Make a Tellurion (sun-earth-moon Orrery) for Your Kid

A tellurion is a module for simulating the movement of earth and moon. This kind of module can be found in museum, but seldom seen in market. Some simplified version of tellurion can be found on internet, however a complete (almost) tellurion module was seldom made by DIYers. In this manual, I will explain how I designed (original) and made the tellurion using material bought from internet stores. The total cost without shipping fee is around $80, which includes gears, copper tubes, bearings, motor, LED, and 3D printed parts. To assemble the tellurion may need 5+ hours. All design use the free online 3D tool onshape.

My son Linxi likes knowledge about solar system a lot. I found a video series about solar system for kids on Youtube, and my son watched them all, again and again. One day, I found a video about wooden tellurion holzmechanik, which inspired me to make one for my son.

The design of the tellurion from holzmechanik is great: simple and elegant. However I don’t have tools to cut wooden gears as shown on the video. Besides, the earth doesn’t spin, which is a pity (I know to add this feature will need more gears, which will weaken the simplicity and elegant of the design)! However, a spinning earth can demonstrate how day and night shift. So, I think that feature must be kept.

The design of Solar System Orrery inspired me a lot. However, the sun in that design will spin, which not match with the truth. But the design of 3D sun with LED gave me new idea to make the sun of my tellurion model illuminate.

Watched more videos, I found that the orbit plane of moon is inclined to the ecliptic by about 5° , and that’s the reason why lunar eclipse occurs (shame! I don’t know that before). So this feature is also very important, must have.

So, my tellurion must have the following features:

• The earth will spin
• The moon rotate around earth with 5 degree inclination
• Sun is a light bulb.
• Axis of earth always point to Polaris.

With above feature, the tellurion can demonstrate day and night shift, seasons change, sun and moon eclipse and moon phases.

There are a lot orrery and tellurion models on **Youtube**, most of them were made in copper, which I don’t have tools to make myself. And I don’t have tools to make wooden gears neither, so I decided to make the tellurion using acrylic. I don’t have tools to cut acrylic neither, but there are many web stores selling this service.
The 3D design for gears and 3D printed parts are available. Note, when cut the gears using laser cutter, the width of the laser should be considered.

• To 6mm coper tube: the outside diameter is 6mm, and the inside diameter is 3mm. and the 3mm tube's outside diameter is 3mm, inside diameter is 1mm. You may need sandpaper to polish the 3mm tube to let it spin smoothly inside of the 6mm tube.
• The ball bearings' size are: 6mm (inside) x 13mm (outside) x 5mm (height) and 3mm (inside) x 8mm (outside) x 4mm.
• The pressing bearings' size is: 7mm (inside) x 17mm (outside) x 6mm (height).
• Acrylic glue

You can use other sizes of the tubes and bearings by modifying the design which I think is always necessary. Note: as "the_tool_man" mentioned, using bushings instead of ball bearings may solve the backlash problem, and I really hope you can have a try.

• Plate A & gear B belong to moon part, they are glued together, and spin around their axis (tube).
• Gear C & D are glued together and fixed to the axis. So they will not spin. When the support arm rotate with its axis, due to gear C is fixed, so gear B will start to rotate, so the plane A. This will simulate the rotation of moon to earth.

The left gear to the biggest gear is designed for moon. Moon has a period about 27.32, so moon will have 365.25/ 27.32 = 13.369 rounds a year. The ratio of diameters of the two gears should be 13.369. We can’t have exact ratio due to the number of gears’ teeth have to be integer. So I wrote a script (in R) to find the best gears:

for (x1 in 110:135) {
  for (x2 in 8:12) {
    ratio <- x1/x2
    if (abs(ratio-R) < d) {
      print(abs(ratio))
      d <- abs(ratio-R)
      print( paste(d, x1, x2, collapse = "  " ))
    }
  }
}

Run above script we can get result:

[1] 13.33333
[1] "0.0359931673987308 120 9"
[1] 13.4
[1] "0.0306734992679356 134 10"

So, the best gears are 134 & 10, however, the diameter is a little bigger (268 cm), so I choose the pair: 120 & 9.

• Gear D, E, F, G and H were designed to make sure that gear H will rotate one round a year, this will lead to the axis of earth always point to Polaris. The number of teeth of gear D&H and gear E&G should be equal respectively.
• Gear I, J, K, L, M, N, O & P were designed to increase gears speed, which targeted to the spin of earth. Gears N&O, gear L&M, gear J&K were glued together and can spin with their axis respectively. Gear I fixed to its axis, while its axis can spine inside the outer tube which finally lead to the spin of earth.
• Gear V, U, T, S, R & Q were designed as reduction gears, which will drive gear G, and finally drive earth rotate with sun. Gear S&R, gear U&T were glued together and spin with their axis respectively. Gear V is fixed to its axis. Gear G is fixed to its axis, so it can drive gear F and E to rotate. While gear D is fixed to its axis, so gear G will actually drive the support arm to rotate with its axis, which simulate the rotation of earth to sun.
• Gear P, Q & I together with plane 3 & 4 were glued together and can rotate with their axis.
• Gear X, Y are reduction gears, and gear Y will be drive by motor.
• Gear I - V were used to ensure that earth rotates 365 rounds a year. The mathematical relationship of the gear group is that when gear V rotate one round, gear I should rotate 365 rounds. To find the correct teeth numbers of gears, I wrote this script (in R):

i0 = 32
i1 = 32
i2 = 32
i3 = 32
d = 100</p><p>for (x1 in 15:24) {
  for (x2 in 15:24) {
    for (x3 in 15:22) {
      for (y3 in 15:22) {
        for (y2 in 15:24) {
          for (y1 in 15:24) {
            for (y0 in 16:21) {
              ratio <- (x1 /(i1 -x1)) * (x2 /(i2 -x2)) * (x3 /(i3 -x3))   * 
                          (y3 /(i3 - y3)) * (y2 /(i2 - y2)) *(y1 /(i1 - y1)) *(y0 /(i0 - y0))
              if (abs(ratio-365.25) < d) {
                print(abs(ratio-365.25))
                d <- abs(ratio-365.25)
                if (d <5) {
                  print(paste(x1,x2,x3,y3,y2,y1,y0))
                  print((y3 /(i3 - y3)) * (y2 /(i2 - y2)) *(y1 /(i1 - y1)) *(y0 /(i0 - y0)))
                  print("")
                }
              }
            }
          }
        }
      }
    }
  }
}

[1] 0.6253846
[1] "21 24 22 22 24 24 19"
[1] 28.93846
[1] ""
[1] 0.5157143
[1] "23 23 22 22 24 24 18"
[1] 25.45714
[1] ""

I got two groups which are very close to 365.25. I choosed the second one, so I can say this tellurion has only half day mistake in one year. Another reason to choose the second gearset is they make earth spine slower than the first gearset.

The tellurion works generally as expected. One issue that unexpected is the moon doesn’t rotate smoothly. One reason caused this problem is the holes for holding bearings on support arm are very tight, which pressed the bearings’ shape from circle to oval, another reason is the gaps between gears, the bigger the worse.