Orrery

DIY

orrerydownload logo.jpg

An orrery is defined as a clockwork mechanism of the solar system (or part of the solar system). The clockwork mechanism is of course the part that I find intriguing and I wanted to make a model that I can sell as a kit. Currently the kit is for sale (buy one here).

This is the result of several weeks of work:

 

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orrery

The assemble instructions are available for free download to anyone who are interested in how the mechanism is put together. The skill required to build this is advanced but very rewarding once done. It can be set for any year.

A video with some instructions to make assembly easier is available HERE:

A few interesting notes on this Orrery: 

The gear ratios for the orrery are very interesting. The bottom gear train (T39:T8:T39), rotates the Earth around its own axis once per year. The ratio is 1:1 and has the effect that the Earth is not tidally locked with the Sun (as the Moon is with the Earth). This simulates the seasons as the poles turns towards and away from the Sun at different stages of the year. The place where the tilt is at maximum, is indicated on the disk (these are the solstices in June and December). When the Sun is directly above the equator, is also indicated on the disk (the equinoxes in March and September). Note that the equinoxes and solstices are not on the exact same date each year and averages were calculated and used on this orrery. It is also interesting to note that the solstices and equinoxes are not equally far apart (i.e. the seasons are not equal in length). This is due to the slightly elliptical orbit of the Earth (definitely not simulated in this orrery).

There is a full Moon every 29.53 days (called the synodic month). Note that a full rotation of the Moon actually takes 27.322 (sidereal month – takes the rotation of the Earth into account) but for the orrery we are interested in predicting the Moon phases and this value is not used here. A full Moon every 29.53 days means there are 12.368 rotations of the Moon every year. This is the value that we need to simulate to predict the Moon phases. The following gear ratios were selected: 39:8 and 33:13. The combined gear ratio is 1:12.375. This means that one full rotation (i.e. one year) there will be 12.375 full Moon rotations. The simulated value is close to the real value and the error is less than 0.06% which means the accuracy is 99.94% over the course of one year.

The inclusion of the additional 13 teeth gear is also important. Having two 13 teeth gears in line does not affect the ratio but it does affect the direction of rotation. I called it the inverter gear (T13B) since it changes the Moon’s rotation from clockwise to counterclockwise when the Earth is moved in a counterclockwise direction (i.e. the direction the Earth rotates around the Sun when viewed from the North Pole).

The drive gears (T12RA and T48RA), does not affect the accuracy of the orrery. It is however interesting to note that the gear ratios for these gears are 1:4. This means with each full turn of the crank the orrery moves by 13 weeks. There are 13 radial lines on the shaft disk (BHS). There is also a line on the crank axel (D83). Turning the crank so that the line on the crank axel moves one segment on the shaft disk will thus advance the orrery by one week.

It is important to note that this orrery is made from wood with some limitations in accuracy. The “slop” between the gears means that the arrow can move 3-5 days without turning the gears (tighter gears will mean the mechanism will be hard to move). This means that the resolution is not accurate on a day basis but rather that is accurate within a 5 day interval. However, if the slop is taken into account and the midpoint of the arrow is taken, each time, when the Moon phase is set/read the accuracy is 99.94% per year (see below). I.e. the orrery will be within the correct 5 day interval for 64 years and start to deviate by one day after subsequent rotations.

In the future I want to make a much larger model with and include celestial items. I want to make it out of nice hardwood and and much much larger. But this is just one of the many things I want to make – if I do it it will definitely be documented!

R