From the reveal of the solar corona, to the deep red hues of the Moon in shadow, eclipses are some of the most striking astronomical events you can see without a telescope.

But an eclipse is also an amazing time to do science. When one celestial body slides in front of another, it can give us surprising insights into the nature of both objects.

And that’s why people have studied lunar eclipses for thousands of years, as a way to make new discoveries about the Earth and its moon. A lunar eclipse happens any time the Earth passes between the Sun and the Moon, casting an Earth-shaped shadow on the lunar surface. Back in the fourth century BCE, the Greek philosopher Aristotle noticed that this shadow was round.

In fact, he observed multiple eclipses and noticed that the shadow was always round, whether the Moon was high or low in the sky. And he knew that the only object that always casts a circular shadow, no matter the angle, is a sphere. In other words, Aristotle saw lunar eclipses as proof that the Earth is round.

About a century later, an ancient Greek astronomer named Aristarchus used a lunar eclipse to calculate the distance to the Moon. Now he did make an assumption that’s not quite right, but was close enough to get a solid estimate: He started with the idea that the Earth’s shadow on the Moon was the same size as the Earth. Then, he timed a lunar eclipse.

He figured out that the Moon takes three hours to pass through Earth’s shadow. Meaning it takes three hours to travel one Earth diameter. Now that Aristarchus knew how fast the Moon was traveling, he could figure out exactly what distance it would travel in about 27.3 days, the amount of time the Moon takes to go around the Earth once.

That distance told him the size of the Moon’s orbit, which he assumed was just the circumference of a really big circle. The Moon’s orbit isn’t really a perfect circle, but again, he was close enough. Then, using some simple geometry, Aristarchus calculated the radius of that circle, the distance from the Earth to the Moon.

And despite his imperfect assumptions, the distance he calculated was basically spot-on, roughly 30 Earths in length. Aristarchus also used trigonometry to estimate the size of the Moon. There were also other ancient Greek astronomers out there making use of math and lunar eclipses, but eventually, they exhausted the astronomical discoveries that could be made this way.

It would be another two millennia before modern telescope technology, and the ability to launch stuff into outer space, allowed scientists to revisit eclipses as a way to learn more about the Moon. Like in October 2014, scientists used a spacecraft called the Lunar Reconnaissance Orbiter, or LRO, to map exactly what happens to the Moon’s surface when its hot and sunny day side is suddenly plunged into temporary darkness. Since the Moon has practically no atmosphere, it lacks the ability to hold onto warmth it builds up during the lunar day.

But different minerals don’t react to that loss of thermal energy in the same way. They have different thermal properties. So by measuring how quickly certain parts of the surface cool during a lunar eclipse, scientists could make some inferences about what’s going on up there.

Like what the rocks and dust are made of, and how densely they’re packed together. LRO’s heatmap targeted an area of the lunar surface with a cold spot, an area surrounding a young impact crater that becomes 5 to 10 degrees cooler than the rest of the surface. Or at least it does during the course of a two week long lunar night.

The heatmap would reveal how much it cooled during an hours-long lunar eclipse. But it turns out the cold spot stayed over 10 degrees warmer than the area around it. There was some sort of short-term insulating effect.

And astronomers still aren’t exactly sure why. One hypothesis about how cold spots work suggests that they’re fluffier than the surrounding surface material, changing how they respond to heat loss. But the fact that there are two different results between a lunar eclipse and a lunar night hints that there’s something more complex going on down there.

There’s still a puzzle to solve, but LRO’s heat map showed that lunar eclipses offer a way to explore the Moon in detail. And sometimes, they also offer a unique insight into Earth. During a lunar eclipse, the Moon looks red because of the way Earth’s atmosphere interacts with sunlight: Most of the atmosphere scatters bluer wavelengths away from the lunar surface and bends the red wavelengths toward it.

Whatever light bounces off the Moon and back to us creates the overall color we see. But the ozone layer absorbs red light and lets bluer wavelengths through, and this creates a turquoise fringe around an otherwise reddish Moon. Based on the location of this ring around Earth’s shadow, scientists have been able to use trigonometry and other mathematical tools to figure out the position and the height of the ozone layer, between 50 and 80 kilometers above the ground.

These recent studies show us that no matter how advanced our technology is today, there’s still plenty to learn from ordinary events like lunar eclipses. And modern astronomers can still explore space through the same phenomena that the ancients used to build their understanding of the universe. So when you’re sitting in class wondering if you’ll ever actually need to know trigonometry, here’s your answer.

And if you’re looking for more help to get you through that math course, check out the new Study Hall series called “Real World College Math.” The series is a tour of foundational math topics that shows you how math applies to the real world, like how in this video we used trigonometry to figure out Earth’s size and shape. Plus many other examples of the math we do every day, like how counting helps us figure out how likely things are to happen. It’s designed to give students a sense of belonging within the field of mathematics.

So this series is a resource to help those who want to continue their education beyond high school accomplish that goal. New episodes come out every Tuesday on youtube.com/StudyHall. Thanks for watching!