The Ptolemaic and Copernican Models

Summary

This video explores the Ptolemaic and Copernican models of the universe. The Ptolemaic model, refined by Claudius Ptolemy, was geocentric and used epicycles and deferents to explain planetary motion, including retrograde motion. It was widely accepted for over a thousand years. The Copernican model, proposed by Nicolaus Copernicus, was heliocentric, placing the Sun at the center and simplifying the explanation for retrograde motion. Despite being more intuitive, it was not significantly more accurate than the Ptolemaic model without additional modifications.

Takeaways

• 📚 The Ptolemaic model was a geocentric system that placed Earth at the center of the universe and was accepted for about 1400 years.
• 🌌 The Ptolemaic model used deferents and epicycles to explain the motion of planets, including the complex retrograde motion.
• 🔄 Retrograde motion is when a planet appears to move backward in the sky, which the Ptolemaic model attempted to explain.
• 🌞 The Copernican model, proposed by Nicolaus Copernicus, was a heliocentric system that placed the Sun at the center of the universe.
• 📈 Copernicus's model offered a simpler explanation for retrograde motion as a result of Earth overtaking other planets in its orbit.
• 📘 Claudius Ptolemy, the author of the Almagest, refined the geocentric model for better planetary predictions.
• 🌐 The Ptolemaic model was almost geocentric, with Earth being slightly off-center, and all celestial bodies orbiting around points near the Earth.
• 📊 The equant was a concept in the Ptolemaic model where the center of a planet's epicycle appeared to move with constant angular speed from a certain point.
• 📚 The Copernican model was not significantly more accurate than the Ptolemaic model initially, and Copernicus added epicycles to improve its accuracy.
• 📖 The transition from the Ptolemaic to the Copernican model was influenced by scholars like Galileo, who supported and expanded upon Copernicus's ideas.
• 📚 The script also suggests readings for those interested in the history of these models, including books by Davis Obel, Arthur Koestler, Owen Gingerich, and Timothy Ferris.

Q & A

What are the two main models of planetary motion discussed in the video?

The two main models of planetary motion discussed are the Ptolemaic model and the Copernican model.

What is the Ptolemaic model and when was it published?

The Ptolemaic model is a geocentric model of the universe that was a refinement of early Greek models. It was published around 150 AD.

How long was the Ptolemaic model accepted before being succeeded?

The Ptolemaic model was accepted for approximately 1300 to 1400 years before being succeeded by the Copernican model.

What is retrograde motion and which planet's motion does the video use to explain it?

Retrograde motion is when a planet appears to move backward in its orbit against the background stars. The video uses Mars' motion to explain this phenomenon.

What is the term for the circular orbit of the sun around a point near the earth in the Ptolemaic model?

In the Ptolemaic model, the circular orbit of the sun around a point near the earth is called the deferent.

What is the term for the small circles that planets move along in the Ptolemaic model?

In the Ptolemaic model, the small circles that planets move along are called epicycles.

Who was Claudius Ptolemy and what did he contribute to the Ptolemaic model?

Claudius Ptolemy was an ancient astronomer who authored the Almagest, which refined the geocentric model for better planetary predictions.

What is the equant in the context of the Ptolemaic model?

The equant is a point from which the center of a planet's epicycle appears to move with constant angular speed in the Ptolemaic model.

What is the Copernican model and how does it differ from the Ptolemaic model?

The Copernican model is a heliocentric model where the sun is at the center of the universe. It differs from the Ptolemaic model by placing the sun, not the earth, at the center.

What was the profession of Nicolaus Copernicus and when did he live?

Nicolaus Copernicus was a canon of the Catholic Church and lived from 1473 to 1543.

How did the Copernican model explain retrograde motion?

The Copernican model explained retrograde motion by the relative positions and speeds of the planets as they orbit the sun, causing the apparent backward motion from Earth's perspective.

Outlines

00:00

🌌 Introduction to Ptolemaic and Copernican Models

The video begins by introducing two major models of the universe: the Ptolemaic and Copernican models. The Ptolemaic model, refined from early Greek models and published around 150 AD, was accepted for approximately 1400 years. It's noted for its ability to predict the paths of the planets against the background stars, including the phenomenon of retrograde motion, where planets appear to move backward. The Copernican model, which succeeded the Ptolemaic model, is also mentioned, with a focus on its acceptance by scholars. The video uses the example of Mars' path from July 2020 to January 2021 to illustrate retrograde motion, which occurs approximately every 26 months. The script also discusses the motivations behind developing these models, including understanding the universe and casting more accurate horoscopes, as many early astronomers were also astrologers.

05:02

📚 Detailed Explanation of the Ptolemaic Model

The second paragraph delves into the specifics of the Ptolemaic model, which was nearly geocentric, placing Earth almost at the center of the universe. It describes the model's structure, which included deferents (large circles) and epicycles (smaller circles on the deferents) for each planet. The model accounted for retrograde motion through the use of epicycles. The script explains the concept of the equant, a point from which the center of a planet's epicycle appears to move at a constant angular speed. Despite its complexity, the Ptolemaic model was effective for many centuries, although it required each planet to have its own unique deferent, epicycle, and equant. The paragraph concludes with a mention of animations that simulate the Ptolemaic model, showing the motion of planets like Mars and the phases of Venus as predicted by the model.

10:04

🌉 Animation of Ptolemaic Model and Venus Phases

The third paragraph discusses an animation that demonstrates the Ptolemaic model, showing the motion of Mars against the background stars and the sun's apparent motion. It corrects a common misconception by clarifying that, in the Ptolemaic model, the sun would be inside the deferent for Mars. The animation illustrates how Mars appears to move backward (retrograde motion) and then forward again. Additionally, the paragraph explores the phases of Venus as predicted by the Ptolemaic model, which were not observable at the time of Ptolemy but later confirmed by Galileo's observations. The animation shows how Venus would appear as a thin crescent and how its phases change over time, according to the model.

15:05

🌏 The Resurgence of the Ptolemaic Model and the Copernican Revolution

This paragraph discusses the resurgence of the Ptolemaic model in Europe after the fall of the Roman Empire, which had been preserved by other cultures such as in India and Arabian countries. It then introduces Nicholas Copernicus, who proposed a revolutionary model with the sun at the center, known as the heliocentric model. Copernicus's work, 'De revolutionibus,' published in 1543, the year of his death, is highlighted. The paragraph contrasts the Ptolemaic and Copernican models, emphasizing the simplicity of the latter in explaining retrograde motion and the relative speed of planets. It also mentions that Copernicus's model was not significantly more accurate than the Ptolemaic model but laid the groundwork for future astronomical discoveries.

20:05

🔍 Copernican Model's Accuracy and Historical Context

The final paragraph addresses the accuracy of the Copernican model, noting that it was not much more accurate than the Ptolemaic model it replaced. Copernicus attempted to improve the model's accuracy by adding epicycles, but this only provided a marginal improvement. The paragraph also suggests readings for those interested in the history of these models, including books by Davis Obel, Arthur Kessler, Owen Gingerich, and Timothy Ferris. It concludes by setting the stage for a discussion of Galileo, who was a significant supporter of the Copernican model in the generations following Copernicus's death.

Keywords

💡Ptolemaic Model

The Ptolemaic Model was a geocentric system developed by Claudius Ptolemy, which placed the Earth at the center of the universe with celestial bodies orbiting around it. This model was widely accepted for over a thousand years. In the video, the Ptolemaic Model is described as having a complex system of deferents and epicycles to explain the motion of the planets, including retrograde motion.

💡Copernicus

Copernicus was a Renaissance-era astronomer who proposed a heliocentric model of the solar system, which placed the Sun at the center instead of the Earth. His model, known as the Copernican Model, is a significant shift from the Ptolemaic Model and is discussed in the video as a model that succeeded it. It's noted for its simpler explanation of retrograde motion.

💡Retrograde Motion

Retrograde motion refers to the apparent backward movement of a planet against the background stars when viewed from Earth. This phenomenon is explained in the video as a result of the relative positions and motions of Earth and other planets in both the Ptolemaic and Copernican models.

💡Deferent

In the Ptolemaic Model, a deferent is a large circular orbit around the Earth with the center not exactly at the Earth. The deferent, along with epicycles, helps to account for the complex motion of the planets as observed from Earth. The video explains that planets had circular orbits around points near the Earth, which were part of the deferent.

💡Epicyclic

Epicyclic refers to the small circular motion of a planet on an epicycle within the larger deferent orbit in the Ptolemaic Model. The video uses the term to describe how planets appeared to move in small circles while simultaneously moving along the larger deferent, contributing to the observed retrograde motion.

💡Equant

The equant is a point in the Ptolemaic Model from which the center of a planet's epicycle appears to move with a constant angular speed. The video mentions that the equant was used to complicate the model to better predict planetary positions, although it made the model more complex.

💡Heliocentric

Heliocentric refers to a model of the solar system where the Sun is at the center and the planets orbit around it. The video discusses how the Copernican Model was heliocentric, which was a significant departure from the geocentric Ptolemaic Model.

💡Geographic Model

The geographic model mentioned in the video refers to Ptolemy's work on mapping the Earth, which was separate from his astronomical models. It highlights Ptolemy's influence on geography and cartography.

💡Astrology

Astrology is the study of the movements and relative positions of celestial bodies interpreted as having an influence on human affairs and the natural world. The video notes that many early astronomers, including Ptolemy, were also astrologers, which was a motivation for developing detailed models of planetary motion.

💡Almagest

The Almagest is a comprehensive work by Ptolemy that detailed his geocentric model of the universe. The video describes it as a work that was highly regarded and used for many centuries due to its effectiveness in predicting planetary positions.

💡Revolutionibus

De revolutionibus is the seminal work by Copernicus that outlined his heliocentric model of the solar system. The video mentions that it was published in 1543, the same year Copernicus died, and it played a crucial role in the scientific revolution.

Highlights

The Ptolemaic model was a refinement of early Greek models and was accepted for about 1400 years.

The Copernican model succeeded the Ptolemaic model in many scholars' minds.

Planetary retrograde motion was a significant challenge for early models of the universe.

Claudius Ptolemy authored the Almagest, which refined the geocentric model for better planetary predictions.

The Ptolemaic model used deferents and epicycles to explain the motion of planets.

The equant was introduced in the Ptolemaic model to account for constant angular speed.

The Ptolemaic model predicted the phases of Venus, which were later confirmed by Galileo.

The Ptolemaic model was lost to European civilization after the Roman Empire's collapse but was preserved in other cultures.

Nicholas Copernicus proposed a heliocentric model of the universe with the sun at the center.

Copernicus's model provided a simple explanation for retrograde motion.

The Copernican model was not significantly more accurate than the Ptolemaic model initially.

Copernicus added epicycles to his model to improve its accuracy.

The Copernican model's circular orbits were not an accurate representation of actual planetary paths.

Galileo was a significant supporter of Copernicus's model in the generations after Copernicus's death.

The video also discusses the importance of understanding planetary motion for casting accurate horoscopes.

The Ptolemaic model's complexity included the Earth being slightly off-center in the universe.

Copernicus's work 'De revolutionibus' was published shortly before his death in 1543.

The video includes animations to illustrate the Ptolemaic and Copernican models' explanations of planetary motion.

The Copernican model's simplicity and placement of the sun at the center was a significant shift from the Ptolemaic model.

Transcripts

in this video we're going to look at the

ptolemaic and the copernican models

the ptolemaic model was a refinement of

the early greek models

and it was published in about 80 150 or

so

it was the model that worked or was

accepted for about the next

13 or 1400 years so for quite a long

time

the copernican model is the model that

succeeded the ptolemaic model at least

in

many scholars minds after this we'll

learn about more people's models but

we'll start with this one for reminders

you may have watched the video that i

made on

the paths of the planets against the

background stars

here's the path of mars back in july

2020 to about january 2021 so for about

a six month period

and it would

be the yellow line that starts over

there

to the right of the center

and then

most of the time mars will be moving

from left to right against the

background stars that's toward the east

but every once in a while it does this

weird little

backwards loop

and it's hard to see that as a loop if

we were viewing this from a different

angle you'd be able to tell but it does

something like that

and

the backwards part of it is called

retrograde motion

here's the path mars will take from

november 2026 to july 2026

the start of this in november 2026 would

be up at this end and

for most of the time it's moving from

west to east against the background

stars but then it reverses direction

retrograde motion here

then it goes back to pro-grade motion

heading from west to east again

and so

that is the motion

of mars against the background stars it

repeats its retrograde motion about

every two years and two months so about

every 26 months or so again and again

the other planets do this as well

sometimes in more complicated ways

especially for mercury and venus

understanding and predicting this stuff

was

a big challenge for early models of the

universe this motion looks complicated

and it is

they had a couple of incentives one was

just understanding

how the universe worked

and another one

another reason for doing so was so that

more accurate

horoscopes could be cast by the early

astronomers virtually all of them

up through galileo and kepler

were

let's see copernicus probably wasn't but

most of them were astrologers as well as

being astronomers

so first claudius ptolemy we have no

idea what he looked like but

this is a picture someone did hundreds

of years after his death

lived from about 85 to 165 we don't know

for sure when he was born or when he

died

he was the author of

something that became known as

almagest

and that's a combination of arabic and

greek the al is

arabic for the the majest is

greek for

the majestic or majestic

it was talking about the majestic things

in the heavens and their motions

but people

also thought of the book itself

as pretty majestic

because

it worked pretty well for a long time as

long as you didn't need to be closer

than about 10 degrees to the actual

position of something

10 degrees on the night sky is about the

width of your fist held at arm's length

in it ptolemy refined the

geocentric model for better planetary

predictions geocentric means

earth-centered you'll see as soon as we

look at ptolemy's actual model that it

was not actually earth-centered earth

was a little bit off-center

but things orbited the earth more or

less ptolemy was also known for a book

on geography mapping

and another on astrology i'm guessing

that is pronounced tetrabiblus or

something to that effect

so here's the ptolemaic model

and this is a fairly simplified version

of it but

it'll have the main features that we're

concerned with i'll show you a somewhat

more complicated model here in a minute

if you can contain this model in your

brain and describe it well

you'll have the hang of the ptolemaic

model first of all the ptolemaic model

was almost geocentric the earth was

almost at the center

but if you look at the

circles that are drawn for mercury's

orbit and venus and the sun and then

mars jupiter and saturn you may start to

notice that they're not exactly centered

on earth the sun had a circular orbit

around a point near the earth

and all of the planets had circular

orbits

around points

near the earth

and they all had epicycles epicycles are

the small

circles

that are on the larger circles the

larger circles are called deference and

the smaller circles are called epicycles

venus and mercury had interesting orbits

both of them orbited points on a line

between the earth and the sun

now the earth stayed fixed in the middle

of this thing

all of these things orbited around the

earth turned around the earth once a day

in fact

while continuing their motion along the

deference and the epicycles here's a

more complete picture of what a

planetary orbit would look like

here's the earth

right there

this is the center of the larger circle

here which is the deferent

there's an equine point

here and i'll talk about that in a

little bit

the planet itself is up here

and it moves around

the epicycle circle at the same time

that the epicycle circle

is moving around the deferent

and so this is pretty complicated

the point marked center

is the center of the deference circle

that puts the

deferent off center from the earth or

eccentric as a way of describing that

and the epicycle is a small circle

the planet moves along that at constant

speed

and that provides the appearance of

retrograde motion

if you look up there at the epicycle

circle the point marked x

when the planet is there

it'll be moving on the epicycle in the

same direction that the epicycle is

moving on the deferent

and so

the planet will appear to be moving in a

counterclockwise circle around the earth

but when the

planet is down here at point y or near

why

it'll be going on the epicycle in a

direction opposite the direction of the

deferent that motion can

produce an appearance that the planet is

moving backwards in space now a

complication tossed in here from earth's

viewpoint the epicycle does not move

along the deferent at constant speed

this would be something you wouldn't

actually try to produce an animation

with this thing or at least the ancient

greeks would not have done so

what they would do is have an equation

that described the speed of the center

of the epicycle

moving along the deferent they could

calculate all this stuff

the equant

equint the equint is a point

from which the center of the planet's

epicycle appears to move with constant

angular speed so if you were standing

there on the equine looking at the

epicycle and you were able to see the

center of the epicycle

that epicycle

would move along the deferent in such a

way that it looked to you like it was

always moving at the same speed to make

things worse each planet has to have its

own deferent

its own epicycle

and its own equine

so that was the ptolemaic model pretty

complicated

we can look at a couple of animations

that simulate things in the ptolemaic

model

here's the simulator

there are

links to this in your textbook if you

read the chapter section on this this is

the ptolemaic model earth is the blue

dot here

the gray dot is the center

of the deferent which is this circle

the green cross here

is the equine

and then

this circle is the epicycle

and then this red dot here represents

mars and that's just the one that we'll

happen to look at

and i'll start the animation

oh we need to back out here a little bit

we want to be able to see this zodiac

strip down here

and

the zodiac strip is where you'll be able

to see the apparent motion of mars

against the background stars

and in this case it actually is caused

by mars moving around this fixed earth

in the center

you can also see the apparent motion of

the sun

against the background stars now one

thing about this animation that isn't

correct is that it has the sun outside

of mars

the sun in the ptolemaic model would

actually be inside

the deferent for mars so it would have

been inside this circle

but appearance wise this will produce

exactly what the ptolemaic model would

show for a view so let's start the

animation

at times i'll slow this thing down

and so you can

see something

so here's just what the model looks like

you can see mars moving along that

epicycle while the epicycle is moving

along the deferent

and

you can watch that for a couple turns

here

and then down here on the zodiac strip

you can watch the sun moving against the

background stars with pretty constant

speed

you can have mars moving against the

background stars but every once in a

while it does something kind of weird so

i'm going to slow it way down

the next time

it starts getting close to

the sun here

mars is falling behind the sun by quite

a bit but it's reversing direction right

now

it's doing its weird little thing on the

epicycle

now the sun's going to catch up to and

past mars

now mars is going to be starting on that

part of its epicycle where it's moving

in toward the earth and it's when it's

along this part that it looks like it's

going backwards

against the background stars

there down here on the zodiac strip you

will soon see mars stopping

reversing direction

and then going forward again

that is the

retrograde motion

that you could see for mars

a simulation of that now there's one

more thing that i want to show you

with the ptolemantic model

and that is the phases of venus now at

the time ptolemy developed the model

the telescope was still let's see about

1

1450 years in the future they didn't

have any idea that there might be phases

of venus when galileo came along

he could talk about the phases of venus

that would be predicted by the ptolemaic

model and compare them to what he

actually saw in the sky

this time we're just looking at venus

and here we do have the correct geometry

we have earth here

venus is

deferent here and venus's epicycle here

and then the sun is outside of that

and

if things aren't lined up just perfectly

with earth venus and the sun

you can see a

small crescent extremely thin crescent

along the right side of venus there

so let's start the animation

and if you look at the bottom picture

here you can see

it's weird venus is a growing crescent

and it always pauses before it gets to a

half venus and then

disappears and goes back to

a crescent on the opposite side

this is what the ptolemaic model would

predict if you could watch venus for a

long enough time

now you'd have to be watching it for

long periods of time to be able to see

this

i'll slow it down a bit

but it's interesting the path of venus

or the phases of venus that would be

predicted by this okay let's move on to

the next model the ptolemaic model was

lost to european civilization after the

collapse of the roman empire

but other cultures in the world kind of

kept it alive in india and in

the arabian countries they hung on to it

translated it into their own languages

sometimes modified things a little bit

in the early years of the renaissance or

shortly after 1200 a.d it worked its way

back into european countries

people started copying it spreading it

around

it made its way back there

eventually someone comes along nicholas

copernicus who proposes a different

model of the universe

he lived from 1473 to 1543

he was a cannon of the catholic church

that's a

like an administrative position

a clerical position kind of thing not

clerical he actually had

administrative powers he would be

responsible for

seeing that taxes were collected in some

area

in those

years the catholic church was the

government in many places in europe and

so

they would have to collect taxes

uh

provide for the defensive areas from

marauding nights or something like that

have some way of delivering charity to

the poor all those sorts of things

his great

work called the revolutionibus it had a

longer title in that but the

revolutionibus is

good enough

it was published in 1543 you may notice

that there's a coincident date with the

top line and

that bottom line there

he may not have been aware of his book's

publication i bought a a new well new to

me book on copernicus it was actually

written in about 1970 i think the author

of this book i'll mention a bit later

you'll see his name here copernicus may

not have been aware of the publication

when the last parts of it were

delivered to where he was living and

working at the time he had had a

cerebral hemorrhage a few months before

it arrived

and one of his co-workers in a letter to

their local bishop said his memory and

mental powers had abandoned him but

here's the copernican model

in the simplified version he made it

more complicated later and i'll mention

those things but

it has the sun at the center it'll look

familiar it's got mercury venus earth

the moon mars jupiter and saturn

it had the approximate correct spacing

for these planets this is a simplified

version of it where

the planets seem to increase in orbital

diameter in a regular way but

copernicus's model wasn't that simple

still

they're all circles

but it's got the sun at the center we

call that

heliocentric helios is an ancient word

for the sun it had circular orbit it had

a simple explanation for retrograde

motion

let's look at another computer animation

for that here we have the sun at the

center we have an observer planet which

will be earth

we'll have a target planet which for

this one will be mars

it's got uh we haven't learned what

these are yet but uh

an au is an astronomical unit

it happens to be the diameter or the

radius of earth's orbit pretty close to

it

and then mars orbit is has an orbital

radius of about 2.4 astronomical units

let me slow down the animation a little

bit for starters

and

again you can watch the motion up here

or you can watch the apparent motion of

the planet against the background stars

as

they're traveling around the center of

this thing

now i maybe slowed it down way too much

but you can see that the sun

has a pretty constant motion

against the background stars

now

earth is going to

be moving into such a position that

mars will be behind the sun at this time

and the sun catches up to and passes

mars

i'll speed this up a bit so you don't

fall asleep

we're soon going to have i paused it

here we're soon going to have

earth catching up to and passing mars in

its orbit

and watch the bottom as that's occurring

mars stops

moves backward for a time

and then moves forward

and that is the simple explanation for

retrograde motion

copernicus said

the narrower a planet is to the sun the

faster it travels

and just by saying that

it takes care of explaining the

retrograde

the retrograde motion of mars jupiter

and saturn it also explains the weird

behavior of mercury and venus that we

can see

not perfectly however

so that's something that we'll have to

concern ourselves with let's have it

catch up earth catch up again and then

i'll

slow things way down

okay mars appears to be frozen in space

but as earth

passes it it looks like it moves

backwards for a time

against the background stars

at some point it freezes in space again

and then starts going forward

or

eastward against the background stars

again

so that's the copernican explanation for

retrograde motion

simple explanation

accuracy well

for starters the copernican model was

hardly any better than the old ptolemaic

model which over the years had gotten

less and less accurate

as far as predicting planetary positions

people had tried to update it from time

to time

but still it suffered from that and

copernicus's model did as well

and so to improve the accuracy of his

model

he made it more complicated he added

epicycles for the planets

and

it only slightly improved things if he'd

spent enough time on it he might have

narrowed it down made it a bit more

accurate but

the problem was you're trying to say

that things are traveling in circular

orbits and they're not doing that so

that's just the way it goes by the way

if you like reading about history

here's some books that i've read dealing

with this era galileo's daughter by

davis obel

interestingly

galileo and one of his daughters maria

celeste will learn about

her or him later

but

she appeared to have been his

intellectual equal

and they wrote letters back and forth

for many years galileo's copies of those

letters were saved but they'd never been

translated to english until

just the first part of the 2000s when

davis obell did that

letters to my father is the letters

themselves galileo's daughter is

in large part a biography of galileo

the sleepwalkers by arthur kessler

is kind of a complete history it's

tough going it's not a really exciting

book

the book i really enjoyed was the great

copernicus chase by owen gingrich

and the book no red nobody read by owen

gingrich

and another coming of age in the milky

way by timothy ferris i really enjoyed

that last book i read it close to 30

years ago and i've re-read it two times

since then he has a a way with words in

writing about history

okay next up will be galileo

galileo was the big supporter of

copernicus in the generations after

copernicus died