Measuring Cosmic Distances: From Earth’s Size to Light Years

Name: Distances: Crash Course Astronomy #25
Uploaded: 2015-07-17T00:00:00+00:00
Duration: 11 min 20 s
Channel: CrashCourse
Description: Summary and key takeaways on Distances: Crash Course Astronomy #25: Summary & Key Takeaways, covering Historical Foundations Eratosthenes measured the Sun’s

CrashCourse

Jul 17, 2015

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11 min video

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2 min read

YouTube video ID: CWMh61yutjU

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Eratosthenes measured the Sun’s angle at noon in Syene and Alexandria, then used the known distance between the cities to calculate Earth’s circumference of roughly 40,000 km. Aristarchus of Samos treated that Earth size as a “stepping stone,” applying simple geometry to estimate the Moon’s and Sun’s distances. These early thinkers produced a solar‑system scale of millions of kilometres more than a millennium before telescopes existed.

The Astronomical Unit (AU)

The astronomical unit defines the average distance from Earth to the Sun—about 149,597,870.7 km—and serves as the fundamental meterstick of astronomy. In the 17th century, Kepler and Newton required an accurate AU to compute planetary orbits. Early astronomers timed transits of Mercury and Venus to infer the AU, but the method remained imprecise. In the 1960s, radar pulses bounced off Venus, and the measured round‑trip travel time, combined with the speed of light, yielded a precise AU value, solidifying the scale for all subsequent distance work.

Stellar Distances

Parallax provides the first direct method for measuring nearby stars. As Earth travels around the Sun, its 300‑million‑kilometre orbital baseline causes a nearby star to appear to shift against the distant background. By measuring that tiny angular shift and applying trigonometry, astronomers convert the angle into a distance. The first successful parallax measurement targeted 61 Cygni in 1838, placing it at about 11.4 light years (≈720,000 AU). A light year—roughly 10 trillion km—expresses how far light travels in one year, while a parsec corresponds to a parallax shift of one arcsecond, equal to about 3.26 light years.

Beyond Parallax

For stars farther than the parallax limit (≈1,000 light years for current satellites), astronomers rely on the inverse‑square law of light. By determining a star’s intrinsic brightness through spectroscopy, then comparing it to the observed apparent brightness, they calculate the distance that would cause the observed dimming. This brightness‑distance relationship also enables estimates of a star’s mass, diameter, and luminosity, extending the cosmic distance ladder to galaxies and the observable universe.

Takeaways

Eratosthenes used Sun angles at Syene and Alexandria to calculate Earth’s ~40,000 km circumference, establishing the first reliable planetary scale.
Aristarchus built on that Earth size to estimate Moon and Sun distances, showing that a simple geometric “stepping stone” could extend measurements to millions of kilometers long before telescopes.
The astronomical unit, defined as the average Earth‑Sun distance (~149.6 million km), became the fundamental meterstick for planetary orbits, refined from transit timings to 1960s radar echoes off Venus.
Stellar parallax, measured using Earth’s 300‑million‑km orbital baseline, gave the first direct distances to nearby stars such as 61 Cygni (~11.4 light years) and established the light‑year and parsec units.
Beyond the parallax limit, astronomers apply the inverse‑square law and intrinsic brightness from spectroscopy to infer distances to far‑off stars and galaxies, enabling calculations of mass, size, and luminosity.

Frequently Asked Questions

How does stellar parallax determine a star’s distance?

Stellar parallax measures the tiny angular shift of a nearby star against distant background stars as Earth moves from one side of its orbit to the other. Knowing the 300‑million‑kilometer baseline and the measured angle, trigonometry converts the shift into a distance, yielding values such as 61 Cygni’s 11.4 light‑year distance.

What method finally gave a precise value for the astronomical unit?

The precise astronomical unit emerged when 1960s radar pulses were bounced off Venus and the round‑trip travel time was measured. By combining the known speed of light with the timing data, scientists calculated the Earth‑Venus distance and, using orbital geometry, derived the average Earth‑Sun separation of 149,597,870.7 km.

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Cosmos By Carl Sagan Book

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Full Transcript YouTube

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.

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Meteors: Crash Course Astronomy #23

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May 04, 2026

The Astronomical Unit (AU)

Stellar Distances

Beyond Parallax

Takeaways

Frequently Asked Questions

How does stellar parallax determine a star’s distance?

What method finally gave a precise value for the astronomical unit?

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