The Guide

AUs, lightyears and par­secs ex­plained.

Sky at Night Magazine - - CONTENTS - With Dave Golder

Space is big, re­ally big, as the open­ing of The Hitch­hiker’s

Guide to the Gal­axy sagely in­forms us. The dis­tances be­tween ce­les­tial ob­jects are so mind­bog­glingly vast that spe­cial­ist units are needed to chart it. To express in miles the dis­tance from Earth to the edge of the ob­serv­able Uni­verse, for ex­am­ple, re­sults in the un­wieldy fig­ure of 270,000,000,000,000,000,000,000 (give or take). Even us­ing math­e­mat­i­cal no­ta­tion to shorten it to 2.7x1023, it’s still so es­o­teric as to be near mean­ing­less. What space needs is re­ally, re­ally big units of mea­sure­ment.

As­tro­nom­i­cal Units, or AU, are the small­est, sim­plest and old­est of th­ese as­tral mea­sure­ments. One AU is equal to the ra­dius of Earth’s or­bit around the Sun; or, to be more pre­cise, the av­er­age ra­dius since Earth’s or­bit is el­lip­ti­cal.

An AU is de­fined as 149,597,870,700m (about 93 mil­lion miles), a value of­fi­cially set by the In­ter­na­tional As­tro­nom­i­cal Union (IAU) in 2012. As­tronomers have been try­ing to cal­cu­late the dis­tance from Earth to the Sun ever since, in the 3rd cen­tury BC, Archimedes es­ti­mated it to be around 10,000 times Earth’s ra­dius, or 63,710,000km – so he was nearly half­way there. Not bad for some­one who lived 2,000 years be­fore the te­le­scope was in­vented. It wasn’t un­til 1695 that Chris­ti­aan Huy­gens made the first close guess of 24,000 Earth radii (152,904,000km) though some sci­ence his­to­ri­ans dis­miss his cal­cu­la­tions as more

luck than judge­ment, pre­fer­ring to cite Jean Richer and Gio­vanni Domenico Cassini’s rig­or­ously cal­cu­lated 22,000 Earth radii (140,162,000km) as the first sci­en­tif­i­cally plau­si­ble es­ti­mate (de­spite the fact they were fur­ther from the mark than Huy­gens).

Lightyears and par­secs

The AU re­mains a use­ful unit for dis­tances within the So­lar Sys­tem. But the So­lar Sys­tem is a tiny corner of the Uni­verse and much big­ger units are needed once we go beyond it. A lightyear is de­fined as how far a beam of light trav­els in one year – around 9.5 tril­lion km. If you want to be pre­cise, the IAU re­gards a year as 365.25 days mak­ing a lightyear 9,460,730,472,580,800m.

The germ of the con­cept orig­i­nated with Friedrich Bes­sel, who, in 1838, made the first suc­cess­ful mea­sure­ment of the dis­tance to a star out­side our So­lar Sys­tem, 61 Cygni. In his find­ings he men­tioned that light takes 10.3 years to travel from 61 Cygni to Earth. He wasn’t se­ri­ously posit­ing the idea of lightyears as a unit; for one thing the speed of light at the time had yet to be cal­cu­lated ac­cu­rately. How­ever, the con­cept was too en­tic­ing to ig­nore and by the end of the 19th cen­tury it was in gen­eral use, even if some as­tronomers ever since – in­clud­ing Arthur Ed­ding­ton who called it ir­rel­e­vant – have been sniffy about its use.

So why is the lightyear use­ful? Take our near­est ex­tra­so­lar star, Prox­ima Cen­tauri. In­stead of ex­press­ing its dis­tance in miles (38,624,256,000,000) or AU (258,064.516) – val­ues too vast to grasp mean­ing­fully – we can say it’s 4.25 lightyears away. Our clos­est neigh­bour­ing gal­axy, An­dromeda, is over two mil­lion lightyears away.

So the lightyear is like metrol­ogy by metaphor, sim­i­lar to “ar­eas of rain­for­est the size of Wales”. But while the gen­eral pub­lic em­braces the lightyear be­cause it’s such an easy con­cept to get your mind around, sci­en­tists, of course, pre­fer a unit that needs a di­a­gram to ex­plain. Of­fi­cially, a par­sec is the dis­tance at which one as­tro­nom­i­cal unit sub­tends an an­gle of one arc­sec­ond, which would leave most peo­ple go­ing, “Huh?” It’s not quite as ar­cane as it sounds.

The par­sec is based on par­al­lax vi­sion. For a prac­ti­cal ex­am­ple, hold your fin­ger in front of your eyes, then al­ter­nate clos­ing each eye; the fin­ger ap­pears to leap from side to side in re­la­tion to the back­ground.

Now imag­ine this on a cos­mic scale. If Earth is on one side of the Sun, when we look at a nearby star, it will ap­pear to be in one po­si­tion in re­spect to the stars in the back­ground. Six months later, when Earth is on the ex­treme other side of the Sun, that same star will ap­pear to be in a slightly dif­fer­ent po­si­tion against its back­ground.

We’re talking tiny amounts of dif­fer­ence, mea­sured in arc­sec­onds (of which there are 3,600 in one de­gree of sky). A par­sec is the dis­tance to a star that would ap­pear to move by two arc­sec­onds over a six-month pe­riod; or, to put it an­other way, one arc­sec­ond as Earth trav­els the lin­ear equiv­a­lent of 1AU. Hence the name: PAR­al­lax, arc­SEC­ond. The term first ap­peared in a 1913 pa­per by English astronomer Frank Dyson.

A par­sec is roughly 30 tril­lion km, or a lit­tle over three lightyears. Re­turn­ing to our pre­vi­ous ex­am­ples, this places Prox­ima Cen­tauri 1.3 par­secs away from us, and the An­dromeda Gal­axy nearly 800 kilo­par­secs. Hang on – kilo­par­secs? Yes, even par­secs aren’t huge enough for some scales, so they’re up­scaled to kilo­par­secs, mega­parsecs and gi­ga­parsecs (one thou­sand, one mil­lion and one bil­lion par­secs re­spec­tively).

Which means we can now in­form you that the edge of the vis­i­ble Uni­verse is 14 gi­ga­parsecs away with­out wear­ing out the zero key on our key­board.

Earth Mer­cury Venus 1 Mars 5 Jupiter A to-scale rep­re­sen­ta­tion of the As­tro­nom­i­cal Units of dis­tance from the Sun to Saturn. The dis­tance to Earth’s or­bit is 1AU 10 Saturn

A and B show how a nearby star ap­pears to move against its back­ground when Earth is at dif­fer­ent po­si­tions; C is equal to an AU; D is a par­al­lax an­gle of one arc­sec­ond; E is a par­sec

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