Distances: Crash Course Astronomy #25

Summary

This script explores the historical quest to measure cosmic distances, starting with the ancient Greeks' determination of Earth's size and the distances to the Moon and Sun. It delves into the astronomical unit's significance, the use of parallax for nearby stars, and brightness comparisons for more distant ones. The script highlights humanity's journey from basic geometry to advanced astrophysics, revealing the scale of the Universe and our place within it.

Takeaways

• 🌌 The ancient Greek perception of stars as holes in a crystal sphere reflects the challenge of understanding the vastness of the universe.
• 📏 The concept of parallax is used to measure distances in space, similar to how our eyes use depth perception to gauge the distance of objects.
• 🌍 Eratosthenes calculated the Earth's circumference using geometry and the angle of the sun's rays at different locations, demonstrating early scientific ingenuity.
• 🌕 Lunar eclipses and the phases of the Moon were used by ancient astronomers to determine the distances and sizes of celestial bodies, including the Earth and the Moon.
• 🔍 Aristarchus of Samos used the Earth's size as a reference to estimate the distances to the Moon and the Sun, showing the progression of astronomical methods.
• 📚 Johannes Kepler and Isaac Newton's work on planetary orbits laid the groundwork for understanding the distances to other planets, highlighting the importance of mathematical principles in astronomy.
• 🌞 The astronomical unit (AU) is a fundamental measure in astronomy, representing the average distance from the Earth to the Sun, and is crucial for understanding the scale of the solar system.
• 📡 In the 1960s, radar pulses bounced off Venus were used to accurately determine the length of an AU, showcasing the advancement of technology in space measurement.
• 👀 The parallax method, using the Earth's orbit as a baseline, was essential for measuring the distances to stars, but initial attempts showed no parallax due to the immense distances involved.
• 🌟 The first successful measurement of a star's parallax was 61 Cygni in 1838, revealing the immense scale of the universe and the limitations of direct observation.
• 🌠 The light year and parsec are units of distance used in astronomy to express the vast distances to stars and galaxies, making these measurements more comprehensible.

Q & A

What is the concept of parallax and how does it relate to measuring distances?

Parallax is the apparent shift in the position of an object when viewed along different lines of sight. It's used in astronomy to measure distances to stars by observing the change in their position relative to more distant objects when the Earth is at opposite points in its orbit around the Sun.

Why did ancient people think the stars were holes in a crystal sphere?

They thought this way because the stars appeared to be fixed points of light in the sky, and the idea of a crystal sphere provided a simple explanation for the distribution of these 'holes' through which divine light shone.

How did Eratosthenes measure the Earth's circumference over 2000 years ago?

Eratosthenes used the angle of the sun's rays at noon in two different cities during the summer solstice and the known distance between them to calculate the Earth's circumference using geometric principles.

What is the astronomical unit and why is it important?

The astronomical unit (AU) is the average distance from the Earth to the Sun, approximately 149,597,870.7 kilometers. It's fundamental in astronomy as it provides a standard measure for distances within our solar system and beyond.

How did ancient astronomers determine the distances to the Moon and the Sun?

They used the Earth's size as a reference and observed phenomena like lunar eclipses and the Moon's phases to apply geometric calculations and determine the relative distances and sizes of the Moon and the Sun.

What is the significance of the transit of Venus in measuring the AU?

The transit of Venus, when the planet crosses the face of the Sun, provides an opportunity to measure the time it takes for the transit to occur from different points on Earth. This timing can be used to calculate the length of an AU using orbital equations.

How did astronomers determine the distance to the first star using parallax?

The first star to have its parallax successfully measured was 61 Cygni in 1838. Astronomers observed its apparent shift in position relative to more distant stars when viewed from opposite points in Earth's orbit and applied trigonometry to calculate its distance.

What is a light year and how is it used in astronomy?

A light year is the distance that light travels in one year, about 9.461×10^12 kilometers. It's used as a unit of distance in astronomy, especially for measuring the vast distances between stars and galaxies.

What is a parsec and how does it relate to parallax?

A parsec is a unit of distance used in astronomy, equal to about 3.26 light years. It's defined as the distance at which a star would show a parallax shift of one arcsecond over the course of a year.

How do astronomers use the brightness of stars to determine their distances?

Astronomers use the inverse square law, which states that the brightness of an object falls off with the square of the distance from the observer. By comparing the apparent brightness of a known distance star with another star, astronomers can estimate the more distant star's brightness and distance.

What role does curiosity play in the advancement of astronomical knowledge?

Curiosity has driven astronomers and scientists to ask questions about the universe, leading to discoveries and methods that have expanded our understanding of the Earth, the solar system, and the cosmos, starting from the simple question of the Earth's size by ancient Greeks.

Outlines

00:00

🔍 Discovering Distances: From Parallax to Earth's Size

The script begins by discussing the challenge of determining distances to celestial objects, using parallax as an example. It explains how ancient beliefs about the stars being holes in a crystal sphere evolved into the understanding that they are distant points of light. The script then delves into the methods used by ancient Greeks to determine the Earth's round shape and size, highlighting Eratosthenes' use of geometry and the angle of the sun's rays to calculate Earth's circumference. This discovery is noted as a significant step in establishing a scale to the universe, which paved the way for further exploration and understanding of distances to the Moon, Sun, and beyond.

05:07

📏 The Astronomical Unit: Unlocking the Solar System

This paragraph focuses on the importance of determining the Earth-Sun distance, known as the astronomical unit (AU), which serves as the fundamental unit of measurement in astronomy. The script explains how the knowledge of the AU enabled the prediction of planetary motions and the exploration of the solar system. It also discusses the use of parallax in depth perception and how astronomers used Earth's orbit around the Sun as a large baseline to measure the distance to stars. The first successful measurement of a star's parallax, 61 Cygni in 1838, is mentioned, along with the introduction of the light year and parsec as units of distance for interstellar measurements.

10:09

🌌 From Stars to Galaxies: The Expansion of Cosmic Understanding

The final paragraph of the script discusses the broader implications of understanding distances in astronomy. It explains how the measurement of distances to stars led to insights about their physical nature, including luminosity, temperature, mass, and diameter. The script also describes how the knowledge of nearby stars' distances was used to estimate the distances to more distant stars through brightness comparison. It concludes by emphasizing the importance of curiosity in scientific discovery, noting that the journey from determining the Earth's size to understanding the scale of the universe began with the ancient Greeks' curiosity.

Keywords

💡Parallax

Parallax is the apparent shift in the position of an object when viewed from different positions. It is used in astronomy to measure distances to nearby stars by observing their change in position against the background of more distant stars as the Earth orbits the Sun. In the script, parallax is introduced as a method to understand the distance to stars, with the example of observing a star's position change when viewed from opposite ends of Earth's orbit.

💡Astronomical Unit (AU)

The Astronomical Unit is a unit of distance used in astronomy, defined as the average distance from the Earth to the Sun, which is approximately 149,597,870.7 kilometers. It serves as a fundamental scale for measuring distances within our solar system and beyond. The script highlights the importance of accurately determining the AU to unlock the scale of the solar system and the distances to other celestial bodies.

💡Eratosthenes

Eratosthenes was an ancient Greek philosopher who is known for calculating the circumference of the Earth using geometric principles and observations of the Sun's angle at different locations. His method and result are mentioned in the script as an early example of applying scientific reasoning to determine the scale of our planet.

💡Lunar Eclipse

A lunar eclipse occurs when the Earth comes between the Sun and the Moon, casting a shadow on the Moon. The script uses the lunar eclipse as a context to explain how knowing the Earth's size allows astronomers to calculate the distance to the Moon by observing the curvature of Earth's shadow.

💡Aristarchus of Samos

Aristarchus of Samos was an ancient Greek astronomer who used the Earth's size as a basis to calculate the distances to the Moon and the Sun, as well as their sizes. His methods, though not highly accurate, were sound and laid the groundwork for later, more precise measurements. The script references his contributions to early astronomy and the understanding of our solar system.

💡Johannes Kepler

Johannes Kepler was a 17th-century astronomer known for his laws of planetary motion, which described the orbits of planets around the Sun. His work, along with Isaac Newton's, provided the mathematical foundation necessary for understanding planetary distances. The script mentions Kepler in the context of the mathematical groundwork that enabled the measurement of distances to planets.

💡Isaac Newton

Isaac Newton was a physicist and mathematician whose laws of motion and universal gravitation were pivotal in understanding the forces governing planetary orbits. The script refers to Newton's work in conjunction with Kepler's to emphasize the importance of their combined contributions to the field of astronomy.

💡Radar

Radar is a method of detecting objects by emitting radio waves and observing the reflections of these waves off of objects. In the script, radar is mentioned as the technique used in the 1960s to bounce pulses off Venus, allowing for the precise measurement of the Astronomical Unit by timing how long it took for the light to travel to Venus and back.

💡Light Year

A light year is a unit of distance equal to the distance that light travels in one year, approximately 9.461×10^12 kilometers. It is used to express the vast distances between stars and galaxies. The script introduces the light year as a more manageable unit for describing the distances to stars, such as 61 Cygni being 11.4 light years away.

💡Parsec

A parsec is a unit of distance used in astronomy, defined as the distance at which one astronomical unit subtends an angle of one arcsecond. It is approximately equal to 3.26 light years. The script explains the parsec as a convenient unit for measuring distances to stars based on the parallax angle, with an example that a star one parsec away will have a parallax shift of one arcsecond.

💡Spectrometry

Spectrometry is the study of the interaction between matter and electromagnetic radiation, often used in astronomy to analyze the composition, temperature, and other properties of celestial bodies based on their emitted or absorbed spectra. The script mentions spectrometry as a tool for determining the type of stars and their intrinsic brightness, which, along with parallax measurements, helps in calculating distances to more distant stars.

Highlights

Ancient Greeks believed stars were holes in a crystal sphere, reflecting the concept of a spherical Earth.

Eratosthenes calculated the Earth's circumference using geometry and the angle of the Sun's rays at different locations.

Aristarchus of Samos used the Earth's size to estimate the distances and sizes of the Moon and Sun.

Johannes Kepler and Isaac Newton laid the groundwork for understanding planetary orbits, which helped in calculating distances to planets.

The astronomical unit (AU) is crucial for understanding the distances within the solar system.

Radar pulses bounced off Venus were used to measure the AU with high precision in the 1960s.

Binocular vision and parallax allow us to perceive distances of nearby objects.

The Earth's orbit provides a large baseline for measuring stellar parallax, essential for determining star distances.

61 Cygni was the first star to have its parallax measured, revealing its immense distance.

A light year was introduced as a unit to express the vast distances to stars more conveniently.

The parsec is a unit of distance based on parallax shift, useful for astronomical measurements.

Proxima Centauri, the nearest star to the Sun, is approximately 4.2 light years away.

Space-based satellites have improved the accuracy of measuring distances to stars.

The brightness of stars and their parallax can be used to calculate distances to more distant stars.

Spectroscopic analysis helps determine the properties of stars, such as mass and diameter, once their distance is known.

Exploding and pulsating stars provide additional methods for measuring vast cosmic distances.

The understanding of star distances has contributed to comprehending the scale of the Universe.

Crash Course Astronomy is produced in association with PBS Digital Studios, offering educational content on various topics.

Transcripts

Oh. Hey! Sorry, I don’t mean to be rude. I’m just trying to figure out how far away my thumb is.

How? Parallax.

Centuries ago, people thought the stars were holes in a huge crystal sphere, letting through

heavenly light. It wasn’t clear just how big the sphere was, but it was pretty dang big.

I have some sympathy for them. By eye, and for all intents and purposes, the stars are

infinitely far away. If you drive down a road you’ll see trees nearby flying past you,

but distant mountains moving more slowly. The Moon is so far it doesn’t seem to move

at all compared to nearby objects — and it’s easy for your brain to think it’s

much closer, smaller, and actually following you, which is a bit creepy. Sometimes people

even think it’s a UFO tailing them.

Finding the distance to something really far away is tough. It’s not like you can you

can just pace off the distance.

Or can you?

The ancient Greeks knew the Earth was round and there are lots of ways to figure that

out. For example, ships sailing over the horizon seem to disappear from the bottom up, as you’d

expect as they slip around the Earth’s curve.

But how big is the Earth? Over 2000 years ago, the Greek philosopher Eratosthenes figured

it out. He knew that at the summer solstice, the Sun shone directly down a well in the

city of Syene at noon. He also knew that at the same time, it was not shining straight

down in Alexandria, and could measure that angle.

There’s a legend that he paid someone to pace off the distance between the two cities

so he could find the distance between them. But more likely he just used the numbers found

by earlier surveying missions. Either way, knowing the distance and the angle, and applying

a little geometry, he calculated the circumference of the Earth. His result, a little over 40,000

km, is actually amazingly accurate!

For the very first time, humans had determined a scale to the Universe. That first step has

since led to a much, much longer journey.

Once you know how big the Earth is, other distances can be found. For example, when

there’s a lunar eclipse, the shadow of the Earth is cast on the Moon. You can see the

curve of the Earth’s edge as the shadow moves across the Moon. Knowing how big the

Earth is, and doing a little more geometry, you can figure out how far away the Moon is!

Also, the phases of the Moon depend on the angles and distances between the Earth, Moon,

and Sun. Using the size of the Earth as a stepping stone, Aristarchus of Samos was able

to calculate the distances to the Moon and the Sun as well as their sizes. That was 2200 years ago!

His numbers weren’t terribly accurate, but that’s not the important part. His methods

were sound, and they were used later by great thinkers like Hipparchus and Ptolemy to get

more accurate sizes and distances. They actually did pretty well, and all over a thousand years

before the invention of the telescope! And I think it also says a lot that these ancient

thinkers were willing to accept a solar system that was at least millions of kilometers in size.

But at this point things got sticky. Planets are pretty far away and look like dots. Our

methods for finding distances failed for them.

For a while, at least.

In the 17th century, Johannes Kepler and Isaac Newton laid the mathematical groundwork of

planetary orbits, and that in turn made it possible, in theory, to get the distances to the planets.

Ah, but there was a catch. When you do the math, you find that measuring the distances

to the other planets means you need to know the distance from the Earth to the Sun accurately.

For example, it was known that Jupiter was about 5 times farther from the Sun than the

Earth was, but that doesn’t tell you what it is in kilometers.

So how far away is the Sun? Well, they had a rough idea using the number found by the Greeks,

but to be able to truly understand the solar system, they needed a much more accurate value for it.

To give you an idea of how important the distance from the Earth to the Sun is, they gave it

a pretty high-falutin’ name: the astronomical unit, or AU. Mind you, not “an” astronomical

unit, “the” one. That’s how fundamental it is to understanding everything!

A lot of methods were attempted. Sometimes Mercury and Venus transit, or cross the face

of the Sun. Timing these events accurately could then be used to plug numbers into the

orbital equations and get the length of an AU. Grand expeditions were sent across the

globe multiple times to measure the transits, and didn’t do too badly. But our atmosphere

blurs the images of the planets, putting pretty big error bars on the timing measurements.

The best they could do was to say the AU was 148,510,000 km -- plus or minus 800,000 km.

That’s good, but not QUITE good enough to make astronomers happy.

Finally, in the 1960s, astronomers used radio telescopes to bounce radar pulses off of Venus.

Since we know the speed of light extremely accurately, the amount of time it takes for

the light to get to Venus and back could be measured with amazing precision.

Finally, after all these centuries, the astronomical unit was nailed down.

It’s now defined to be 149,597,870.7 kilometers. So there.

The Earth orbits the Sun on an ellipse, so think of that as the average distance of the

Earth from the Sun.

Knowing this number unlocked the solar system. It’s the fundamental meterstick of astronomy,

and the scale we use to measure everything. Having this number meant we could predict

the motions of the planets, moons, comets, and asteroids. Plus, it meant we could launch

our probes into space and explore these strange new worlds for ourselves, see them up close,

and truly understand the nature of the solar system.

And it’s even better than that. Knowing the Astronomical Unit meant unlocking the stars.

We have two eyes, and this gives us binocular vision. When you look at a nearby object,

your left eye sees it at a slightly different angle than your right eye. Your brain puts

these two images together, compares them, does the geometry, and gives you a sense of

distance to that object.

And you thought your teacher lied when she said math was useful in everyday life.

We call this ability depth perception. You can see it for yourself by doing the thumb

thing: as you blink one eye and then the other, your thumb appears to shift position relative

to more distant objects. That shift is called parallax. The amount of shift depends on how

far apart your eyes are, and how far away the object is.

If you know the distance between your eyes — we’ll call this the baseline — then

you can apply some trigonometry and figure out how far away the object is. If the object

is nearby, it shifts a lot; if it’s farther away, it shift less. It works pretty well,

but it does put a limit on how far away we can reasonably sense distance with just our eyes.

Stars are a bit beyond that limit. If we want to measure their distance using parallax,

we need a lot bigger baseline than the few centimeters between our eyes.

Once astronomers figured out that the Earth went around the Sun rather than vice-versa,

they realized that the Earth’s orbit made a huge baseline. If we observe a star when

the Earth is at one spot, then wait six months for the Earth to go around the Sun to the

opposite side of its orbit and observe the star again, then in principle we can determine

the distance to the star, assuming we know the size of the Earth’s orbit.

That’s why knowing the length of the astronomical unit is so important! The diameter of Earth’s

orbit is about 300 million kilometers, which makes for a tremendous baseline. Hurray!

Except, oops. When stars were observed, no parallax was seen. Was heliocentrism wrong?

Pfft, no. It’s just that stars are really and truly far away, much farther than even

the size of Earth’s orbit. The first star to have its parallax successfully measured

was in 1838. The star was 61 Cygni, a bit of a dim bulb. But it was bright enough and

close enough for astronomers to measure its shift in apparent position as the Earth orbited

the Sun. 61 Cygni is about 720,000 astronomical units away. That’s a soul-crushing distance;

well over 100 trillion kilometers!

In fact, that’s so far that even the Earth’s orbit is too small to be a convenient unit.

Astronomers came up with another one: The light year. That’s the distance light travels

in a year. Light’s pretty fast, and covers about 10 trillion kilometers in a year. It’s

a huge distance, but it makes the numbers easier on our poor ape brains. That makes

61 Cygni a much more palatable 11.4 light years away.

Astronomers also use another unit called a parsec. It’s based on the angle a star shifts

over the course of a year; a star one parsec away will have a parallax shift of one arcsecond—1/3600th

of a degree. That distance turns out to be about 3.26 light years. As a unit of distance

it’s convenient for astronomers, but it’s a terrible one if you’re doing the Kessel Run. Sorry, Han.

The nearest star to the sun we know of, Proxima Centauri, is about 4.2 light years away. The

farthest stars you can see with the naked eye are over a thousand light years distant,

but the vast majority are within 100 light years.

Space-based satellites are used now to accurately find the distance to hundreds of thousands

of stars. Still, this method only works for relatively nearby stars, ones that are less

than about 1000 light years away. But once we know those distances, we can use that information

on more distant stars.

How? Well, like gravity, the strength of light falls off with the square of the distance.

If you have two stars that are the same intrinsic brightness—giving off the same amount of

energy—and one is twice as far as the other, it will be ¼ as bright. Make it ten times

farther away, it’ll be 1/100th as bright.

So if you know how far away the nearer one is by measuring its parallax, you just have

to compare its brightness to one farther away to get its distance. You have to make sure they’re

the same kind of star; some are more luminous than others. But thanks to spectroscopy, we can do just that.

A star’s distance is the key to nearly everything about it. Once we know how far it is, and

we can measure its apparent brightness, we can figure out how luminous it is, how much

light it’s actually giving off, and its spectrum tells us its temperature.

With those in hand we can determine its mass and even its diameter.

Once we figured out how far away stars are, we started to grasp their true physical nature.

This led to even more methods of finding distances. The light given off by dying stars, exploding

stars, stars that literally pulse, get brighter and dimmer over time. All of these and more

can be used to figure out how many trillions of kilometers of space lie between us and them.

And we see stars in other galaxies, which means we can use them to determine the actual

size and scale of the Universe itself.

And all of this started when some ancient Greeks were curious about how big the Earth was.

Curiosity can take us a great, great distance.

Today you learned that ancient Greeks were able to find the size of the Earth, and from

that the distance to and the sizes of the Moon and Sun. Once the Earth/Sun distance

was found, parallax was used to find the distance to nearby stars, and that was bootstrapped

using brightness to determine the distances to much farther stars.

Crash Course Astronomy is produced in association with PBS Digital Studios. Head over to their

YouTube channel to catch even more awesome videos. This episode was written by me, Phil

Plait. The script was edited by Blake de Pastino, and our consultant is Dr. Michelle Thaller.

It was directed by Nicholas Jenkins, edited by Nicole Sweeney, the sound designer is Michael

Aranda, and the graphics team is Thought Café.