Lego projects

Orrery

 

Should this be under Astronomy or under Lego?  The project was prompted by a question from one of our daughters.  To illustrate the “problems” I built an orrery from Lego, but the main subject is astronomy of course, not Lego.

The purpose of the orrery was to show the paths of the Earth and the Moon around the Sun, in an attempt to explain eclipses.

The astronomy part about eclipses is under Astronomy.

The main characteristic of this Lego orrery is that it shows the effect of the inclination of the Moon's orbit and keeps the nodeline at a fixed orientation.

It is to my knowledge the only Lego orrery with this property.

These pages are not yet complete!  Patience…

Textures of bodies:  Sun:

Purpose

The orrery attempts to show why the inclination of the Moon’s orbit prevents eclipses from happening except at some specific times and why lunar and solar eclipses often occur together with about two weeks in between.

An eclipse of the Sun or Moon occurs only when the plane of the Moon’s orbit is at a certain orientation relative to the line connecting the Earth and the Sun.  At those positions there is a fair probability for a Solar eclipse at New Moon, followed or preceded by a lunar eclipse at Full Moon (see the eclipses page under Astronomy).

Main Components

moon orbittrain main arm triangularbracing triangularbracing main armcounterweight main armbearing Sun Earth Moon gear traindays to year gear train“days to month” motor motor/crankclutch crank RCX battery box
main components [SVG]

The orrery consists of a main arm extending between the Sun and the Earth-Moon system.  It moves around horizontally and describes the ecliptic.

At one end sits a turntable carrying the moon orbit train, which is inclined relative to the ecliptic.  The Moon turns on a second turntable whose orientation is always kept parallel to itself.  That turntable is driven by a gear train that reduces the Earth rotation from “days” to “months” (see main mechanism).

Because the main arm is so long and carries the fairly heavy weight of the Earth-Moon system, it needs a counterweight.  For counterweight I used two blocks of leftover brass, nestled in a Lego-built box.

The arm with its counterweight needs to be stiffened by triangulating bracing rods on each side.  This makes the contraption look much like a building site crane.

There was too much friction to support the arm on a Lego turntable and still have it turn smoothly.  I built a special vertical “bearing” from eight wheels, running on flat-top plates, and moved around (but not supported by) a turntable, all built on a base.

There is a single driven axle, which turns at the period of a “day”.  A gear train fixed to the base converts “days” to a “year”.

Since it is nice to be able to run the orrery also by hand, the driven axle has a clutch which engages with either a crank or an electric motor.

Although it is possible to build the Earth and Moon from Lego pieces, the Sun is rather big and would need to be made from an awkward looking stack of tyres.  I chose to buy some styrofoam balls from a do-it-yourself shop.  There are so-called “gore-maps” available on Mitchell Charity’s site, I downloaded the maps of the Earth and Moon, printed them at the scale of the styrofoam balls and fixed them onto the balls with double-sided adhesive tape.

One could replace the Sun ball with a lamp or even a small LED torch so as to cast real shadows.

Considerations

Relative periods of orbits

Since the purpose is to show the relative motions of the Earth, Moon and Sun, it is not necessary to represent the actual ratios of the orbit times accurately:  as long as there are a sufficient number of months in a year (revolutions of the Moon around the Earth) and a sufficient number of days in the year (rotations of the Earth on itself) the effects can be convincingly demonstrated.

Relative sizes of bodies and orbits

An orrery cannot show the distances between the three bodies proportional to reality either:  the Moon is only 384’000 km away but the Sun is at 149’000’000 km.

Forms of orbits, inclinations, orientations

The inclination of the Earth’s axis relative to the ecliptic and the Moon’s orbit is not very important;  it is not accurately represented in the orrery.

The real orbits are elliptical, the orrery’s orbits are circles, but the difference is extremely small and not important for showing the effects.  For example, the difference between the major and minor axis of the Earth’s orbit is only about 0.01%, less than the diameter of the Earth..

The orbit of the Moon rotates itself with a period of about 18 years;  in the orrery it always stays parallel to itself.

Lastly, the inclination of the Moon’s orbit is about 5º, in the orrery model it is greatly exaggerated (almost 21º) which is necessary to compensate for the relative distances and body sizes being different from reality.

Earth and Moon Gear Reductions

The orrery has a single driven axle from which all other motions are derived.  This is the rotation of the Earth, or the “day”.

The actual periods of the year and the month are not whole numbers of days.  There is not a whole number of lunar rotations in a year either.

Approximations usually are 365 days for a year and 29 days between two full moons.  Neither of these is easy to achieve with Lego gears.

In the orrery these numbers have been used instead:

Using a gear train the main arm of the orrery can be made to turn once for 288 rotations of the Earth, i.e. the “year” is then 288 “days”.

A reduction by a factor 21 gives 13.7 “months” but of only 21 days each.  Other reductions that are relatively compact but not so easy to build are 24, 25 and 27, and all of those give fewer “months”, which is not good for achieving the purpose.

Cheats

There are a few cheats in this model.

A turntable lets two axes coincide but be driven at different speeds, much like the hands of a clock.  The central turntable under the main arm has a part with an outer rim of teeth, that part needs to be kept stationary.  Therefore the arm must be moved around by rotating the other part.  But that can only be driven from its 24-tooth inner ring.  There are two ways to move the inner ring:  either use a differential cage or use a 24-tooth normal gear whose axle hole has been drilled out round.  The differential cage would have been a pure Lego solution, but the cage itself can then only be driven from its other gear, a 16-tooth ring on a flange.  That would have made too much friction, since yet another intermediate gear must be used before a worm can be applied, as the flange is in the way.  I happened to have two 24-tooth normal gears whose axle holes I had already drilled out earlier for some other purpose, and they solved the problem.  It is a pity that Lego has no other “loose” wheels than the 16-tooth clutch and the differential cages.  See the page on “Missing Pieces”.

There are a number of conical meshings where one of the conical wheels cannot be positioned firmly with the help of whole or half bushings.  Using only pure Lego parts a small gap remains.  The conical parts may then slide on their axles and disengage unless some type of washer keeps them in place.  In Lego there are only two sizes of bushing that can fulfill the role of a washer:  a full bushing (8mm) and a half bushing (4mm).  But the gap is less than a half bushing.  As there were more instances in other projects where a washer the size of a quarter bushing (2mm thick) was useful, I also had a number of them ready-made. They are not really necessary in the case of the orrery, but they did come in handy.  An alternative would be to cut washers from a drinking straw of the right diameter and stiffness.

Further pages

Here is a sequence of pages on how to build it: