How far away is the moon?

When the grade school­ers show up at Perkins Obser­va­tory, they invari­ably ask, “How far away is that.” Since 650 bil­lion miles doesn’t make a whole lot of sense to them (or me, quite frankly), the temp­ta­tion is to say, “Really, really far away.”

Even the dis­tance to the moon —­ about a quar­ter of a mil­lion miles —­ is incomprehensible.

One of my col­leagues at Ohio Wes­leyan Uni­ver­sity once said to me, “It’s easy, just 10 times around Earth.” I replied, “So how many times have you trav­eled around Earth, even once?”

It helps to go out and look. You can see the moon from your back­yard, and it looks very obvi­ously close. Binoc­u­lars show the craters as small dots on the moon’s sur­face. A small tele­scope shows the craters in more detail, plus moun­tain ranges and giant lava fields, to boot.

These details were invis­i­ble to human­ity before the inven­tion of the tele­scope about four cen­turies ago. Sur­pris­ingly, many of the things we know about the moon, we have known for a lot longer than that.

The ancient Greeks knew that the moon and Earth were spher­i­cal — balls, not plates. Some of them even knew that the moon was very far away. Given that they had only what they could see with their eyes to work with, the meth­ods that they used to make these dis­cov­er­ies were quite ingenious.

Not that they drew the right con­clu­sions from the very begin­ning. Around 460 B.C., Anaxago­ras announced that the sun was a flam­ing rock 100 miles wide. The impli­ca­tion was that the moon, which looks about the same size in the sky, was large as well.

Of course, fig­ur­ing out the moon’s size and dis­tance are inter­re­lated. If the moon is large, it has to be far away to look so small in the sky.

These enor­mous esti­mates were so shock­ing to the cit­i­zens of Athens that Anaxago­ras was charged with impi­ety (a seri­ous offense back then), and the good astronomer was forced to flee the city in fear of his life.

The Athen­ian reac­tion was nat­ural enough. Anaxago­ras’ ideas vio­late sim­ple com­mon sense. A hun­dred miles is an incom­pre­hen­si­ble dis­tance to a cul­ture where peo­ple rarely trav­eled out­side their city or village.

Besides, the moon looks close. On a clear night, you can almost reach out and touch it, can’t you? It takes a brave sci­en­tist to con­tra­dict what most peo­ple can expe­ri­ence directly with their senses.

The Greeks couldn’t quite reach the moon, so they couldn’t run a tape mea­sure. How­ever, they soon fig­ured a way of actu­ally mea­sur­ing the moon’s size and dis­tance using the bud­ding sci­ence of trigonometry.

Come on. Keep read­ing. We can fig­ure out what the ancients did with­out all that icky math.

Try this: Go out­side. Hold your index fin­ger out at arm’s length, and close your right eye. Notice with your left eye where your fin­ger appears against some back­ground object. Now switch eyes. Did you notice that your fin­ger seems to move to a dif­fer­ent loca­tion with respect to the back­ground? Your fin­ger “moves” because you’re see­ing it from a dif­fer­ent angle each time. As you move your fin­ger closer, the dis­tance of the shift will get larger. As you move your fin­ger far­ther away, the shift gets smaller.

Your finger’s shift of posi­tion is called “par­al­lax.” By mea­sur­ing the size of the par­al­lax, you can tell the dis­tance of an object using trigonometry.

Really far-away objects like the moon don’t shift very far at all, so the key is get­ting your dif­fer­ent eye­balls as far apart as pos­si­ble. An astronomer must mea­sure the angu­lar dis­tance of the moon from a back­ground star on a given night. At the same moment, another astronomer at a dis­tant loca­tion must mea­sure the same dis­tance. Plug the infor­ma­tion into a trigono­met­ric for­mula and voila — instant distance.

Around 150 B.C., the Greek astronomer Hip­parchus did just that and dis­cov­ered that the moon’s dis­tance was about 30 times the diam­e­ter of the Earth.

The Earth, as we know now with absolute cer­tainty, is about 8,000 mile wide. That puts the moon at about 240,000 miles away, an amaz­ingly accu­rate fig­ure given the Greeks’ level of technology.

Hip­parchus’ dis­cov­ery must have been star­tling to his con­tem­po­raries. It placed the moon not just far away but really far away. In one amaz­ing act of sci­ence, a sin­gle astronomer had vastly increased the size of the universe.

These days, we can mea­sure the dis­tance to the moon with an accu­racy of a few feet by bounc­ing a radar sig­nal off its sur­face. The great­est dis­cov­er­ies of ancient times have now become commonplace.

That fact doesn’t lessen the accom­plish­ments of the Greeks. They didn’t have radar or com­put­ers. Instead, they had the most remark­able and flex­i­ble tools of all — the human mind and the will­ing­ness to fol­low their obser­va­tions to their log­i­cal con­clu­sions, even if they seemed to con­tra­dict com­mon sense.

These days, we would be far bet­ter off as humans if we fol­lowed their exam­ple with­out prej­u­dice or pre­sup­po­si­tion. It took a lot of guts to do it then, and it takes a lot of guts to do it now.

Tom Burns is the direc­tor of Ohio Wes­leyan University’s Perkins Obser­va­tory, and he would be very happy to answer your ques­tions or sell you a ticket to one of its upcom­ing Friday-night pro­grams. He can be reached at tlburns@owu.edu or 740–363-1257.

Posted by Tom Burns on Apr 29 2012. You can follow any responses to this entry through the RSS Feed. Comments can be made below.