earth's Moon, in the Moon's mean of orbit. Exclude thermodynamics and simply line up the bodies in a straight line, so that you can sight straight along the base line and see the points of center of each of the bodies lined up precisely as if one, except for their distances apart. You of course are positioned as if at the very center of planet Earth from your observer's position at a standstill, station keeping in the Mean of Earth's orbit. At a far distance, beyond Venus, is Mercury, and the Sun at the solar center. But these two bodies do not count in the imaginary array just outlined, just you the observer, an Earth or Venus sized body in the Moon's orbit, and the three transparent Suns in the orbit of Venus, these comprise the first system. When the Sun is moved from Venus Perihelion to Mean, then from Mean to Aphelion orbital positions at Venus, the body in the Moon's orbit of Earth shifts accordingly in precise hops to accomodate perfect eclipses, ie, that the full cross sectional diameter of the body superimposes the full cross sectional diameter of the Sun in each of the Sun's three positions at Venus. This array as a working apparatus embodies the mechanics of a TELESCOPE, in that the eyepiece at the observer stays stationary (like an astronomer looking through the eyepiece of a long thin telescope in a back yard), while the object being viewed moves in an out (for instance for different planets - or the 3 Suns at Venus), as the adjustable lens (body in the Moon's orbit) moves discretely in and out accordingly, to focus the distant objects, as seen through the fixed unmoving eyepiece of the back yard TELESCOPE. This is the same mechanical embodiment as a mariner's spyglass, which was the same kind of telescope Galileo used. Simple proportional equations can calculate the intervening distances between the bodies; the cross sectional diameters of the focal lens bodies, and the Sun target, in the 3 different positions of the Sun. In order for the system to work perfectly the cross sectional size of the focal lens body must be allowed to flex ever so slightly to accomodate superimposure of the Sun, if the incremental shifts of the focal lens are made to equal radii of a particular focal lens body, for instance, the planet Earth, or Venus, in the Moon's orbit, in which case the focal lens shifts are equal to the radius of a Venus sized planet. In precise working, the flexing (adjustable focal lens cross sectional radius) adjusts (or 'flexes') by no more than the Polar vrs Equatorial radii size of the planet, wherein the radii size of the planet found in the niches created by the skips the focal lens makes along the sighting base line, also flexes by minute quantas exactly equal to the radii sizes (Polar vrs Equatorial) of a focal gap the size of planet Venus. These duo synchronous 'flexings' can be called a 'hyper fine distinction' that defines the most fundamental functions of such a focal lens array. SYSTEM 2 The whole array can be cloned to operated mathematically in exactly the same way, but perform functionally in a different way, by moving the whole system (the array between Earth and Venus) in toto to the center of the solar system, re-erected anew inside the orbit of Mercury, this time with you the observer again stationary but now at the very center of the Sun, and 3 massless Suns again in a Venus orbit whose orbital distance from the real Sun is now only a fraction of before, that is, at an orbital length equal to the original short distances between Earth and Venus. Effectively, the working principles are still the same as a mechanical embodiment of a TELESCOPE, as a new massless Sun is moved in and out at the new Venus-like orbit (inside the orbit of Mercury), with you as the stationary observer viewing from the center of the real Sun. Relative to the Sun, there is a Venus Perihelion, Mean, and Aphelion positions, just the same as in the real Venus orbit. When the array is moved in toto to the innermost region of the Solar System with you the observer now at the center of the Sun, what happens is a subtle difference, relative to a 4th body introduced into the system in the first array (SYSTEM 1), in which the real Sun is the 4th body, and relative to it, the real Venus Perihelion of orbit is closest to the real Sun, yet farthest from you when you are further out in the real Earth's orbit. In the psuedo Venus orbit re-erected close in around the Sun, inside the orbit of Mercury, there is a change in terms. That which was the original Aphelion of Venus, now becomes the Perihelion of the new Venus, and visa versa for the real original Perihelion of Venus. Here is a schematic in the switcheroo in terms: SYSTEM 1 - schematic terms for 4 body system - TELESCOPIC 1 2 3 4 Observer at Earth | target at Venus | focal lens Moon | | | | ||| | | | *...|*|..............* * * ..................................* ||| | | | Sun | | | A 0 Perihelion .....................| | .........................| | .............................| LONGEST target length from observer SYSTEM 2 - schematic terms for 3 body system - TELESCOPIC target at new Venus Earth | | | focal lens Moon Moon | | | ||| Sun *....*......................... * * *...............|*|...* | | | ||| | | | | observer A 0 Perihelion | |.............................. | |.......................... | SHORTEST target length from observer |...................... In the TELESCOPE array, local terms ABC switch to become CBA when the system observer is switched from body 1 to body 4. Otherwise the global mechanics of the system array remain unchanged, still a TELESCOPE, except the system changes globally from a 4 body to a 3 body fundamental array. ABC, are the Aphelion = A, Mean = B, and Perihelion = C, of the original system's Venus orbit (SYSTEM 1). And CBA, are the Aphelion = C, Mean = B, Perihelion = A, of the new Venus system re-erected close to the Sun (SYSTEM 2). IN ABSTRACT: (LOCAL SYMMETRY SWITCHES HERE) | 1 2 3 | 4-body SYSTEM 1 4 | OBSERVER 1 TARGET 1 A B C A 0 P | FOCAL 1 | | | | | | | ||| | | | | | | ||| SUN *...|*|..............* * * ....* * *...............|*|...* ||| | | | | | | ||| | | | | | | FOCAL 2 A 0 P C B A TARGET 2 OBSERVER 2 3-body SYSTEM 2 3a 2a 1a SUMMARY: In switching the observer in a 4-body TELESCOPE system, the global system switches to a 3-body global system, and the fundamental mechanics remain unchanged, it is still a TELESCOPE system. ---------------------------------------------- SYMMETRY 2 - A MICROSCOPE ARRAY ---------------------------------------------- SYSTEM 3 Picture, now, the Earth-Moon-Sun system of Total Solar Eclipses, as currently exists in the solar system. The observer is at Earth, the Moon is the focal lens, and the far distant Sun is the target. Since the Earth has eccentricity in orbit, it moves in and out yearly carrying you the observer along with it on an occilating yearly journey, in which the Moon discretely shifts in and out accordingly in its orbit to accomodate Total Solar Eclipses. Since you, the observer, are moving in and out, rather than the target moving in and out, this, the Total Solar Eclipse system, embodies the fundamentals of a MICROSCOPE in that the mechanics of a MICROSCOPE are involved, that is, you the eyepiece move in and out, to accomodate a target (Sun) that is always fixed on the microscope's immovable viewplate. In this instance the MICROSCOPE array is entirely unlike either of the Venus formed TELESCOPE arrays cited above as SYSTEM 1 and SYSTEM 2. Also, it is a fundamental 3-body system only. SYSTEM 4 Now, alter your picture. Do the same as you did with SYSTEM 1 with you at Earth orbit looking at massless transparent Suns projected into the nearby orbit of Venus, in which you then picked up and moved that system intact to the center of the Solar System to create SYSTEM 2. And so, do the same, only this time pick up the Earth-Moon part of the Total Solar Eclipse system and move it (effectively you the observer) to the center of the Solar System and bring along the Moon in orbit, which will now be orbiting roughly half way inside the Sun toward its center. That doesn't matter, ignore the real Sun as if it wasn't there, and move 3 massless Suns out to the orbital positions of the new Earth, that is, to the new Earth's new Perihelion, Mean, and Aphelion positions, just as you did with Venus. In fact now you have exactly the same kind of system as you had with new Venus (SYSTEM 2), with you the observer stationary at the Solar center, in the middle of the stationary real Sun, and massless Suns moving in and out as targets in the orbit of the new Earth. Except, rather than locating in very forshortened new orbits around the Sun on hte inside of Mercury's orbit, the 3 new massless Suns become projected into orbitals (as SYSTEM 4) which are the same as those you occupied when observing Total Solar Eclipses out at Earth in SYSTEM 3. ---------------------------------------------- FUNDAMENTAL GLOBAL SYMMETRY SWITCH ---------------------------------------------- CONVERTING A MICROSCOPE SYSTEM TO A TELESCOPE SYSTEM, BY INTERCHANGING THE LOCATIONS OF THE OBSERVER AND TARGET. Notice at once, that switching the positions of observer and target of a MICROSCOPE symmetry system, as just described imediately above, instantly switches the system from a MICROSCOPE to TELESCOPE mechanical assembly, a global change, even though other aspects of the system otherwise remain unchanged. For instance, locally it is still a 3-body system, and postions marked ABC for Aphelion, Mean, and Perihelion for the MICROSCOPE system still continue as ABC for the new TELESCOPE system, when you the observer are now at the Solar System's center. In other words, SYSTEM 4 has fundamentally transformed from a MICROSCOPE array to a TELESCOPE array identical in kind to global SYSTEM 2. ---------------------------------------------- FUNDAMENTAL DIFFERENCES ---------------------------------------------- At this point, it is easy to reveal fundamental differences between MICROSCOPE and TELESCOPE arrays, as modelled by the Solar System. Fundamentally, in a MICROSCOPE system, the focal lens stays with the observer, who is travelling in and out, as modelled by the Total Solar Eclipse system for the Earth and Moon. Whereas, in a TELESCOPE system (as modelled by massless Suns projected into the nearby orbit of Venus and viewed by an observer at a stationary Earth), the focal lens still stays with the observer, who is now locked stationary in one position only, unmoving. When the observer and target switch places in the MICROSCOPE system, the highly mobile Moon and Earth (observer and focal lens), become immobile at one position only, and so become TELESCOPIC in fundamental mechanics, due to the switcheroo. Here is how the global switch looks in simple schematic form: SYSTEM 3 - schematic terms for 3 body system - MICROSCOPIC 1 2 1 2 1 2 3 OBSERVER 1 - AT EARTH A B C | moon | moon | moon (focal lens) TARGET 1 | | | | | | * *| * * * |* ....... .............................* | | | | | | SUN | | | A 0 Perihelion |........... shortest target length from observer |............................ |................................. The Moon orbit travels in and out long distances, in synch with you the observer moving in and out in accord with the eccentricty of Earth. SYSTEM 4 - schematic terms for 3 body system - MICROSCOPIC system converted to TELESCOPIC 3a 3a 3a 2a 1a TARGET 2 - AT EARTH A B C | | | OBSERVER 2 | | | ||| * * * .......................................|*|...* | | | ||| SUN | | | Moon A 0 Perihelion focal lens |........... shortest target length from observer |............................ |................................. The Moon orbit stays locked, immobile, in synch with you the stationary observer at the center of the Solar system. ---------------------------------------------------- FUNDAMENTAL NON-SYMMETRICAL MATHEMATICS ---------------------------------------------------- Examples taken from the PERFECT file (Perfect.txt). EXAMPLE 1 - a TELESCOPE system is arrayed. Moon orbit - 0 Venus POLAR ----------------------------------- x Sun radius Earth orbit - Venus PERIHELION = Earth POLAR radius Moon orbit - 2 Venus EQUATORIAL ----------------------------------- x Sun radius Earth orbit - Venus APHELION = Earth EQUATORIAL radius For a stationary observer at Earth, observing a mobile target Sun in the orbit of Venus, in this case at Venus Perihelion, then Aphelion. Proportion 1 calculates a resulting focal lens cross section diameter (Earth POLAR radius) located at the Moon's Mean of orbit. In this emodiment, there is no incremental shift of the focal lens (Earth sized) inward from the Moon's Mean of Orbit. When the array is viewed with a massless Sun at the Aphelion of Venus' orbit, Proportion 2, the Earth shifts inward toward Earth by two increments equal to Venus' Equatorial Radius, and swells (flexes) to an Equatorial sized Earth, to accomodate the more near position of a same sized Sun seen larger, closer to Earth. EXAMPLE 2 - a MICROSCOPE system is arrayed. Below: For a mobile observer at Earth, observing a stationary target Sun at the center of the Solar System (a classic Total Eclipse embodiment). The proportion calculates a resulting focal lens cross section diameter (Moon POLAR radius) located at the Moon's Mean of orbit altered by + 1 increment equal to the Moon's Polar Radius, then - 3 Earths of Earth Polar radius size), which moves the Moon incrementally in closer to the Earth when a total eclipse is viewed at a Perhelion position in Earth's orbit. When viewing is from the Aphelion position of Earth, only 1 Earth sized increment occurs, of Earth EQUATORIAL size, for locating a Moon of EQUATORIAL radius size in accord with viewing a Sun which is farther away. MOON orbit + 1 Moon POLAR - 3 Earth POLAR ----------------------------------------- x SUN radius Earth PERIHELION = Moon POLAR radius MOON orbit + 1 Moon POLAR - 1 Earth EQUATORIAL ----------------------------------------- x SUN radius Earth APHELION = Moon EQUATORIAL radius Here again, for reference, is EXAMPLE 1. Moon orbit - 0 Venus POLAR ----------------------------------- x Sun radius Earth orbit - Venus perihelion = Earth POLAR radius As you can see, except for obvious different terms, the proportions are mathematically identical, ie. the same equation works for both systems. You cannot therefore tell which kind of system (TELESCOPE or MECHANICAL) is being factored by the equations, in such proportionate forms. The mechanical aspects of the array are hidden from view by the nature of such proportions and their expressed simple yet utterly accurate equation form. In form, here is the proportion as a fundamental: Focal lens position -------------------------- x Target SIZE Observer position = Focal lens SIZE This form can calculate any eclipse array you want, regardless of it being TELESCOPIC or MICROSCOPE in mechanical embodiment. For the Solar System, a proviso is that calculations have to be done to double precision (to at least 12 significant digits of accuracy), otherwise absolutely nothing is seen in the results. DONE. Greydon Moore Greely (south of Ottawa) (former address circ. year 2000). September 9, 1997. greydon@look.com