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 firstname.lastname@example.org or 740–363-1257.