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Build a tel­lu­rion.

Sky at Night Magazine - - CONTENTS - With Mark Parrish

Con­struct a home-built work­ing model of the Sun, the Moon and Earth

This month’s project is a tel­lu­rion – a work­ing model of Earth, the Moon and the Sun. As well as be­ing ed­u­ca­tional, this model looks great when dis­played in your liv­ing room or study. We de­signed our tel­lu­rion so that it’s sim­ple to build, util­is­ing parts that are read­ily pur­chased on­line. By mak­ing some care­ful cal­cu­la­tions we were able to choose gear ra­tios to pro­duce ac­cu­rate move­ments of the Moon and Earth as the main arm is ro­tated by hand around the Sun.

The de­sign is built around a cen­tral ‘year disc’. This has a sec­tion of GT2 belt glued around its cir­cum­fer­ence, form­ing a gear with 267 teeth. The model Moon is ro­tated by a 20-tooth pul­ley mesh­ing with this gear, which gives a ra­tio of 20/267 (1/13.35). This means it will com­plete 13.35 or­bits of the Earth per year or one or­bit ev­ery 27.34 days – very close to the real Moon’s side­real month of 27.32 days. Like the real thing, model Earth’s axis is in­clined on its mount­ing by 23.4° from ver­ti­cal and a pair of 20-tooth pul­leys and a toothed belt make sure it main­tains this in­cli­na­tion as the sys­tem or­bits the Sun.

Sea­sons

One full or­bit around the Sun rep­re­sents a cal­en­dar year. By adding a printed disc (free to turn so it can be syn­chro­nised with the po­si­tions on a known date) you can in­di­cate the cur­rent month. Dur­ing the north­ern hemi­sphere’s win­ter, Earth’s south pole is tilted in the gen­eral di­rec­tion of the Sun, which ap­pears low in the sky for us in the UK. In the north­ern hemi­sphere’s sum­mer, the north pole is tilted in the Sun’s di­rec­tion with a cor­re­spond­ingly high Sun for us. This demon­strates our sea­sons very nicely.

The trop­ics are observed as the most northerly and southerly points where the Sun is di­rectly over­head.

It is pos­si­ble to turn the Earth sphere by hand to demon­strate the pas­sage of days and how the Sun ap­pears to rise and set. By imag­in­ing the ‘fixed’ star field on the walls of your room and vary­ing the po­si­tion of Earth around the Sun it is pos­si­ble to ex­plain how the stars ap­pear to move across the sky dur­ing the night, and why much of the night sky is only vis­i­ble for part of the year.

Phases of the Moon

Be­cause the Moon is fixed on its axis arm the same face al­ways looks to­wards Earth (as it does in re­al­ity). We in­cor­po­rated a small bulb in our model so the Sun can be il­lu­mi­nated, but a torch can also be used

to sim­u­late the Sun’s rays strik­ing Earth and the Moon. It should there­fore be pos­si­ble to demon­strate how the phases of the Moon are formed dur­ing a month. Note that in the model there is a so­lar and a lu­nar eclipse ev­ery month in­stead of the usual New Moon and Full Moon. The rea­son we get far fewer eclipses than this in re­al­ity is be­cause the real Moon’s or­bit of Earth is in­clined to Earth’s or­bit of the Sun by 1.54°, which means that most of the time the Moon is slightly above or be­low the plane of Earth’s or­bit as it passes be­hind us or in front of the Sun – hence no eclipses. It is be­yond the scope of our model to recre­ate this, but nev­er­the­less it is easy to imag­ine the New and Full Moon.

The crucial el­e­ments of the model are the sup­port­ing arms. We found that model shops sell packs of 4mm, 5mm and 6mm brass tube that fit in­side each other – per­fect for the job. Earth and the Sun are ta­ble ten­nis balls; the Moon is a wooden ball from a craft shop. To build the rest of our model we used 6mm ply­wood, which is flat and quite easy to cut. We were go­ing to stick a few layers to­gether for the base but sourced a nice of­f­cut of hard­wood in­stead. It got us think­ing that there are many ways to cus­tomise the tel­lu­rion. Whether you keep yours sim­ple or get fancy, we are sure that you will have a lot of fun build­ing and demon­strat­ing it.

A tel­lu­rion shows the move­ments of Earth and the Moon around the Sun

An il­lu­mi­nated Sun means the tel­lu­rion can demon­strate Moon phases

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