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Continue tellurion assembly, begin solar and lunar eclipse demo - November 2015

This month we continue the fabrication of the tellurion complication.

 

These photos show the central mounting for the tellurion. It can be removed as a single unit and released with a simple twist.

Buchanan now continues with the moon armature. The first photo shows one of three holes being drilled for screws that will secure the hollow post upon which the moon’s mounting will slide. Notice how close the drill is to the hollow post, next a few of the completed components with the hollow post shown. The third photo shows a spring that will bias the rod upon which the moon is secured within the hollow post. That spring is needed to hold the moon against the node ring upon which it will ride. Most tellurions are horizontally mounted so the weight of the moon and its mount use the force of gravity to ride on the node ring. But since this one will be rotated 900 we must use a spring to keep it seated on the ring.

 

The slider is now mounted within the tube. Notice that a jewel is used here. We use no metal-to-metal contacting surfaces where there is sliding or rotational surface contact. Those would need oil, and we are avoiding oil in this machine. The next photo shows the beginnings of the artwork for the ring set that will surround the Earth globe. Notice the plastic indexing plate behind the drawing to aid in the accuracy of the artwork.

 

The armature is now beautifully shaped ‘comma’ along with the rest of the parts for the moon apparatus. Note in the second photo the jewel ‘foot’ that is attached to the spring-loaded rod upon which the moon will be fixed. That foot will slide along the node ring. The reason we must use a sliding scheme rather than a wheel is that the moon rotates as it orbits along the node ring, so a wheel would not stay aligned. A roller within a cup was considered, but the diminutive size and the susceptibility of the ball jamming and simply sliding itself on the smooth ring resulting in a metal-to-metal frictional surface made that option risky and impractical.

 

The completed Moon armature assembly ready for installation into the rest of the tellurion. Next the unit is installed. Notice the guide fork installed on the tube that has the sliding rod for the Moon. The circular disc is the node ring which is angled at 5.140 reflecting the tilt of the Moon’s orbit to the Earth along the ecliptic. This ring is what will move the Moon up and down on the jewel slider as it orbits the Earth. That ring also rotates once every 346.6 days representing when the nodes makes a full circle in relation to the Sun. The combination of this cycle and the cycle of Earth’s orbit around the Sun in 365.24 days produces the Saros cycle that closely predicts the repetitive pattern of just over 18 years of where an eclipse will occur on the Earth.

The first photo shows the top set of nested bearings used in this assembly. The center photo shows part of the curvilinear multi-level frame, next a mockup of the node dial.

 

I received several photos of the tellurion, in particular Buchanan’s design for the moon’s node cam disk. In a similar nod to prior makers, that disk has a thin enamel dial. He has written “Ascending Node and “Descending Node”. The actual point on the cam where this occurs is marked with a diamond pattern identical to that found on the main tellurian dial. It is an elegant design and ties in nicely with the main dial work. He indicated that there will need to be a counterweight to the earth/ Moon system attached to the rotating armature. He then suggested that we use a sickle-shaped weight with an enamel cover as a counter-point to the enamel dial ring for the Moon’s nodes. All of the planets, Moon, Sun and Earth are just temporary mockups at this point.

 

At that point I was beginning to wonder if the node ring was looking a bit too heavy; making the entire Earth/ Moon system look cluttered; especially if an enamel covered sickle counterweight is included at the opposite end of the armature. This was especially brought to my attention with the photos of the tellurion mounted upon the clock. I suggested that we try eliminating the enamel dial ring entirely; replacing it with a thin rim upon which the moon would ride to give the inclined lunar orbit. The position of the ascending and descending nodes, and the position of the Moon’s orbit relative to the ecliptic could be denoted by the astrological symbol for the dragon’s head which looks very much like the Greek letter Omega. That sign in the inverted direction depicts the descending node.

 

An overall front elevation of the dial work. The next photo shows the detailed turning for each of the two inner planet stalk mounts.

 

Buchanan now has substituted a thin rim for the the enamel dial chapter ring. I like this much better. It eliminates the clutter around the Earth / Moon system. I also asked that the rim have a rounded edge for the perimeter, like a steering wheel. We will still be able to include the information on the ascending, descending nodes within the framework of the eclipse prediction indicators that are yet to be designed. We will also try to hide the sickle counterweight behind the main dial. The globe is now painted white to simulate the eventual Walrus tusk material which will be scrimshawed to reveal continental and longitude, latitude details. This is in keeping with our intention to have all of the celestial bodies made of natural materials.

  

The tellurion assembly is now installed within the context of the rest of the machine. There are yet many other additions to be made to this complication before it is complete.

Now begins the work on the solar and lunar eclipse prediction system.

I will now describe the components involved with the eclipse prediction system. This is an example of our coming into a good idea as the machine is being built. We had not thought of having such a capability during the initial design phases of the tellurian. But as Buchanan thought through the elements needed to produce an eclipse, he began to formulate a way to incorporate this important complication within the structure of the tellurion. This process also occurred with the addition of the dials for the Moon's synodic and sidereal orbital periods.

There are two sector ‘windows’ that are attached to the base of the mounting for the Earth, and parallel to the ecliptic for the Earth and these do not move. The ecliptic is an imaginary line running from the center of the Sun to the center of the Earth. As the Earth rotates that line traces out a circle around the Earth. The slightly larger window resides between the Earth and Sun and is used for the solar eclipse reading. The other is 1800 around, is a bit smaller and is used for the lunar eclipse reading. Each window is 34.340 and 22.960 around the circumference of the Earth. Since there are 365.242 days in the tropical year, these translate into 32 and 22 day windows. The two windows represent what is known as the ‘eclipse seasons’ when the Moon’s nodes are close to the parallel line between the Sun and Earth, the ecliptic, this is about plus or minus 180 either side of a node. In the tellurian the Moon rides upon an inclined circular track that is tilted 5.140 in relation to the Earth’s orbit around the Sun, the ecliptic. A node is where the Moon’s inclined orbit crosses the ecliptic. This occurs twice per orbit of the moon and is known as rising and falling nodes depending on whether the Moon is rising, northward or falling, moving southward beneath the ecliptic. The Moon’s orbit also has an 18.6 year precession, where the locations of the nodes make a complete orbit also known as the Saros cycle. This is 19.60 per year. There is a set of hands attached to midpoints between the highest and lowest points on the tilted track indicating the nodes. There is also a hand located under the Moon’s support armature and it has an orbit of 27.322 days, the sidereal month.

A solar eclipse occurs when the node hand is within the eclipse season window and the Moon hand is directly between the Earth and Sun. That is the Moon is very near a node and directly between the Sun and Earth, otherwise it would be a regular New Moon when not aligned on a node. The eclipse window covers when an eclipse would be visible somewhere on the Earth all the way from the northern to the southern latitudes. The windows have a scale in degrees that will allow one to directly read at what latitude the eclipse should be visible. The Earth will have surrounding rings showing the degree of latitude. There will be an indicator telling if the degree reading is north or south of the equator. The same conditions apply when the Moon is on the opposite side of the Earth for lunar eclipses. Given the diminutive size of this whole arrangement of machinery the accuracy of the predictive qualities of when and where a solar or lunar eclipse will take place is somewhat limited. But it will make for a beautiful demonstration! At the end of this segment is a detailed explanation of the why and how solar eclipses happen. Conditions for an eclipse.

 

The artwork for the Earth latitude and longitude rings is now complete. One must remember that these are very small, just over 1.5” or 4 cm in diameter and the surface upon which the numerals are engraved only 2 mm wide. The first is demarked in degrees 0 through 180 running clockwise and anticlockwise and is the equatorial ring. This is the longitudinal ring. The second is divided in quadrants with 0 through 90 degrees. The letters CAP, for the Tropic of Capricorn and CAN for the Tropic of Cancer at the 20 degree locations. This is the latitudinal ring.

These six photos show the engraving process for the Earth rings. At this small scale a computer controlled engraver was the only practical solution. After the rings are engraved they are milled out from the brass blank.

 

The small scale is revealed by the first photo; no larger than a wristwatch. Next some of the finished engravings on the rings.

The initial trial fitting of latitudinal and longitudinal engraved rings. Notice the topography of the land masses.

Here we see the drive for earth’s rotation, next the axis. All pivots for the gears and axis are jeweled.

 

The earth support mounted to the tellurion, next the Earth mounted within the rings. The knurl knob allows one to position the inner two rings at will. This will allow the user to set the inner ring at any location for the ‘zero’ time reading. They also serve to interpolate between the latitude degrees readings given from the eclipse season window onto the actual location of the Earth’s surface. Buchanan has decided to fill in the continental, longitude and latitude lines on the globe. Again this is merely a rough mockup.

At this juncture we will also be adding another two complications to the tellurian, two dials to indicate the synodic and sidereal orbit of the Moon.. The synodic dial will have 29.53 days and the sidereal would be 27.32 days. The dials will move in relation to each other and be located at the base of the earth.

 

The diagram explains the difference between the synodic and sidereal lunar months. This strongly parallels the relationship between sidereal and mean solar time. In both instances the sidereal period is related the movement of a body, in this case the orbit of the Moon as it relates to the distant fixed stars. In this case the orbit of the Moon as it relates to the fixed stars takes 27.3 days, whereas it takes 29.5 days for the Moon to go from one New Moon (or Full Moon) to the next New Moon. This occurs because of the additional distance the Earth, and therefore the Moon, has rotated around the Sun. Next the artwork for the two dials.

 

The basic components for the eclipse prediction system are now in place, albeit in a preliminary mockup form. The first photo shows the two eclipse season window sector dials, these are 1800 from each other with the other just above the moon drive wheel. The small hand within the eclipse season sector dial is attached to the Moon node ring at the point of one of the nodes and rotates counterclockwise a full circle one every 346 days, another hand is on the opposite side of the ring. It takes 346 days for the nodes to make a complete circle relative to the Sun. The next photo shows a hand connected to the armature of the moon which rotates clockwise once every 27.3 days, the sidereal period, the Moon's orbit in relation to the stars. The combination of these two hand indicators upon the sector dial along with the latitude rings will allow one to predict where a solar or lunar eclipse will appear on the surface of the Earth. The tellurion is connected to the calendar assembly as well as the world time dial, so in the celestial demonstration mode one will be able to predict down to the hour when an eclipse will take place. Using these two systems together we have the ability to predict when and where these events will occur. In both photos we see the dial mockups for the synodic and sidereal moon orbits.

 

In this video for the first time we demonstrate the interaction between the Moon's node ring indicator, the season eclipse window and the position of the Moon in predicting eclipses. The system is very preliminary and there are still obvious glitches, but the basics are here. The latitude rings will later be used to interpolate the position on the face of the Earth an eclipse will take place as well as the length of its path.

 

Now begins the fabrication of the components for both the eclipse prediction function and the synodic, sidereal Moon orbit dial work. In these photos we see the dial base as well as the tiny pillars that will support that dial being incorporated into the Moon armature for the synodic, sidereal dials. Even at the scale of one millimeter, the pillars are finely turned. It is at these scales that the workmanship and attention to detail separate this clock from most others that have been built. 

The dial base is now installed on the tellurion. Note the hand rendered drawings in the background, the same design methods used by horologists for millennia. While modern methods are not eschewed, the vast majority of this project is done in the traditional ways.

Here the node indicator hand is being fabricated. First the steel blank is drilled and then positioned upon the node ring for attachment. The size and tolerances here are extremely small. 

 

The eclipse season windows begin from a thick brass sheet. The next two photos show the turning of the flat stock into a dish-shape with a tall lip.

 

That lip around the edge of the dish will become the individual season windows with the balance of the rim removed. The mockup for the eclipse season windows support piece is shown above the dish with the node ring placed within the dish to check for fit in the second photo before the dish is shaped into the final part.

 

First a drawing for the eclipse season window support is prepared with the dish next carefully cut away. While the location of the windows stayed in the same positions as that on the mockup part, the actual configuration of the part took a decidedly more decorative turn. Notice how the raised rim of the dish now becomes the area where the dial frames are located. Other clockmakers might have taken the route of making the windows separate from the support frame and simply soldering the two together to avoid the extra complex machining steps. No such shortcuts are in this project.

   

Now the eclipse season windows and support piece are checked for fit within the tellurian. Next holes are drilled and tapped for screws to secure the eclipse season sector dials.

Below we will see Buchanan's use of computer aided design and manufacture, CAD-CAM, in the creation of the Earth's rings and dial work for the eclipse prediction mechanism. Up to this point there has been virtually no employment of the technology. I have emphasized in the past the hand-made nature of this project and it remains so. But in some limited applications the use of this technology allows us to do things that otherwise would be impossible or nearly so as in the case of the Earth globe. Or as it allows us to make something with a high quality standard that would be difficult by hand as in the case of very small scale engravings.

 

Buchanan uses a computer simulation to determine the dial layouts for the solar and lunar eclipse season dials. The first screen shot represents a solar eclipse, the second a lunar eclipse. Both the Moon and Earth are divided into 24 sections equaling 150 per section. The solar eclipse season is 33 days per year with the lunar season being 22 days. These are the times where the Moon’s nodes are close enough in alignment to the Sun’s ecliptic that the Moon will cause a partial to full solar eclipse or in the case of a lunar eclipse the Earth’s umbra will cause a partial to full eclipse of the Moon. The node ring revolves once every 346 days which is the time for the position of the Moon’s rising or falling node to make a complete orbit all the way back to that same position in relation to the Sun. Each season’s length translates into 33 days/346 days x 3600 = 34.340 and 22 days/346 days x 3600 = 22.890 of a full orbit of the earth around the Sun. These arcs are reflected within the circled areas of the photos and translate into the size of each dial sector plate. The parallel lines from 600 North to 600 South are projected onto the sectors and determine where the dial degree indications will be located. It is not a linear scale as the lines are closer together near the edges of each dial than the center.

 

The two sector dials with corresponding demarcations according to the designs described above appear in these two screen shots for the computer controlled engraver. Note how the degree spacing is spread out as they move from the center to the edges of the dial. This has been mathematically calculated as the inverse of the line spacing seen on the computer screen shots above.

 

The two node ring dials are now designed as shown in these two screen shots. These indicate whether the node is ascending or descending and whether the eclipse will appear north or south of the ecliptic. 

 

The first photo shows one of the eclipse window dials being engraved. The second shows a completed node ring dial engraving before removal from the brass blank. Buchanan has silvered the area and filled the engraved lettering with black wax to make them more legible for the photo.

After the engraving is finished, the parts are milled free of the surrounding supporting material.

  

These videos show the computer controlled engraving tool used to create the script for the node ring sector dials. In the first video the outline of the dial is being milled out.

 

This video shows the computer controlled machine and the computer screen in real time as it creates the tiny script used on the eclipse window and node ring dials as well as the degree demarcations on the latitude and longitude Earth rings all used in our eclipse prediction assembly.

 

The completed dial work engraving.

Here we see how Buchanan cuts a tiny slot in the head of a small screw using a precision hand fret saw. The tiny screw is held in the vise by a lathe collet within a jig that has the two upright pins. Those keep the thin saw blade straight and perfectly aligned down the center of the screw head. The head is less than 1 mm in diameter. These screws will secure the dial work. Here we are back to hand work and elbow grease.

The dial work shown mounted to their respective positions. The first photo shows one of the season eclipse window dials. Next we see a node dial plate secured to the node cam ring. Notice the clever way Buchanan secures the plate, third photo. He uses the rim pointer which is secured to the underside of the rim in the first photo with two tiny screws and then uses the dark area of the dial plate pointer on the other side to hide the screw that secures the plate to the steel back of the rim pointer. This not only secured the dial plate, but allowed it to rest upon one of the spokes and below the edge of the perimeter rim; giving the entire presentation a nice reveal under the rim. This is necessary as the Moon must ride upon this perimeter without obstruction. There is no other way I could think of doing this without the evidence of screws, say on the rim’s outside perimeter secured to the edge of the dial plate. The alternative would be the use of adhesives which is not allowed in this project, all parts have to be mechanically secured in a reversible fashion.

 

The first photo shows all four dials in place, the pair of node ring dials at the three and nine o'clock positions and the pair of the eclipse season window dials at the six and twelve. Next the node dial is rotating counterclockwise into place over the eclipse season window dial. Nearby is the Moon, which at this point does not have its indicator hand yet installed moving clockwise. When the Moon passes over the 'E' tab, an eclipse takes place. That tab represents just over 40 representing the time of a typical eclipse of about 8 hours.

Conditions for an Eclipse:

One can predict eclipses by understanding the conditions that make them possible. As you begin to think about these conditions, be sure you are aware of your point of view you must imagine that you can look up into the sky from your home on Earth and see the sun moving along the ecliptic and the moon moving along its orbit.

Since there are two nodes in the Moon’s orbit there will be at least two solar eclipse seasons per year and with the moon on the opposite side of the Earth, two lunar eclipse seasons. So why do these eclipses seem so rare? The reason is that in the instance of a solar eclipse the shadow of the moon on the Earth is extremely thin and the duration of the eclipse very short. A typical track for a full eclipse is only 100 to 150 miles wide (161 to 240 km) depending on how close the Moon is to perigee and about 1000 miles long (1610 km) before the show is over. Although a solar eclipse occurs about twice yearly, a given place on Earth only averages one total eclipse of the Sun every 360 to 410 years.

Following are descriptions and diagrams to illustrate the concepts.

 

Figure 1a and b. Eclipses can occur only near the nodes of the moon’s orbit. (a) A solar eclipse occurs when the moon meets the sun near a node. (b) A lunar eclipse occurs when the sun and moon are near opposite nodes. Partial eclipses are shown here for clarity. Next an animation of this.

Eclipses can only occur when the sun is near one of the nodes of the moon’s orbit. A solar eclipse happens at new moon if the moon passes in front of the sun. Most new moons pass too far north or too far south of the sun to cause an eclipse. Only when the sun is near a node in the moon’s orbit can the moon cross in front of the sun, as shown in Figure 1a. A lunar eclipse doesn’t happen at every full moon because most full moons pass too far north or too far south of the ecliptic and misses Earth’s shadow. The moon can enter Earth’s shadow only when the shadow is near a node in the moon’s orbit, and that means the sun must be near the other node. This is shown in Figure 1b.

So there are two conditions for an eclipse: The sun must be crossing a node, and the moon must be crossing either the same node (solar eclipse) or the other node (lunar eclipse). That means, of course, that solar eclipses can occur only when the moon is new, and lunar eclipses can occur only when the moon is full.

Figure 2a and b. Eclipses can occur only near the nodes of the moon’s orbit. (a) A solar eclipse occurs when the moon meets the sun near a node. (b) A lunar eclipse occurs when the sun and moon are near opposite nodes. Partial eclipses are shown here for clarity

The view from Space:

Change your point of view and imagine that you are looking at the orbits of Earth and the moon from a point far away in space. You would see the moon’s orbit as a small disk tipped at an angle to the larger disk of Earth’s orbit. As Earth orbits the sun, the moon’s orbit remains fixed in direction. The nodes of the moon’s orbit are the points where it passes through the plane of Earth’s orbit; an eclipse season occurs each time the line connecting these nodes, the line of nodes, points toward the sun. Study Figure 2 and notice that the line of nodes does not point at the sun in the example at lower left, and no eclipses are possible. At lower right, the line of nodes points toward the sun, and the shadows produce eclipses.

The shadows of Earth and moon, seen from space, are very long and thin, as shown in the lower part of Figure 2. It is easy for them to miss their mark at new moon or full moon and fail to produce an eclipse. Only during an eclipse season, when the line of nodes points toward the sun, do the long, skinny shadows produce eclipses.

 

Figure 3. A calendar of eclipse seasons. Each year the eclipse seasons begin about 19 days earlier. Any new moon or full moon that occurs during an eclipse season results in an eclipse. Only total and annular eclipses are shown here. Figure 4. The Saros cycle at work. The total solar eclipse of March 7, 1970, recurred after 18 years 11⅓ days over the Pacific Ocean. After another interval of 18 years 11⅓ days, the same eclipse was visible from Asia and Africa. After a similar interval, the eclipse will again be visible from the United States

If you watched for years from your point of view in space, you would see the orbit of the moon precess like a hubcap spinning on the ground. This precession is caused mostly by the gravitational influence of the sun, and it makes the line of nodes rotate once every 18.6 years. People back on Earth see the nodes slipping westward along the ecliptic 19.4 per year and the sun takes only 346.62 days (an eclipse year) to return to a node. This means that, according to the calendar, the eclipse seasons begin about 19 days earlier every year Figure 3.

The cyclic pattern of eclipses shown in Figure 3 should give you another clue how to predict eclipses. Eclipses follow a pattern, and if you were an ancient astronomer and understood the pattern, you could predict eclipses without ever knowing what the moon was or how an orbit works. All you need know is the cycle.

 

The Saros Cycle:

Ancient astronomers could predict eclipses in a crude way using the eclipse seasons, but they could have been much more accurate if they recognized that eclipses occur following certain patterns. The most important of these is the Saros cycle (sometimes referred to simply as the Saros). After one Saros cycle of 18 years 11⅓ days, the pattern of eclipses repeats. In fact, Saros comes from a Greek word that means “repetition.”

The eclipses repeat because, after one Saros cycle, the moon and the nodes of its orbit return to the same place with respect to the sun. One saros contains 6585.321 days, which is equal to 223 lunar months. Therefore, after one Saros cycle the moon is back to the same phase it had when the cycle began. But one saros is also equal to 19 eclipse years. After one Saros cycle, the sun has returned to the same place it occupied with respect to the nodes of the moon’s orbit when the cycle began. If an eclipse occurs on a given day, then 18 years 11⅓ days later the sun, the moon, and the nodes of the moon’s orbit return to nearly the same relationship, and the eclipse occurs all over again.

Although the eclipse repeats almost exactly, it is not visible from the same place on Earth. The Saros cycle is one-third of a day longer than 18 years 11 days. When the eclipse happens again, Earth will have rotated one-third of a turn farther east, and the eclipse will occur one-third of the way westward around Earth Figure 4. That means that after three Saros cycles—a period of 54 years 1 month—the same eclipse occurs in the same part of Earth.

 

Figure 5. This graphic shows the path of solar eclipse over the surface of the earth over the past 100 years.

While Figure 4 shows a few thin tracks that are produced during a four year saros cycle, over a very long period of time nearly the entire surface of the earth does experience an eclipse, Figure 5.

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