Update 18 June 2024: As discussed in the comments, a reader pointed out that I was misinterpreting the indication of the month of the year, and Lego’s instructions are correct. I’ve struck out the incorrect portions of this post. (And I’ve corrected the model on my desk.)

When I saw that Lego was releasing an orrery, I knew that I had to get my hands on it — for work! I deal with new space mission concepts around the Moon with some regularity, and you have no idea how often I find myself thinking, okay, that lamp is the Sun and my hat is the Earth, so the spacecraft has to point its solar panels over there — but then the Earth moves, so it has to point over there now…. A functional desk orrery would actually come in handy! Well, I’ve finally purchased and built Lego set #42179: Planet Earth and Moon in Orbit.

Here’s what I think of the model and how well it captures the real motions of the Sun-Earth-Moon system.

The Model

To build the full orrery, you build up a few discrete sections and assemble them piecemeal. There’s a base containing the hand crank and the beginning of the gear train, topped by a ring labeled with months of the year on stickers. (The base therefore represents the orientation of the fixed stars, a Sun-centered inertia frame.) On top of this is a rotating armature on a turntable that continues the gear train, and mounts an arm that rotates around the Sun, representing the motion of Earth over a year. On top of the armature is the Sun, which is a simple assembly of two halves of a 3.5″ diameter sphere (parts created for this set, I believe). There is a circular platform fixed to the end of the arm. This includes more gearing, with the Earth in the center and the Moon revolving around its perimeter on a turntable, as well as stickers labeling phases of the Moon.

It’s a pretty nice-looking model. The rings on the base and the Earth-Moon platform give it a minimalist style, and a good portion of the base, armature, and platform are open-sided so that you can see the gears turning as you crank it. It’s not to scale at all, except that the size relationship of the Moon to the Earth (approximately 1/4 the diameter) looks close-ish. But the Moon is actually about 60 Earth radii away from the Moon, and of course the Sun is a full astronomical unit — or over 23,000 Earth radii — away from the Earth, as well as much bigger. Most orreries take liberties with scale in order to fit in some reasonable area.

Turning the crank clockwise causes the platform (with the Earth and Moon) to orbit around the Sun, the Moon to orbit around the Earth, and both the Earth and Sun to rotate. I counted roughly 3 Earth rotations (days) per turn of the crank, and therefore about 27 days per lunar orbit around the Earth (actual value ~29.5), and about 13 and a bit lunar periods per year (actually ~12.4). The Earth is mounted to a 157.5° angle element so it’s off from vertical by 22.5° (actually 23.4°). The model seems to get reasonably close to actual values!

There’s a fair amount of backlash in the gear system. When I turn the crank, there’s a bit of dead motion, and then first the Moon starts orbiting the Earth, then the Sun starts rotating, then the Earth starts rotating, and finally the arm engages to orbit the Earth around the Sun. I figure the backlash obscures most accuracy errors.

As you can see from my photos, I modified mine with a Sharpie.¹ The Earth model has a printed map of simplified continents, but there was nothing on the Moon or Sun to really indicate their rotations. I sketched in some sunspots and coronal loops on the Sun to break up the symmetry of the globe as it rotates around. On the Moon, I sketched some of the surface features, most prominently the maria on the nearside.² I thought getting some features on the Moon was important, because the way this model is set up, the Moon is attached so that it always keeps one face pointed toward the Earth — which is what the real Moon does!

There’s one clear error in the build: the Earth’s axial tilt is represented in the wrong direction! It should tilt the northern hemisphere towards the Sun in June-July, and tilt the southern hemisphere towards the Sun in December-January. (This is why we have seasons!) Fortunately, it doesn’t interfere with other parts of the model to just install the Earth the other way around from what the instructions tell you.³ So I corrected mine.

I wish there was a counterweight opposite the arm, or that the base was heavier, because when the arm is aligned to the narrowest radius of the base the model gets a little tippy. Holding my hand on the base to keep it on the table is good for turning the crank, but when I leave the model, I tend to crank the arm around so that it’s on a diagonal with the feet of the base for more stability.

The Build

I hope your thumbs like pushing lots of connector pegs into Technic beams.

This was a bit of a challenging build. The instructions require spatial reasoning to puzzle out some of the steps. (I also just built a couple of the Lego Star Wars 25th Anniversary sets, which practically handhold you through which pieces to install each step and where. This build is more like the old-style instructions where you have to examine the cartoon for whatever changed.) Several times, the instructions required me to insert four or six connector pegs simultaneously into the holes on a sub-assembly. Occasionally I wouldn’t seat one of those simultaneous connections properly and would end up scrutinizing the pages of the instructions to figure out why my build seemed to be one brick misaligned from the next step. Eventually, though, I figured all these things out.

The month of year and Moon phase stickers are pretty roughly aligned. The intended alignment of the month labels appears to be with the start of each month’s name indicating the start of the month, so that the equinoxes — when the line from the Earth to the Sun goes through the Earth’s equator — line up with approximately 21 March and 21 September (or at least are toward the ends of those months). There’s a page in the instructions to help register the alignment of everything during the build to the proper angles. (You can see in the picture that they show the Earth’s northern hemisphere tilting away from the Sun — northern winter — during the summer months. Perhaps this is a misprint that Lego can correct.)

I thought the build instructions were a huge missed opportunity for at least a few notes about the actual motion of the planets, how the model represents the orbits, or perhaps historical notes about orreries, which can be pretty fascinating. (Especially since Lego’s web page for the model talks about its educational value.) This was another funny contrast with my recent build of the 25th Anniversary Millennium Falcon, which has three little Easter egg scenes from the movies built into it. The corresponding pages in the instruction booklet have a quote from each scene and some notes about the characters. A few sentences here and there during the build could have really increased the educational value of the Planet Earth and Moon model.

The Motion

Hey, I thought you said you were an engineer? What’s all this “I counted about 13 and a bit months per year” rough estimation junk about?

Okay, anonymous reader, challenge accepted! Here’s the kinematic graph of the gear system leading from the hand crank to each of the rotating elements. The numbers separated by slashes represent a transition from one size gear to another along each path, for example the first “12/36” means there was a transition from a 12 tooth gear to a 36 tooth gear. As the note indicates, this reduces the rotational speed of the axle going out of the final gear to 1/3 of the speed of the axle coming in to the starting gear.

Using this as my map, I could multiply out each path down the gear train to figure out how many rotations each element ideally⁴ makes for a single turn of the crank. You can see that there’s a convenient unit conversion in that the Earth rotates 3 times for every turn of the crank, so 1/3 of a crank is a day. (Hooray, I eyeballed it correctly earlier! But now I have the math to back it up.)

Sun

The Sun is geared to 1/9 of a rotation for each turn of the crank. At 3 cranks per day, this means that the Sun is geared to rotate once every 27 days. This is pretty close to the Sun’s actual equatorial rotation period of ~25 days! (The Sun rotates much more slowly at the poles. It’s a blob of boiling gas. It’s sloshy.)

I realized after looking at the model again, though, that my kinematic graph didn’t tell the full story. It captured the gear ratios, but since the Sun sits on top of the rotating armature, its mechanism crosses from the base to the armature and thus picks up the additional rotation of the armature — one revolution per year. I carefully cranked the model through a full year of rotation and, sure enough, instead of counting the expected 13.5 rotations of the Sun that I get just from the gear ratios⁵ I counted 14.5. For the Sun to go around one extra rotation over the course of the model’s year works out to a solar rotation rate of 25.1 days. Much more accurate to the real Sun’s equatorial rotation period! Was that intentional design, or just a happy accident because the Sun’s mechanism had to pass through the armature?

Earth

I’ve already talked about how the Earth’s axial tilt was backwards (before I corrected it), how the angle element the Earth is mounted on is less than 1° off from the actual value, and how the crank spins the Earth 3 times.

The rotating arm defines the equatorial plane — in the Earth’s sky, this is the plane defined by the position of the Sun over the course of a year. From outside the Earth, it’s the plane defined by the position of the Earth relative to the Sun over the course of the year. The Earth-Moon platform, marked with Moon phases, defines an Earth/Sun rotating frame. As the arm rotates, the gearing mechanisms connected to the turntable inside the platform essentially un-do this rotation to hold the Earth’s axial tilt steady relative to the model’s base, so that the Earth’s rotation axis is constant relative to the fixed stars. This is correct!⁶ This is how we get the model showing Earth’s seasons as the arm cranks around a full orbit: on either the northern or southern hemisphere, the hemisphere is tilted towards the Sun in summer, away from the Sun in winter, and at the equinoxes in the middle of spring and fall the Sun falls on Earth’s equator.

The gearing moves the arm through a full rotation around the base for every 364.5 rotations of the Earth model. This is only 0.2% off from the Earth’s actual year (365.25 days). I’m pretty impressed that Lego found the right combination of gearing to hit that number.

Moon

As with the real Moon, the model has the Moon rotate about its axis once per orbit — keeping its near side always towards the Earth, and the far side always away from the Earth. (This happens without any special rotation mechanism for the Moon — it is just fixed to the orbital motion mechanism.)

Before I look at the Moon’s gearing, this would be a good time to talk about synodic versus sidereal orbit periods. The Moon has one sidereal period every time it completes a full rotation relative to the stars — on this model, that would be a full rotation relative to the base or, to the table the base it sitting on. In the picture below, the arm holding the Moon starts horizontal to the image frame, and then after rotating through a full 360° it is horizontal again. The Moon’s sidereal orbit period is 27.32 days.

On the other hand, the Moon completes one synodic period when it goes through a full rotation from one conjunction (lining up with the Sun) to that same conjunction.⁷ In other words, from full Moon to the next full Moon, or from new Moon to the next new Moon — one month — is one synodic period. The Moon’s synodic period is 29.53 days.

Why is the synodic period longer? Well, in the time it took the Moon to complete its sidereal period, the Earth also moved relative to the Sun, so the Moon has to go a little farther to line up with the Sun in a conjunction again.

(See, having this orrery is useful for explanations already!)

From the gear ratios, the Moon model’s orbit around the Earth is designed to complete one synodic period every 27 days.⁸ That should have been 29.53, and is an 8.6% error. It’s possible that Lego’s designers didn’t recognize the difference between synodic and sidereal periods. It’s also possible that this is as close as they could get with the gear sizes available: there are 10 gear size transitions between the Earth and the rotating arm, which means 10 multiplications of gear ratios to get the correct number of days per year (remember, that was the number with only 0.2% error!), but there are only 3 gear size transitions between the Moon’s orbit and the Earth. A 1:27 final ratio might just be hard to hit with 3 gear ratios from the Lego catalog — especially when you are trying to pack them into the platform at the end of that moving arm.

There are a range of inaccuracies that come with any circular orrery model of orbital motions, which are also present here. The Earth’s orbit is not actually circular, but slightly elliptical — though that difference is so small as to be inconsequential. The Moon’s orbit around the Earth is also elliptical, and more so to matter: it’s about 10% closer to the Earth at perigee compared to when it’s at apogee. In addition, the Moon’s orbit plane around the Earth is tilted relative to the ecliptic by just over 5°. There are ways to depict both mechanically, but they could be pretty difficult to render with Lego pieces. (The combination of the Moon’s inclination and eccentricity results in libration,⁹ an effect that lets observers on the Earth see more than half of the Moon’s surface even though the Moon’s near side is tidally locked to always face the Earth.)

Is the Model Good Enough for Spacecraft Engineering?

Well, it depends exactly what you want. Does it capture the motions and timing relationships accurately? It’s pretty close, but I’m not going to be able to crank it around to a particular date and see the actual Sun-Earth-Moon geometry. The biggest inaccuracies probably come from the slack and backlash in Lego gearing. I’m still impressed at how well it captures the overall timing relationships — days to months and days to years. Of course I am happy to be armed with all the numbers, now that I plan to take the model in to work and sit it on my desk. People will ask me.

Does the model capture the overall geometric relationships between the Earth, Moon, and Sun, though? Absolutely! You can easily crank the model to a particular Earth season and a particular phase of the Moon’s synodic cycle, and see the directions to the Sun and Earth from a spacecraft in a particular place. No more picking random objects across the room¹⁰ to point at! Perhaps I will figure out a way to annotate on a few of the key Lagrange points for reference.

Overall, it’s a cool model with lots of information to dissect. My biggest complaint is that this content could have accompanied the model to make even more of an educational impact.

Disclaimer

I purchased this Lego set on my own and have not been paid by the Lego group or anyone else for this review. If they like it, though, they are welcome to send me a 75394!

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1. I tried Copic Multiliners, Pigma Microns, and a couple other fineliner pens I have, but Sharpie was the only one that didn’t smudge off with a single swipe of my finger. From experience, Sharpie on Legos does eventually fade, especially under UV — but I think that might make the Moon look even better. ↩︎
2. Yes, that Moon piece is pretty little and it was tough to sketch accurate-looking maria and craters on it. Good thing I like drawing tiny trees and stars. ↩︎
3. In step 191 of the build instructions, rotate the sub-assembly you construct by 180° about the yellow axle when you install it. It’s also relatively easy to pop this assembly and the gear above it off at a later step, or even after you finish the entire build. ↩︎
4. Because of the backlash, it’s pretty easy to get a quarter to a half rotation of the Earth before other stuff starts moving. ↩︎
5. From my examination of the gear train: 364.5 days per year (in the model) divided by 27 days per Sun rotation. ↩︎
6. To first order, at least. The Earth’s rotation axis does wobble around a bit, because of things like water sloshing around or new mountains pushing up. Also, the Earth does not pick up an extra rotation for the rotation of the arm over a year, because of this mechanism that un-does that rotation to hold the Earth’s tilt steady. ↩︎
7. In general, any alignment of three celestial bodies is called a syzygy, which is one of the coolest words to exist. ↩︎
8. Why doesn’t this motion pick up an extra rotation like the Sun did? Well, it does — rotating the whole Earth/Moon platform around the Sun once per year. If I backed out that extra rotation, I’d have the sidereal period. ↩︎
9. Cool link. Watch the video! Here it is again. ↩︎
10. Or random coworkers. ↩︎