A little later today (April 8th) a ball of rock the size  of Australia will drift directly between the   Earth and theSun.

That ball—our Moon—will  cast a shadow that will pass across the   North American continent, carving a narrow  line from Mexico to Newfoundland.

For anyone   lucky enough to be on that line the sky will go  twilight-dark for up to four and a half minutes,   and the Sun will be transformed into a black  disk crowned with the ghostly filaments of its   corona.

will witness a total solar eclipse.

Of  all the astronomical phenomena you can witness,   the total solar eclipse has to be the most  visceral--the most in-your-face reminder that   our reality consists of giant balls of rock  spinning around stars.

And it's also the eclipse   and phenomena like it that set us on the path to  understanding that reality in the first place.

On this show we tend to speak from a position  of already knowing stuff.

We know that space   is big and that moons orbit planets orbit  stars, and we go from there to some pretty   crazy places.

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But imagine what it must  have been like to know nothing.

I mean,   nothing about the scale of the cosmos or the  nature of the solar system.

Imagine how terrifying   and mysterious a total solar eclipse would be.

But also inspiring--you might feel inspired to   figure out what in the world--or out of it--was  going on.

And in fact the eclipse and phenomena   like it were the very first tools used by the  ancients on our path from that place of mystery   and not-knowing to our modern understanding of  the universe.

So, today, as a celebration of   the impending eclipse I want to retrace some of  that cognitive journey so that when the eclipse   happens we can appreciate a bit better how  we know what we know about what we're seeing.

This particular telling of how we figured  out the universe starts with the ancient   greeks.

Many other peoples contributed  different things to our modern story,   but it was the Greeks who kickstarted the whole  science thing.

So what did they figure out?

Well,   despite the common notion that we thought  the world was flat until Christopher Columbus   sailed around it, the ancient Greeks were  well aware of the roundness of the planet.

They knew that boats disappear ‘hull’ first  as they head out to sea with their large   sails disappearing last.

They knew  that, when moving north or sound,   the altitude of stars change in the way you’d  expect for moving on the surface of a sphere.

And they knew the Earth was round because  of eclipses.

Lunar eclipses in this case.

As long as you know that these are caused  by the Moon moving through Earth’s shadow,   it’s hard to imagine a non-round object  causing that distinctly round shadow.

And, as it happens, the ancient Greeks were  fully aware of the cause of both lunar and   solar eclipses.

That was first worked out  by Anaxagoras in the fifth century BCE.

He   realized that only one configuration made  consistent sense of our observations.

For   it to all make sense the Moon must travel around  the earth, must be spherical, and must be closer   to us than the sun.

That gives us a changing  partial view of the illuminated side of the   Moon—hence phases—and a lunar shadow for solar  eclipses and Earth shadow for lunar eclipses.

But the subtle details of the eclipses revealed so  much more than their basic nature.

As I mentioned,   the shape of Earth’s shadow pointed to our  planet’s roundness.

There’s also the fact   that eclipses don’t happen every lunar orbit,  but rather can only happen twice per year.

That   fact was a clue that Earth orbits the Sun.

See, there’s a slight misalignment between   the Earth’s orbit around the Sun and the Moon’s  around the Earth.

That means the Moon usually   ducks under or over Earth’s shadow, and  its own shadow usually missing the Earth also.

But twice a year the Moon’s orbital tilt  is perpendicular to a line connecting   Sun and Earth.

At those times the Moon has to  pass through Earth’s orbital plane while it’s   on the Sun-Earth line On this “line of nodes”  we’ll typically get a solar and a lunar eclipses,   and sometimes more than one depending on the  Moon’s orbital position.

This periodicity to   the eclipses tells us that the positions of  the Sun and Earth change in a regular manner,   and we now understand this  to be due to Earth’s orbit.

OK, great, so eclipses gave us the basic shape  of the Moon-Earth-Sun system.

But they also give   us the relative size scales for our growing  model solar system.

Those details are hidden   in deeper subtleties of the eclipses, and  it took our next ancient Greek—Aristarchus   of Samos—to figure them out in the 3rd century  BCE.

Aristarchus figured out three clever ways   to use the shadows cast by celestial bodies to  map the solar system.

The shadows of eclipses,   but also the shadow that the Moon  casts on itself causing lunar phases.

The amount of time the moon spent in its different  phases tells us the relative distances between   Earth, Moon and Sun.

You might think that  the moon spends equal time in its different   phases.

For example, the time spent as a crescent  should be the same as the time spent gibbous.

For   simplicity, by “crescent” I’m going to mean  anything less than half full—including a new   moon—that’s when the Moons is closer to the Sun.

I’ll use gibbous for anything more than half full,   including actually full—when the Moon is  further from the Sun.

Okay, and confusingly   those half-full points are technically called  quarter moons.

Don’t ask me why.

So surely   the Moon should be in the crescent and gibbous  phases for the same amount of time.

After all,   the Moon does spend the same amount of time on  each side of its orbit, on average at least.

But, oddly, the Moon is gibbous for a  bit longer than it’s a crescent.

The reason   for this is that the distance to the Sun also  matters.

If the Sun were infinitely far away,   then indeed we’d expect equal time in gibbous and  crescent phases.

We see a half moon when the Sun’s   light illuminate the Moon at 90-degrees to our  view of the moon.

If the Sun was extremely far   away compared to the size of the Moon’s orbit  then its rays arrive nearly parallel across   that orbit, and so the half-moon points  would be on opposite sides of the Earth.

But if the Sun isn’t “infinitely” far  compared to the Moon then its rays reach   the Moon at a different angle on either  side of the Earth.

The quarter-moon points   end up being a little closer to the Sun,  which means the crescent phase between   these points is shorter than the gibbous  phase beyond these points.

By measuring   the difference in the length of the  gibbous versus crescent phases it’s   potentially possible to get the distance of  the Sun relative to the distance to the moon.

The quarter moon points are only about  0.5 degrees off the locations expected   for an infinitely distant sun.

That tells us  that the Sun is nearly 400 times more distant   than the Moon.

Aristarchus measured a  bit high—he got 3 degrees, which told   him that the Sun is at 20 times the  lunar distance.

But remember that he   was working without clocks and without  telescopes, so let's cut him some slack.

Aristarchus’s second calculation is simpler.

It  uses the fact that the Moon exactly blocks the   Sun during a total solar eclipse—as indeed many people witness today (April 8th).

That told him that the ratio   of the size of the Moon to the size of the Sun has  to be the same as the ratio of the distance to the   moon to the distance to the Sun.

Now that sure would be helpful if he knew either of those distances.

But that brings us to the third thing that  Aristarchus figured out, this time using lunar   eclipses.

The Moon takes some time to pass through  Earth’s shadow during such an eclipse.

The width   of that shadow depends on the size of the Earth,  the distance between the Earth and the Moon,   but also on the size to and distance of the Sun.

Aristarchus used simple geometry to write down   some equations that related the ratios of sizes  and distances.

The ratio of sizes of the Earth to   both the Sun and Moon and the ratio of distances  between Earth and both the Sun and Moon, all in   terms of the ratio of the width of Earth’s shadow  to the Moon’s size—how many moons fit across that   shadow.

And that last one could be measured just  by watching a lunar eclipse.

It’s 2.6 moons, FYI.

Aristachus concluded correctly that the Moon  is approximately a third the diameter of the   Earth.

You might remember that he had  already gotten the ratio of Earth-Sun   to Earth-Moon distances from the phases of  the Moon—and he got a number that was too   small.

This error propagated to his estimate  of the Sun’s size, and so he found a ratio   between the Earth and Sun’s diameter that  was also about a factor of 20 too small.

But this was nonetheless all very impressive.

Aristarchus, using little more than shadows   and geometry, was the first to seriously present  evidence for our modern picture of the solar   system.

But you might have noticed that all these  distances and sizes are relative—for example,   it’s the size of the Moon or Sun compared  to the size of the Earth.

In order to pin   down the actual scale of the solar system,  we needed just one real physical value.

This came from the chief librarian  of the great library of Alexandria,   Eratosthenes, also in the 3rd century  BCE.

Erastonthenes realized that,   on a curved world, the Sun could be  directly overhead at noon at one latitude,   but at another latitude might be lower in  the sky.

He had heard that at noon on the   summer solstice the Sun illuminated the bottom  of a deep well in the city of Syene, far to the   south of Alexandria—he concluded that it must  be directly overhead at that time and place.

But he also knew that at  the same time in Alexandria,   the Sun wasn’t quite overhead.

A  vertical pole would still cast a shadow.

Again with simple geometry, and by measuring  the length of shadows cast on that day in   Alexandria as well as the distance to Syene,  Eratosthenes was able to calculate the radius   of the Earth.

And he got it right, to  within less than 2% of the true value.

Adding Aristachus’s measurement for the size of  the Earth to Erastothenes’ measurements of the   relative sizes of Earth, Moon and Sun, we got  our first real physical values for the sizes of   these bodies.

At the very least the size and  distance of the Moon was now pretty solid.

But there was still the uncertainty in  the distance to the Sun.

And we found new   motivation to get that distance right when we  finally figured out the motion of the planets.

We’ll breeze past Copernicus who verified the  suspicion of some of the ancient Greeks that   the Sun really is in the center of the solar  system, and go straight to Johanne Kepler.

His laws of planetary motion told us that the  relative speed of planets through space depends   on their distance from the Sun.

Finding the  distance between the Earth and Sun—what we   call the Astronomical Unit—would lock into place  our first ever precise model of the solar system.

And again, it was an eclipse of sorts  that gave us that number.

It was the   observation of another world passing  in front of the Sun—in this case a   planet rather than the moon, so not  really an eclipse, but a transit.

If you look at the Sun through a pinhole  camera when Mercury or Venus transit the Sun,   you’ll see a tiny black dot moving slowly  across a bright disk.

The line traveled by   the planet depends on the relative positions of  all three bodies—but also on your own position   on the Earth.

A transit observed from New  York might cross near the edge of that disk,   but might cross deep into the disk if observed  in Puerto Rico.

This is due to parallax—the   same effect as when your finger appears to  move side to side relative to the background   when you blink your eyes back and forth.

But in this case it’s called solar parallax.

Measuring the difference in position of  the transit at two different locations   tells you the distance to the  transiting planet and to the Sun.

There was an early attempt to measure a transit  of Mercury back in the 1660s—but Mercury’s tiny   size made the observation difficult and this  effort failed.

A century later the astronomer   Edmund Halley realized that Venus- being closer  to the earth, would make the measurement easier.

The only problem was that it transited much less  often - only twice per century, eight years apart.

So, when the regularly scheduled transits  of Venus arrived in 1761 and 1769,   the astronomy world was prepared, scattering  themselves across the world to observe the   1769 transit from as many places as possible.

Observations were made everywhere from   Philadelphia to St Petersburg to Tahiti that,  when combined, provided the first accurate   measurement of the size of the solar system.

It’s  a really cool moment in the history of science- a   massive international collaboration, requiring  large government grants to fund expeditions to   the far side of the planet.

It’s almost  like a precursor to modern ‘big science.’ So did they succeed?

Yes they did.

Put all of their measurements together, and you get the distance to the sun   as 153 million km.

That’s only 2% above  the modern accepted value.

With the earth’s   orbital radius and orbital period known, and  with the help of Kepler’s laws, the orbital   radii of every planet in the solar system could  be calculated immediately.

Not bad for watching   a dot move across the face of the Sun.

But this  achievement was really the crystallization of   two thousand years of astronomy, a final  synthesis of the revelations brought by   asymmetric lunar phases and of measuring ancient  lunar and solar eclipses.

Ultimately, though,   the credit goes to those clever humans who  witnessed these mystical-seeming phenomena and,   rather than credit gods and myths, resolved to  make sense of our once-mysterious space time.