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Parts referred to in the discussion above:
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Script for the model A movie
Pretty nearly all the orrery designs I have done so far,
have at their core,
this design by Allan Ayres who is associated with the NASA Kepler mission.
It uses a planet gear system inside the large turntable,
and a differential housing
to make three planets turn with relative periods of 1, 2 and 4.
These simple, exact, ratios
might seem rather artificial and unrealistic,
but they actually happen in real life.
Three moons of Jupiter, Io Europa and Ganymede,
orbit with precisely this ratio because of a Laplace resonance.
This modified version of Ayres three-planet model represents Io with the little red moon, Europa in tan and Ganymede in gray.
Whenever Io and Europa are aligned, Ganymede is 90 degrees ahead or behind.
Whenever Europa is aligned with Ganymede, Io is 180 degrees away.
Script for model B2 movie
Dave Koch took the Allan Ayres design and added another planet and a moon to produce something similar to this model.
The 4 planets orbit at relative rates of 12, 7, 4 and 3, and the moon's rate is 52.
The small yellow gear is on the central axle. The turntable base, which is black, has a 24-tooth ring gear for its inside edge. A gear below and identical to the blue gear, fits between this edge and the yellow gear, and as it moves, the top part of the turntable moves with it. This creates the 4-to-1 ratio between the rotations of the 1st and 4th planets.
There is also a 24-tooth gear running an 8-tooth gear which turns the differential housing attached to the 3rd planet arm. This ensures that the 3rd planet will overtake the 4th planet once for every three times the 4th planet orbits the sun.
The arm for the 2nd planet carries gears that pick up the relative motion of the 1st and 3rd planets and interpolate it. These gears act as a differential. They ensure that the 2nd planet will overtake the 3rd at 3/5 the rate the 1st planet overtakes it.
Additional gears on the outer end of the 2nd planet's arm ensure that every time the 1st planet overtakes the second, the moon orbits the 2nd planet nine times, as seen from the 2nd planet's point of view while facing the sun.
Script for model D YouTube video
[INTRO]
An orrery is a model demonstrating the motion of astronomical bodies.
This is my improved version of a design by Allan Ayres and Dave Koch of the NASA Kepler Mission project.
I added a fifth planet, with two moons of its own, and made some improvements to the old design.
[0:19]
Here it is in motion. Here are the original four planets.
Here is my fifth planet, with its two moons.
The moons are driven by a miniature orrery that rides on the end of the fifth planet's arm.
[CAMERA CLOSEUP]
An axle running the length of the arm drives a crown gear, and four gears of different sizes make two concentric shafts rotate at different speeds.
[FOCUS ON TT BASE]
The fifth planet moves by means of a second turntable base, located below the turntable of the 4-planet design. This lower turntable is driven by the green gear you see here.
The upper turntable, belonging to the 4th planet, turns faster, and a crown gear on the 5th planet's arm catches its relative motion to turn the axle that goes to the moons.
[DOLLY ALONG AXLE]
I used two bits of flexible tubing, called Flex System and Technic Ribbed tubing, both of which are standard LEGO parts. However, I had to use a bit of copper wire to clip the ribbed tubing to the 16-tooth gear, and to support the 2nd moon.
[NOW LOOKING AT SUN]
The sun is a foam ball that came with the RoboSports Mindstorms expansion set.
[CUT to IMPROVED AYRES/KOCH ARMATURE]
Here is my version of the original 4 planets, based on the design from the URL shown here.
[CUT to MODIFIED BASE]
I modified the base by adding this green gear, it is driven by a new shaft that turns along with the original crank shaft.
If you take the green gear off, the original shaft turns the original 4 planets as before.
[SHOWING BOTTOM OF 4-PLANET ARMATURE]
However, you can leave the green gear in place, and remove the crown gear from the bottom of the armature, and run the 4 planets this way.
(Wait until it's running)
The green gear is turning the outside edge of the turntable. A small gear on the inside edge of the turntable, which we cannot see from here, is making the others gears turn, which drives the inner 3 planets.
[CUT to BARE TURNTABLE WITH GREEN GEAR]
The basis of the design for adding a 5th planet is to add another turntable. Here it is running by itself, driven by the green gear.
You can put the 4 planets on top of this, and use the original yellow gear to drive the central vertical axle, which will make those 4 planets turn relative to the new turntable.
[CUT: HOLDING OLD ARMATURE WITH SHAFT EXTENSION]
The central axle is extended to accommodate the height of the new turntable. The crown gear will be driven by the yellow gear.
[CUT: 2ND TT IS ON]
The new turntable is on now. It should be about like this. You'll need to adjust the crown gear a bit to make it mesh with the yellow gear.
Let's put it on the base.
[CUT: REMOVING GREEN GEAR]
I'm also going to remove the green gear for some demonstrations.
[CUT to RUNNING MODEL]
Now it's running.
If I let it run and don't touch anything, the turntables both rotate together.
(HOLD bottom turntable)
If I hold the bottom turntable, the planets move as in the original design.
(TURN it retrograde)
If I rotate the turntable backward, I can make the outer planets move retrograde, and the inner planets stand still.
(TURN it forwards)
If I rotate it forwards fairly fast, I can make the outer planets revolve more quickly than the inner planets.
(SYNCHRONIZE)
If I turn it at just the right speed, I can make the planets all revolve at the same rate.
[CUT: PUTTING GREEN GEAR BACK ON]
So I'll put the green gear back in.
Switch it on. The 4 planets move normally, and the bottom turntable is moving slowly.
If you look closely, you can see the yellow gear turning the crown gear inside the base.
[CUT: ASSEMBLED 5TH PLANET ARM]
Here is the arm for the 5th planet, with its two moons.
This is a counterweight.
Here's what the bottom looks like.
[CUT: 5TH ARM INSIDE BOTTOM OF TURNTABLE]
Here is how it fits into the upper turntable.
[CUT: ADDING 5TH PLANET ARM]
The arm for the 5th planet will be attached here.
(Rotate it around a bit)
And the counterweight goes here.
[CUT: FULL MODEL ASSEMBLED AND RUNNING]
And here we go. Let's watch it run for a bit.
The outer planet and its moon jiggle a lot, mainly because of the flex tube components. Those parts were really not meant to be used as concentric axles.
The moons revolve with a ratio of 27 to 40.
You can see some colored pegs on the base plate, which I have been using to measure the various rotation rates and try to figure out what the ratio are. They are very complex. In the 4-planet design it only takes a minute or two for all the planets to return to the starting position. In this design it takes about 3 times as long, and even then the whole system is rotated about 15 degrees.
(It stops)
So there you have it. A LEGO orrery with 5 planets and 3 moons.
I hope you enjoyed watching!
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