By the early 20th century, astronomers had determined the basic structure of the Milky Way. Our galaxy is a flattened disk about 100,000 light years in diameter.

Beyond that, the internal structure was still a mystery. The key was to determine the distance to the stars. By determining the distance to a lot of them (millions, even billions), astronomers could map out the detailed structure of the disk.

That quest began over 2,000 years ago with the work of Hipparcos, a Greek astronomer who first determined the distance to the moon.

You can see the moon from your backyard. Given the knowledge we bring to it, it looks pretty close. After all, binoculars show the craters as small dots on the moon’s surface. A small telescope reveals the craters in more detail, plus mountain ranges and giant lava fields.

Those details were invisible to humanity before the invention of the telescope about four centuries ago.

Of course, the Greeks couldn’t measure the distance to the moon mechanically (the way we might determine a room’s dimensions).

However, they soon figured out a way of indirectly measuring the moon’s distance using the budding sciences of geometry and trigonometry and a notion we now call parallax.

A simple experiment will illustrate how parallax works. Close one eye and hold your index finger at arm’s length. Line up your finger with some object on the other side of the room.

Without moving your hand or finger, close the open eye and open the closed one. Notice how your finger is no longer lined up with the object? Since your eyes are not in the same place, you are observing your finger from slightly different angles.

Next, bring your finger closer to your head and do the same thing. Your finger seems to shift more against the background object because it’s closer.

Your finger “moves” because you see 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 simple geometry.

Faraway objects like the moon don’t shift much against the starry background, so the key is getting your eyes as far apart as possible.

An astronomer must measure the moon’s angular distance from a background object on a given night. At the same moment, another astronomer at a distant location must measure the same angular distance. Plug the information into a trigonometric formula and voila — instant distance.

More than two millennia ago, the Greek astronomer Hipparchus did just that.

As his background object, he chose the sun during a solar eclipse, probably the eclipse of 190 BCE. It was briefly total in the region of Greece called the Hellespont, a narrow strait we moderns call the Dardanelles.

However, at the exact moment some distance away in Alexandria, the eclipse covered only four-fifths of the sun. From that set of observations, Hipparchus drew a simple triangle and determined that the moon’s distance was at least 35.5 times the diameter of the Earth.

He later refined the minimum distance to 30.5 Earth diameters using a similar geometric technique.

Unfortunately, Hipparchus could not determine Earth’s diameter, but we can.

The Earth is, on average, 7.917.5 miles wide. If he had accurately determined Earth’s diameter, Hipparchus would have calculated the lunar distance as 241,284 miles away.

Modern radar technology has determined that the moon is 238 855 miles away on average. That’s 30.17 times Earth’s diameter, remarkable precision given the ancient Greeks’ technological level.

To this day, surveyors use a similar method to measure the distance to faraway objects on planet Earth.

The stars were a different story. There was no way of determining their distance. They were obviously farther away than the moon, but they all looked the same distance away.

What was needed was a startling advance in technology. That development would have to wait 2,000 years or so for the invention of the telescope and an astronomer’s dogged observation of a single star designated “61” in the constellation Cygnus, the Swan.

Tom Burns is the former director of the Perkins Observatory in Delaware.