Orrery- a Mechanical Solar System Model From Plywood

This project explores the use of plywood to make mechanical, decorative, and structural parts.

This instructable is about how to build a desktop orrery. An orrery is a mechanical model of the movement and position of the planets in our solar system. The device accurately depicts where the earth is with respect to other planets, the sun, and the moon and how they move relative to one another. It can be used for education, decoration, demonstration, a gift, and a fun project to build.

I built my orrery with half a sheet of plywood and less than $50 in other materials.

However, full disclosure, constructing the orrery required some specialized tools. My design requires a CNC machine to cut the gears from the plywood. A laser cutter or a 3D printer might also work here, but I don’t know enough about them to be sure. I’m sure someone in the comment section will correct me if I’m wrong.

The design relies on custom cut gears, which need to be perfectly centered, symmetrical, and have identical teeth. I would strongly advise you not to try this with non-computerized tools. Unless you’re like the Michael Phelps of the scroll saw perfectly cutting 19 small gears with almost 900 total teeth is probably more frustrating than possible. Even small imperfections in gear cutting can cause problems because the gears all need to work together. Moving Saturn on the model, for example, requires 12 of the gears to all move together perfectly.

Step 1: Tools and Materials

I'll start by talking about the tools and materials that I used:

Tools

• CNC or laser cutter
• Small file set
• Soldering iron
• Pipe/tube cutter (a hacksaw would probably work here)
• Drill or drill press

Materials

• 3/16 inch plywood (which is actually like 0.19 inch thick) - 2 ft by 4 ft section [<$10]
• Brass tubes and rods (3 foot sections) - found these at a local art supply store, I've also seen displays at some hardware stores, and you can certainly order them online [$25 total]
  • 2 x Brass rod 3/32
  • Brass tube ⅛ inch diameter
  • Brass tube 5/32 inch diameter
  • Brass tube 3/16 inch diameter
  • Brass tube 7/32 inch diameter
  • Brass tube 1/4 inch diameter
  • Brass tube 9/32 inch diameter
• Washers [$2]
• Super glue
• Marbles, wooden balls, plastic models, or whatever you want your planets to be
• Wooden golf tees (again, optional depending on your planets)
• Dow rod (you could substitute some of the brass tubes for dows here)

• Wood stain or paint (optional, against depend on how you want it to look)

Step 2: Design

I started by hitting the internet hard and seeing what had already been done. Orreries come in all shapes, sizes, makes, models, and designs. Some take up entire rooms; some can sit on a desktop. They can be made from anything from Legos to steel, but most are made of brass. They also range wildly in complexity. If you want to make something smaller and less complex, consider just making a model of the sun, moon, and earth. There are tons of ideas and designs out there, so be creative when making your own.

I decided to building mine out of plywood because it was a material that was easy to work with given the tools I had on hand. Because the parts are mechanical, I avoided real wood because I was concerned about creating weak points at the gear teeth when they don't align well with the wood grain, and I wanted to avoid even slight post-production warping that you may see with real wood. Any warping would throw the gears out of alignment. Plywood is also relatively inexpensive, so I could experiment with a bunch of designs and toss the ones that don’t work.

Proportionality

The whole idea of an orrery is for it to be a model of the relative positions of the planets and sun. I also wanted to include earth’s moon because it is readily observable. I had to be realistic about how accurate and complete it could be give constraints on size and buildability.

I figured the model can be proportional in three ways:

Orbital period - The planets all spin around the sun in the same direction (relative to the sun) on roughly the same plane. The amount of time it takes them to revolve around the sun varies by planet. For the earth, it takes 365 days. The orbital period of a planet (or planetary year) increases exponentially as you move further from the sun. For every time the earth goes around the Sun, Mercury has to go around about 4 times. Saturn only goes about 12 degrees in that time. I decided that it’s not worth representing any planets farther from the sun than Saturn because they would barely move. That is, they have very small angular velocity that's difficult to observe in an orrery. Simply showing the first six planets captured most of the variation. For example, for every rotation of the earth (or ~ 4 rotations of Mercury), Uranus would only move 4 degrees. Neptune would move a barely noticeable 2 degrees. I decided I’d just do the first 6 planets. Sorry, Neptune and Uranus (and possible mysterious ninth planet that may or may not exist. - https://student.societyforscience.org/article/bey... )

Planet size - I quickly found I couldn’t make the planets and sun proportional in size to each other. Even if I made the moon a pinhead, the sun would need to be a beach ball. Instead, I resolved to have them represented in size order, but not proportional. The sun would be the largest object but not as large as it should be. The moon, the smallest but not as small as it should be. I still wanted this size difference to be demonstrated, so I did end up carving out the relative size of all the planets in the solar system inside the largest gear, more on that further down.

Planet distance- Similar to planet size, the orrery would need to be gigantic to represent the distance between the planets properly, so I figured I just have them in the proper order and that would be good enough.

Completeness

In addition to being not totally accurate, the model is also not totally complete.

Moons - I also choose not to depict any moons except for Earth’s. Saturn and Jupiter together have over 100 and that would quickly clutter things. There are also asteroids, dwarf planets and a whole bunch of other stuff floating around, but none of them are represented in the model.

Axial rotation- I also choose not to depict any axial rotation, that is, the planets would not spin on their own axis. I considered just having the earth spin, but the 1/365 gear ratio was very intimidating. If anyone has any great ideas for easily incorporating axial rotation, I'd love to hear about them in the comments.

Step 3: Gears

Start by designing gears. The gears are the heart of the orrery. The gears need to have specific teeth ratios to ensure the planets move that the proper speed relative to one another.

For each gear, you’ll need to know the number of teeth (which is proportional to its diameter) and the size of the shaft in the center of the gear. All the gears should have the same thickness, the thickness of the plywood.

For the gears, I modified the design found on http://brassorrery.blogspot.com/ . The blogger was limited by what brass gears were available commercially. Since I was cutting my own gears from plywood, they can be any size and have any number of teeth. Therefore, I could make the model far more accurate. I used Excel to find a combination of gears that (a) were within the size range I could cut with my material and (b) accurately showed planetary speed within 1% error.

I used 19 gears with the following number of teeth:

• 11
• 15
• 16 (x2)
• 18
• 30
• 32
• 35
• 40 (x3)
• 46 (x2)
• 57
• 60
• 61
• 74
• 76
• 146*

*For the largest, 146-toothed gear, I etched the months of the year around the circumference. Note that the months should be COUNTERCLOCKWISE. I messed up the first time and put them in clockwise, which is not accurate.

In the center of each gear, you’ll need a hole that will snuggly fit your brass tube. Refer to the diagram which shows which gears have common axles. Solid lines that connect gears show they have a common axle. Hollow lines show that the axles fit inside one another and should be able to spin independently of each other.

• The 74, 57, 46, and 32-tooth gears need to fit on the same tube.
• The 15 and 30-tooth gears also need to fit on the same tube.
• Two pairs of 16 and 40-tooth gears need to have the same diameter shaft.
• The last 40-tooth gear needs a shaft that slides into one of the 16 and 40-tooth pairs.
• The 18, 35, 46, 146, 60, 61,and 76- tooth gears all need different and increasingly larger tubes because they will slide into one another in that order and need to spin independently of each other.
• The 11-tooth gear can have any size tube.

Spends some time figuring out which gears will use which tubes.

To determine the gears’ total diameter, the only consideration was that the largest gear (146 teeth) has to be about the diameter of the earth’s rotational path. The Sun, Mercury, Venus, and the moon all had to fit within that path. I lined up my planet marbles at a spacing that looked good and found they all fit into a circle about 9 inches in diameter with the sun at the center and the earth on the edge. The gear that the earth rotated against had 146 teeth, So 9 inches/146 teeth became the proportion I used to calculate the size of all the other gears. (X teeth)*(9/146) = Y inches in diameter.

To make the gear, I used the following steps:

1. Draw up each gear in gear generator (http://geargenerator.com/)
2. Press "export it as a svg file"
3. Import that svg file into my CNC program (or laser cutter or 3D printer)
4. Scale it to the proper diameter according to the tooth/ diameter ratio (for me, multiply teeth by 9/146),
5. Add a shaft hole of the appropriate size in the exact middle
6. Run the machine to cut the plywood
7. Use small files to clean up the cut

Since the earth would rotate around the 146-tooth gear each year, I added the months to it as point of reference. I also cut out circles in this gear relative to the size of the planets because I wanted that represented somewhere, even if just decoratively. The whole gear is the relative size of Jupiter. The ring inside the month labels is the relative size of Saturn. The three large cutouts are the relative size of Neptune and Uranus (they are very similar in size). The three set of four cutouts are the relative size of Earth, Mars, Venus, and Mercury.

I stained all my gears to make them look less like cheap plywood. Certain plywoods don't take stain well because they are a combination of different materials that absorb stain differently. Consider paint or test your stain before using it on your cut pieces.

Step 4: Top and Bottom Plates

Nearly all the gears (except for the 146 and 11 tooth) are sandwiched between a top and bottom plate. These plates play several roles:

• The bottom plate acts as a base for the orrery. Later, I put cork shelf liner under mine to protect the surfaces it sits on.
• Both plates hold all the axles in position. The gears to need to be in a precise location. Close enough to that the teeth mesh but not so close that they bind. Finding that point can be a bit difficult, so take your time and try a few things out. For me, I found the distance between the axles needs to be the sum of the radii of the gears minus 0.125 inches. At that distance, the gears ran very smoothly.
• Both plates hold the vertical supports in position. I cut six dow rods to act as vertical supports, but you can use brass tubes just as effectively. These supports keep the plates from getting too close together and preventing the axles from rotating freely. They also prevent the plates from getting too far apart and letting the axles fall out of vertical alignment.

I machined a top and bottom plate on my CNC. A started with the bottom plate. I found the distance between each of the axles, and I machined 0.1 inch indents into the top and bottom where the five shafts would fit in to ensure they stayed in place and were perfectly vertical. I also placed indents for 6 wooden dows in a circle.

For the top plate, I used the same CNC file with four changes.

1. The bottom side of the top plate will be a mirror image of the top of the bottom plate. So I flipped the coordinates.
2. The center axle will need to be a hole all the way through large enough to accommodate the tubes that drive the planets
3. I made the top plate smaller in diameter than the bottom plate because I though it looked good and it allowed some of the gears to stick out and be more visible
4. I also put some decorative cutout circles in the top plate to make the inner gears more visible.

Step 5: Brace

The brace plate is a strange but necessary part of the orrery. It's purpose is to prevent the 146-tooth gear from spinning. That gear needs to remain stationary. The brace holds the tube that the 146-tooth gear is mounted on.

To make the brace, I used the same file as the top plate with a few changes:

1. The center hole needs to be the exact same diameter as the hole at the center of the 146-tooth gear.
2. Instead of indents for the axles and vertical supports, the brace requires holes all the way through the material because all the axles run through the brace.They can be in the same location and the same size as the indents on the top plate though.
3. I changed the decorative circle design.

Step 6: Gear Assembly

By now, you should have all the plywood parts cut:

• 19 gears
• Top plate
• Bottom plate
• Brace

With all these parts, you can start assembling the main body of the orrery.

First you'll need to cut the brass rods and tubes to the appropriate length. To calculate the length for each rod, look at the diagram to see what that rod or tube needs to go through, then added all thicknesses of those materials together. For my materials:

• 0.11 inches for the indents on the top and bottom plates
• 0.056 inches for each washer (A washer goes above and below each gear)
• 0.193 inches for each gear and the brace

For example, the length of four of my axles (from the indent in the bottom plate to the indent in the top plate) was 2.268 inches. That's 7 layers of gears, 1 brace, 2 indents, and 9 washers.

All the tubes should end at that the top plate except for the tubes that hold the planets, they should extend through the top plate.The rods and tubes that go through the center of the top plate need to be long enough to not only protrude through the top of the top plate, but also continue on to each have an exposed 0.5 inches of brass. You can see in the photo how these nest tubes look like an old timey telescope if done correctly. Mercury, for example, will have a tube that extends from the 18 tooth gear, through 6 other layers of gears, through the top plate, through the half inch sections for Saturn, Jupiter, Mars, the brace, Earth, and Venus, and an additional 0.5 inches of exposed brass.

Cut the rods to size using a tube cutter. Use a small round file to smooth out the cut so a smaller diameter tube will spin freely within the tube.

Add the gears and cut the rods according to the diagram.

Important: Remember to place a brass washer around the axle underneath each gear. The washer will reduce friction between gears spinning at different speeds or reduce the friction between stationary plates and spinning gears. Even on gears that spin at the same speed, the washer will maintain the proper spacing. A little lubricant between brass tubes will also help tubes that sit inside one another spin freely.

Even though the holes in the center of gears were the exact diameter of the tubes and a tight fit, I used a few drops super glue to make sure the tubes rotate with the gears they are attached to.

Start assembling from the bottom.

The sun needs no gears because it’s the point of reference and stationary. Mine sits on top of a 3/32” rod at the center. That rod should drop into the indent on the base plate.

The first four planets (Mercury, Venus, Earth, and Mars) are the easiest mechanically.The planets are driven by a stacked set of drive gears on a common axle that sit on a washer that sits on the base plate. This stacked set of drive gears spins, but they do not move relative to each other. They have the same angular velocity. These drive gears articulate with the planets’ gears, which also sit on a washer that sits on the base plate. Each planet has it’s own gear and axle that move independently from the other planets. The smallest axle, Mercury’s, fits inside the axle for Venus, which fits inside the axle for Earth, etc. etc.

On the bottom of the drive gear stack, a 74-tooth gear drives the 18-tooth gear that’s attached to Mercury’s axle. Second from bottom, a 57-tooth gear drives the 35-tooth gear that’s attached to Venus’s axle. Third from bottom, a 46-tooth gear drives another 46-tooth gear that’s attached to Earth’s axle. The 146-tooth’s brace should be added above the 46-tooth gears. It does not rotate but instead holds a tube that will support the 146-tooth gear between Earth and Mars. Fifth from bottom, a 32-tooth gear drives a 60-tooth gear that’s attached to Mars’s axle.

Note:The gear ratios are proportional to the orbital period of that planet. The earth’s orbital period is 365 days, 1 year. Earth's drive gear and planet gear are both 46 teeth. 46/46 = 1. For every one rotation of those gears, one earth year has passed in the model. Mercury's gears a 18 and 74 teeth. 18/74 = 0.24. Mercury orbits the sun in 88 days or 0.24 years. Notice also that all the tooth combinations add up to 92. This is so they are always the same distance apart.

For Jupiter's gear, the rotation needs to be slowed down further. This will require two more stacks of gears. The Mars gear drives a 40-tooth gear that shares an axle with a 16-tooth gear. That 16 tooth gear drives a second 40-tooth gear, which also shares an axle with a 16-tooth gear. That second 16-tooth gear drives a third 40-tooth gear on its own axle that sits inside the axle of the first 40-tooth gear. The final 40-tooth gear drives the Jupiter gear.

A final stack of gears a 30- tooth and 15-tooth on a common axle use the rotation of the Jupiter gear to drive the Saturn gear.

Dry fit the vertical supports and add the top plate.

Once you have all the gears and plates assembled. Test the rotation by rotating the 74-toothed gear with your finger. It should run smoothly and the center axles should spin at different rates (except the one braced axle, it shouldn't spin at all). If you're satisfied with the motion, add the dow or brass tube vertical supports and glue those in place.

Step 7: Planets

I decided to use marbles from a local store for planets because they came in various colors and sizes and had an abstract quality to them. You could so use beads, wooden balls, custom make planets from clay, or purchase plastic models. The planets would need to be mounted on brass arms. To join the brass rods to the marbles, I used wooden golf tees. I drilled a hole the same diameter of the rod straight down the tee. I then cut the bottom off the tee and used super glue to secure the marble on the top of the tee. If you are using a material that you can drill into, you can skip the golf tees and stick the rods directly into the planets. I found I was more likely to crack the marbles trying to drill into them.

Step 8: Planet Arms

Bend the 3/32 inch rods into arms to hold the planets. Bend eye hooks into the opposite end that are roughly the diameter of the tubes they are to be attached to.

Make sure the arms for each planet's arm is long enough that they can each pass by each other without colliding.

I looked up the appropriate relative positions of the planets on http://www.theplanetstoday.com/ to find out where to place Saturn, Jupiter, and Mars. Do not solder on Earth, Venus, and Mercury just yet.

I then soldered the brass eye loops onto the appropriate tube with a soldering iron. I filed down any extra solder.

Note: Because I used marbles, the large glass balls for Jupiter and Saturn were quite heavy and tended to flex the 3/32 inch rods. I reinforced those rods with a sheath of thicker brass tubing, which prevented much of the bending.

Step 9: Moon Mechanism

After installing Jupiter, Saturn, and Mars on their axles. Add the 146 tooth gear to its braced axle above Mars's. Use a few drops of super glue to make sure it doesn't spin.

Note: The moon rotates around the earth once every 27.32 days. That's 13.36 times a year. We can approximate this by having an 11-tooth gear rotate around the 146-tooth gear. 146/11= 13.3.

To make the moon rotate around. I drilled two holes in one of the larger brass tubes. One to fit over the axle that moves the earth and a hole on the opposite end of the tube large enough to allow the moons axle to spin freely. As the earth's axle rotates (driven by the gears between the plates), it moves the arm around the outside of the 146-tooth gear. The 146 tooth gear spins the 11 tooth gear which spins the small moon arm. The earth sits on a rod that slides into the moon's axle. A small washer is added to reduce friction between the arm and the gear.

Step 10: Last Planets and Sun

After the moon mechanism is running smoothly. Solder on Venus and Mercury's planetary arms and add the planets to the end of those arms. The Sun should be put in last, just mounted on the center rod.

Step 11: Final Touches and Thoughts

I added a crimped clear plastic ring around Saturn to represent its prominent rings. I also added some cork shelf liner to the bottom of the base plate to protect any surfaces I put the orrery on.

I'm very happy with how the orrery turned out. If I ever made another, I would change a few things that you could take into consideration.

• I operate the orrery by moving the 74 -tooth gear with my hand. Adding a small crank knob might make that a little bit easier.
• I really like the way the marbles look, but they are very heavy, especially at the end of long arms. I had to make my base big enough so that if Jupiter and Saturn are on the same side, the device wouldn't tip over. Painting wooden balls of various sizes might reduce weight.
• This design is also scalable, so it can be as large or as small as your materials will allow. I'd love to see an outdoor kinetic sculpture like this.

Special thanks to the folks who created: http://brassorrery.blogspot.com/ and http://geargenerator.com/ They are free and very useful.