Ptolemy's Almagest

Summary

In this lecture, the author Stefan explores the life and work of Ptolemy, the renowned ancient astronomer. Ptolemy's 'Almagest' is highlighted as a pivotal scientific text, detailing his geocentric model of the universe. The lecture delves into Ptolemy's observations on celestial bodies, his views on the Earth's sphericity, and the complex motions of stars and planets. Despite his accurate predictions, Ptolemy's model was eventually superseded by Copernicus's heliocentric theory. The script also discusses Ptolemy's other works and his attempts to measure the size of the universe.

Takeaways

• 📚 Ptolemy's 'Almagest' is one of the most influential scientific texts in history, detailing his geocentric model of the universe.
• 🌌 Ptolemy believed the Earth was at the center of a spherical universe, with celestial bodies moving in complex, predictable patterns.
• 🔍 Ptolemy's geocentric model was remarkably accurate in predicting the motions of celestial bodies and dominated for over 1200 years.
• 🌟 Ptolemy's model included the use of epicycles to explain the retrograde motion of planets, a concept later refined by Copernicus's heliocentric model.
• 📊 The 'Almagest' is filled with extensive astronomical tables and mathematical diagrams illustrating the complex motions of the celestial bodies.
• 🌍 Ptolemy provided evidence for a spherical Earth, including the observation that not all observers see the same stars at the same time.
• 📈 Ptolemy recognized the Earth's tilt and its effect on the changing visibility of stars and the length of daylight throughout the year.
• 🌞 He explained the changing position of the Sun's apparent path across the sky, leading to the understanding of solstices and equinoxes.
• 📐 Ptolemy's work was deeply rooted in Greek philosophy, particularly the belief in the divine order and symmetry found in mathematics.
• 🌐 Despite his detailed observations hinting at a heliocentric model, Ptolemy did not embrace the idea of the Earth moving around the Sun.

Q & A

Who is the author of the Great World History book mentioned in the script?

The author is Stefan, a trained astronomer.

What is the name of the most important work by Ptolemy?

Ptolemy's most important work is called the Almagest.

In what century did Ptolemy live?

Ptolemy lived in the first and second century A.D.

What was the original title of Ptolemy's work, the Almagest?

The original title of the Almagest is not known, but the title 'Almagest' is derived from the Arabic translation of the work, which means 'The Greatest'.

What type of knowledge did Ptolemy consider as providing true scientific knowledge?

Ptolemy considered mathematics as the type of knowledge that provides true scientific knowledge.

What did Ptolemy believe about the Earth's shape?

Ptolemy believed that the Earth was spherical.

How did Ptolemy explain the phenomenon of stars appearing to rise and set at different times in different locations?

Ptolemy explained that the stars appear to rise and set at different times because the Earth is spherical, and changing positions on the globe results in seeing different stars.

What is the term for the slow motion of stars known as, which is caused by the periodic spinning of the Earth's axis?

The slow motion of stars is known as precession.

What is the name of the belt of constellations that the Sun and planets move along?

The belt of constellations that the Sun and planets move along is called the zodiac.

What is the reason behind the retrograde motion of the planets?

The retrograde motion of the planets is observed due to the relative positions and movements of the Earth and other planets in their orbits.

What did Ptolemy's model of the solar system include to explain the complex motions of the planets?

Ptolemy's model included epicycles, which are small orbits that rotate along a larger orbit, to explain the complex motions of the planets.

Outlines

00:00

🌌 Introduction to Ptolemy and His Work

The script begins with an introduction to the author, Stefan, who is an astronomer and the author of a great world history book. He expresses his interest in Ptolemy, the renowned ancient astronomer, and his seminal work, 'Almagest'. Ptolemy, who lived in the first and second centuries AD in Alexandria, Egypt, is noted for his remarkably accurate model of the solar system that prevailed for 1200 years until the heliocentric model was introduced by Copernicus. The lecture aims to demystify Ptolemy's complex work, which includes extensive astronomical tables and intricate figures, and starts with an analysis of different types of knowledge, emphasizing the superiority of mathematical knowledge for its certainty and its ability to provide insight into the divine.

05:03

🌍 Earth's Sphericity and Celestial Observations

The second paragraph delves into the evidence supporting the spherical shape of the Earth as observed by Ptolemy. It includes the observation that stars rise and set at different times depending on one's location, the varying visibility of stars as one travels north or south, and the differences in eclipse timings. Ptolemy also describes how the appearance of mountains or ships changes with distance, indicating the curvature of the Earth. The paragraph further explains the apparent daily rotation of the stars around a common axis, near the North Star, and the slow precessional movement of stars, which was discovered by Hipparchus. Additionally, it discusses the annual motion of fixed stars along the zodiac, which is explained by the Earth's revolution around the Sun and its axial tilt.

10:05

🌞 The Solar System and Earth's Position

This section discusses the complex motion of the stars and the Sun's orbit as observed from Earth. Ptolemy theorized that the Earth must be at the center of the celestial sphere because we always see exactly half of the zodiac. He also argued that if the Earth were not at the center, day and night would not be equal during equinoxes. Despite having the correct idea that the Earth revolves around its axis, Ptolemy rejected the notion as it seemed absurd to him. The paragraph also touches on the variable speed of the Sun and planets along their paths, known as 'animalistic motion,' and the retrograde motion of the planets, which was later explained by Apollonius using epicycles.

15:05

📚 Ptolemy's Geocentric Model and Contributions

Ptolemy's geocentric model is further elaborated upon, with him placing the Earth off-center in the solar orbit and introducing the equant, a point from which the motion of the Sun appears uniform. This model was able to approximate the observed motion of the Sun remarkably well. The paragraph also highlights how Ptolemy's observations hinted at the heliocentric model, such as the constant angular distance of inner planets from the Sun and their equal mean motion with the Sun, but he failed to make the leap to a Sun-centered system. The paragraph concludes with a mention of Ptolemy's other work, 'Planetary Hypotheses,' where he attempted to measure the size of the universe by stacking the planetary spheres.

20:08

🌐 Transition to Heliocentrism and Modern Understanding

The final paragraph discusses how Ptolemy's observations laid the groundwork for the eventual acceptance of the heliocentric model. It points out that Ptolemy noted the inner planets' proximity to the Sun and their equal mean motion with the Sun, which are consistent with the heliocentric model. However, Ptolemy was unaware of the distances to the planets, which hindered his understanding. The paragraph concludes with a demonstration of the retrograde motion of planets using a JavaScript model that transforms the simple heliocentric model into the complex geocentric view observed from Earth. It also visually presents the orbits of inner and outer planets, emphasizing the patterns and evidence supporting the heliocentric model.

Keywords

💡Ptolemy

Ptolemy was a renowned astronomer from the ancient world, living in the first and second century A.D. He is best known for his work 'Almagest', which was a cornerstone in the field of astronomy for over a millennium. In the script, Ptolemy's geocentric model of the universe is discussed, which placed Earth at the center with other celestial bodies revolving around it.

💡Almagest

The 'Almagest' is a significant work by Ptolemy and one of the most influential scientific texts in history. It contains extensive astronomical tables and complex mathematical diagrams explaining the motion of celestial bodies. The script highlights how this work dominated astronomical thought for 1200 years until the heliocentric model was proposed.

💡Geocentric model

The geocentric model is an astronomical model that posits the Earth as the center of the universe, with the sun, moon, and planets revolving around it. This model was accurate in predicting planetary motions and was widely accepted until the Copernican heliocentric model was introduced. The script discusses how Ptolemy's work supported this model.

💡Heliocentric model

The heliocentric model is an astronomical model that places the sun at the center of the solar system, with the planets orbiting around it. This model was proposed by Nicolaus Copernicus and eventually replaced the geocentric model. The script mentions how this model was a significant shift from Ptolemy's geocentric view.

💡Astronomia

The goddess 'Astronomia' is depicted in the script as a figure representing the field of astronomy. This personification symbolizes the study of celestial objects and their motions, which is a central theme in the video as it discusses Ptolemy's contributions to this field.

💡Epicycles

Epicycles are small circular orbits that a planet was thought to move along while also moving along a larger orbit. This concept was used by Ptolemy to explain the complex motions of the planets, particularly their retrograde motion. The script explains how epicycles were a part of Ptolemy's geocentric model.

💡Retrograde motion

Retrograde motion is the apparent westward motion of a planet when viewed from Earth. This phenomenon occurs when a planet appears to move backward in its orbit. The script discusses how Ptolemy's model accounted for this complex motion using epicycles.

💡Precession

Precession is a slow, continuous change in the orientation of an astronomical object's rotational axis. The script mentions that Hipparchus discovered this effect related to the Earth's axis, which influences the positions of stars over long periods.

💡Zodiac

The zodiac is a circle of astronomical significance, divided into 12 equal parts, each corresponding to the path of the sun across the sky over one year. The script discusses the zodiac's inclination and its relationship to the Earth's axial tilt, which affects the visibility of constellations throughout the year.

💡Equinox

An equinox is one of two points on the celestial sphere where the ecliptic (the path of the sun across the celestial sphere) intersects the celestial equator. The script explains that during an equinox, day and night are of equal length, and this is due to the Earth's axial tilt.

💡Solstice

A solstice is an event that occurs when the sun reaches either its highest or lowest position in the sky at noon, marking the longest day (summer solstice) or the shortest day (winter solstice) of the year. The script discusses how the Earth's axial tilt causes the sun's apparent path to shift, leading to the solstices.

Highlights

Introduction to Ptolemy's work and his importance in ancient astronomy.

Description of Ptolemy's Almagest as one of the most influential scientific texts in history.

Ptolemy's belief in the accuracy of mathematical knowledge over theology and physics.

Ptolemy's view that mathematics can help people achieve a spiritual state similar to the divine.

Ptolemy's recognition of the Earth as a sphere based on various observations.

Explanation of the stars' apparent motion due to Earth's rotation.

Discovery of the slow motion of stars known as precession by Hipparchus.

Understanding the zodiac as the plane of the solar system and its tilt compared to the equator.

Ptolemy's analysis of the sun's orbit and the cause of seasons.

Ptolemy's proof that the Earth is at the center of the sphere of fixed stars.

Ptolemy's incorrect assumption that the Earth is at rest due to the complexity of Earth's rotation.

Observation of the non-uniform motion of the sun and planets, known as animalistic motion.

Retrograde motion of planets and its explanation using epicycles by Apollonius.

Ptolemy's challenge to explain complex planetary motions with simple circular motion.

Ptolemy's model placing the Earth off-center in the solar orbit.

Introduction of the equant by Ptolemy to explain the non-uniform motion of the sun.

Ptolemy's hints at the heliocentric model despite maintaining a geocentric view.

Ptolemy's Planetary Hypotheses and his ambitious attempt to measure the size of the universe.

Creation of a JavaScript model to understand the retrograde motion of planets.

Visualization of the heliocentric model through the JavaScript model for inner planets like Mercury and Venus.

Outer planets' motion mimicking the sun's motion as evidence for the heliocentric model.

Transcripts

hey everybody i'm stefan author of the

great world history book

given that i'm a trained astronomer you

might find it interesting to get my take

on the greatest

astronomer from the ancient world namely

ptolemy

and in this lecture we'll look at his

greatest work which is named

the alma guest let's dig right in

so let's start with a depiction this one

is from the 16th century hundreds and

hundreds of years after his death

here we see ptolemy looking at the stars

and behind him we see the goddess

astronomia

so who was tommy ptolemy lived in the

first and second century a.d and he's

considered to be the most

important ancient astronomer he was born

in alexandria in egypt which at the time

was part of the roman empire

and he was a greek descent its model of

the solar system was remarkably accurate

at predicting the complex

motions of the planets it remained

dominant for 1200 years until it was

finally replaced by the heliocentric

model

of nicolas copernicus ptolemy's main

work is called the alma guest and it is

one of the most influential scientific

texts in world history

the current title the alma guest is

actually not the original title it is

derived from the arabic translation of

the work

and that title was all majesty meaning

the greatest

and that in the west later turned into

all my guests

now almagus did a massive work hundreds

of pages thick

filled with extensive astronomical

tables and complicated figures

and today i made a massive effort to

make this

complex topic very clear and

understandable for you today

here we see one of those tables from a

16th century

version of the book and here we see

another one

and then finally here we see a piece of

text supplemented on the side with these

complicated

mathematical drawings that depict the

motions of the planets

and we'll get into some of what these

complicated drawings mean

later on

but let's start at the beginning ptolemy

starts his work with an

analysis of different types of knowledge

it becomes relatively simple

the first line reads those who genuinely

engaged in philosophy

cyrus seemed to me quite rightly to have

distinguished the theoretical part

from the practical part of philosophy

cyrus is the name of a man we don't know

who it is but he is

but it seems he has dedicated his work

to this person

he then further divided theoretical

knowledge into

three different types theology physics

and mathematics

only mathematics he claimed gives us

true

scientific knowledge we read

one might call the other two kinds of

theoretical knowledge conjecture

so unsure rather than scientific

knowledge

the theological because it is utterly

super sensible it's beyond the senses

and it is unobtainable and the natural

meaning physics

because it is unstable and obscure in

matter

meaning that things that happen on this

earth they are all transient they perish

for this reason he continues those who

pursue philosophy would never hope to

come to agreement about them

so about theology and about physics

but the mathematical kind alone he

continues provides certain

and steadfast knowledge to those who

practice it as its mode of proof arises

through

indisputable paths arithmetic

and geometry and those indisputable

paths are of course

the logical certain side that

mathematics has to it

he then continues and this is a very

greek thought

with regard to virtuous conduct and

character this science mathematics

above all things could make men see

clearly from the constancy

the order the symmetry and the calm

which are associated with the divine

it makes its followers lovers of divine

beauty

accustoming them and reforming their

natures as it were

to a similar spiritual state

so the beauty of the divine helps people

cleanse

their souls basically

now let's build ptolemy's systems step

by step

first of all following aristotle ptolemy

recognized the earth as a sphere that is

very important starting point

we read the earth 2 is sensibly

spherical

for it is not possible for all observers

on the earth

to see the sun the moon and the rest of

the stars rising and setting

at the same time and he continues

rather those living in the east

invariably see them rise and set

earlier all those in the west later

this of course makes sense on the globe

if you change your position you're going

to see different stars

he continues the farther north we travel

the greater numbers of suddenly stars

are hidden

and a greater number of northerly stars

are revealed

so if you move east west the setting

and rising of the stars changes and when

you move

north and south different stars appear

and disappear

on the horizon

he continues with even more evidence of

the spherical earth

eclipses he continues that occur at the

same time are not recorded by all

observers

at the same hour and since the

difference in the hours is found to be

proportional to the distance of the

regions

one might reasonably suppose that the

surface of the earth

is spherical and finally one last proof

if we sail towards mountains their

magnitudes are observed to

increase gradually just as if they were

rising out of and had previously sunk

into the ocean itself or the sea itself

due to the convexity of the surface of

the earth

this phenomenon is depicted in the

photograph below

we see i think the city toronto and when

you see it from a large distance

it is as though the bottom side of the

buildings

is hidden behind the curvature of the

earth and when you move towards the city

the city seems to rise out of the water

and this is what ptolemy was describing

using a mountain instead of a city and

here by the way we see a 16th century

example

where they've used a ship that seems to

arise from

below the horizon so we've established a

swirl called earth

now let's look at the stars if you

follow the stars at night

they seem to rotate around us every 24

hours making a full circle as you see in

the picture

the stars all seem to move around an

axis

and this axis points by accident to the

polar star

as you can see in the image as well

and here we see an interesting

photograph of that phenomenon

if you're taking a picture which you

keep the lens open for an extended

period of time

you can see the trails of the stars as

they move

and you see they all seem to move around

that common axle

point and very close to that point is

the polar star the polar star in exactly

in the center but it's close

to it

the stars all seem to move in unison

leaving the distances between all those

stars constant and that is why

we have like consistent constellations

that people made up

aneximonas in the 6th century bc had

explained this phenomenon by assuming

that all the stars were stuck to a

crystal swear

that was rotating around every 24 hours

today we know of course that the motion

of the stars is just

apparent it's the stars seem to move

while in fact

it is the earth that is rotating around

its own axis

but of course the greeks did not know

that

secondly there is a very slow motion of

the stars known as precession

which we now known as caused by the

periodic spinning of the axis of the

earth

every 26 thousand years or so

hipparchus in the second century bc had

already discovered this effect

he had done this by comparing his own

measurements of the stars

with those of his predecessors

thirdly the fixed stars also make an

annual motion along the zodiac

every 365.24

days and you see that zodiac the belt of

the constellations

depicted in the image on the right as

you can see the zodiac is inclined

at an angle and the angle is 23.5

degrees

compared to the equator of the earth

that also requires explanation

so what is the zodiac exactly well we

now know that it is the plane of the

solar system so if

the sun in the middle and the planets

that wrote it around it

all move in one two-dimensional plane

and that is the plane that we see

inclined at an angle

from the earth so how does this

cause the stars to slowly shift during

the year

well as the earth revolves around the

sun as you can see in the image on the

right

the night side of the earth the side

that is pointing away from the sun

points to different parts of the sky at

night

is making different constellations

visible so for instance

the right earth in the image has the

night sight on the right side

so it looks at the constellations on the

right

while the earth on the left instead has

the night sight on the left side

and he looks a totally different sky

finally you have to answer why that

zodiac plane is tilted compared to the

equator

well that's not because the solar system

itself is tilted

it is because the earth is tilted in

comparison

to that plane you can see that at the in

the image as well

and the tilt of the earth is exactly the

same 23.5 degrees

that we've discussed earlier

as i've told you before the sun the moon

and the planets they all

move along this zodiac as you can see in

the image

the sun appears to orbit along this

zodiac every 24 hours of course

and this is of course also because of

the rotation of the earth

around its own axis but the orbit of the

sun

is a little bit more complicated than

that

this is because that tilt of the earth

also causes the orbit of the sun

to shift back and forth during the year

as you can see in this image

it shifts furthest north in june

this is called the summer solstice and

it shifts further south in december

which is called the winter solstice

when the orbit is right in between those

two solstices

right in the middle we speak of an

equinox there's one equinox during

spring

and another one during autumn

during the summer solstice as we've just

seen the

orbit of the sun reaches highest north

giving the northern hemisphere

maximum sunlight causing there somewhere

there and here we see that phenomenon on

the right we have the summer

solstice because the earth is tilted a

little bit towards the sun

that northern hemisphere receives more

direct sunlight

the sun appears higher there above the

horizon and that is

how the seasons are caused similarly

during the winter solstice the orbit of

the sun was

highest on the southern side at that

point it gives the northern hammer

square a minimal amount of sunlight

we see that on the picture in the left

when the earth is tilted away from the

sun

now the southern side experiences summer

and the northern side gets

lesser sunlight the sun appears lower on

the horizon

and that is why we have winter there

and then finally let's look at those

equinoxes we have and spring equinox as

you can see in the image

and an autumn equinox and in most cases

the sunshine

shines straight on the equator as you

can see in the image

and this is causing day and night to be

of equal length

this is the only time when you have a 12

hour day and a 12 hour night

everywhere on a planet in fact the word

equinox means equal day that is an easy

way to remember it

so we have a spherical earth we have

stars rotating around it in complicated

manners and we have a sun that orbits

around it

now ptolemy wondered that earth is it

centered

at the center of that swear of the fixed

stars

he believed this was the case because we

always see exactly half of the zodiac

if this is the sphere of the stars and

we're centered right in the middle

when you're standing on this side of the

earth you see the half

half of the zodiac and when you stand on

the other side you see the other half

if instead the earth was more to the

side you would see

only a small part of the zodiac during

one half of the day

and a larger part of the zodiac during

the rest

also if the earth was right at the

center day and night would not be of

equal length

during those equinoxes if the earth was

centered for instance right here

then the sun would have just a very

short orbit on this side and a very long

orbit on the other side

so this was his proof that the earth was

in the center of that sphere of the

fixed stars

very interesting idea

but now ptolemy went astray since the

earth is

always at the center of that square of

the fixed stars

it must be at rest he reasoned

we quote assume that for argument sakes

the heavens are unmoved

while the earth revolves around the same

axis from west to east

such a thing would seem quite ridiculous

based on what occurs

around us and in the air

he actually had the correct idea that it

was revolving around his axis

but then he called it ridiculous and for

the following understandable reason

the revolution of the earth is the most

violent of all motions he says

causing everything not standing on earth

to make a single motion

opposite to the earth so

if i would throw up a ball while the

earth is rotating shouldn't that ball

just

fly all the way to one side a very

reasonable idea and one that was only

solved by galileo

hundreds and hundreds of years later

to refine his model even further ptolemy

also had to include the observation that

the sun and the planets speed up

and slow down along their paths this he

called animalistic motion

hipparchus in the second century bc had

already measured this

by measuring that the seasons were a

slightly different length

it took for instance 94.5 days from the

spring equinox to the summer solstice

while only took 92.5 from the summer

solstice to the awesome equinox

and these changes in the time of the

seasons were caused by a speeding up and

a slowing down

of the sun from this observation

hipparchus concluded that the earth was

not in the center of the solar

orbit so if you have the orbit of the

sun

around the earth like this the earth was

not in the center but slightly

off-center he calculated that it must be

off-center about

1 24 of that solar radius of the radius

of

the radius of the orbit of the sun

in addition the planets also exhibit

what is called retrograde motion

if you for instance follow the planet

mars you'll see that it will continue

along its orbit for a period of time

but it will slow down and stop return

turn backwards for a moment and then

finally continue in its orbit again

this backward motion is called the

retrograde motion

and it is observed in all the planets

this makes the motion of the planets

insanely complicated here we see

an 18th century drawing of some of the

planets and you see how complicated

those orbits tends to be

this is the earth in the center and some

of the planets

circling around them

in the third century bc apollonius

another astronomer

had described this retrograde motion

with what is called epicycles

an epicycle is a small orbit as you can

see in the image

that is rotating along a larger orbit

creating those circles so this was a

mathematical mechanism

to better understand what was going on

it was though the planets moved on a

circle within a circle

in the 4th century bc plato had

challenged the intellectuals of his day

to attempt to explain these animalistic

motions of strange retrograde motions

and so on

in terms of simple circular motion

he was convinced that there must be a

way to simplify that messy movement of

the planets

and ptolemy finally took on this

challenge

we quote it is necessary to premise in

general that the motion of the planets

eastward in the heavens are all uniform

meaning of constant velocity

and circular by nature so this was

plato's challenge

and then it continues their uniform

either on circles non-concentric with

the universe

this was hipparchus idea that the orbit

of the sun was slightly off center

or else on circles that are concentric

but not upon them simply but rather upon

circles carried by them and called

epicycles so circles in circles

so he actually names those two ideas

from

hipparchus and apollonius

so firstly ptolemus follows hipparchus

in placing the earth

off center as we see on the image in the

right the plus sign is the center of the

orbit of the sun

and the earth we've drawn just below it

ptolemy then added the acquaint which is

his most important contribution

to the system from this point we see a

quaint

slightly above the center of the orbit

of the sun

the motion of the sun appears constant

so whether the sun moves from a to b

or b to c it seems to move at the same

angle as you can see in this image

while as seen from the earth the same

motion suddenly appears

non-uniform so if we look at the same

motion in this image

as seen from the earth we now see that

the motion from a to b

appears smaller at a smaller angle than

a motion from

c to d ptolemy then showed that this

model approximated the observed motion

of the sun

extraordinary well and plato must have

been very happy with this model

for as seen from the acquaintance from

the equate only

it seems as though the sun was moving at

a constant velocity

and now things get really interesting

some details which

ptolemy mentions clearly in his text

already

hint at the heliocentric model of the

solar system but he just

couldn't see it even though it was right

there in his own writing for instance

ptolemy tells us that mercury and venus

the inner planets

always stay very close to the sun

mercury always stays within 8

28 degrees of the sun as seen from the

earth and venus within 47 degrees

so they always stay close to the sun why

is this

this is because they are orbiting the

sun why else would they

always stay close to the sun but even

though ptolemy knew this fact he did not

make that conclusion similarly ptolemy

notes that the mean motion of the inner

planets

the motion of the planet around the

earth is equal to the mean motion of the

sun

this is of course for the same reason

that the planets are orbiting the sun

so obviously the rotation time of the

sun

is the same as the rotation time of that

planet as seen from the earth

in fact and then it becomes even more

clear the center of the epicycle

of mars and venus the inner planets is

the sun itself it is revolving around

the sun

but unfortunately ptolemy did not know

this he actually believed

that the inner planets were rotating

below the sun

like this so this is the sun and this

other this didn't know the distances

to the planets so you cannot blame him

from not knowing that the planets were

actually

revolving around the sun for then the

heliocentric model would be immediately

clear

but yeah he didn't know that

thirdly ptolemy also knew that the

radius of the

epicycle you can see an epicycle on the

top right in the image and you see its

radius

is always parallel to the radius of the

sun

so in the middle or just below the

middle of the image we see the earth and

circling around it we see the sun

and we see again that radius and as you

can see at the image those two radiuses

are perfectly parallel

also the epicycles of the outer planets

all have periods of exactly one year

the same time it takes the sun to

revolve around

the earth this is again clear evidence

of the heliocentric model

for the planet simply seems to move with

the sun

and from this we can easily imagine that

that seeing this motion from the sun

from the perspective of the sun

that that strange epicycle movement

would immediately disappear

in this drawing i've also shown that the

orbit of the sun

is actually exactly equal to the orbit

of the epicycle of the outer planets but

autolemy also didn't know that

so ptolemy knew about all these curious

coincidences

the inner planets the outer planets they

all have something to do

with the orbital time of the sun itself

so he mentioned all this but he saw no

need to explain it

he simply posits those facts as just

attributes of the planets

but he was so close so close in seeing

the bigger picture finally i want to

quickly discuss

another work by ptolemy known as the

planetary hypotheses

ptolemy attempted to measure the size of

the universe in this text

to do this he used the assumption that

the spheres of the planets were all

stacked

on top of each other in this way there

was no

vacuum between those spheres which

aristotle

earlier philosopher had claimed did not

exist in nature

so he believed that those spheres of the

planets must be stuck

on top of each other to avoid a vacuum

using that assumption and estimating the

sizes of those epicycles

he couldn't calculate the distances to

the planets

we quote the distances of the planets

may be determined without difficulty

from nesting the swears adding the

swears on top of each other

he then equated the distance to the

sphere of the fixed stars with the

radius of the cosmos so

he thought he was calculating the radius

of the cosmos itself

his results of course these distances

were way off

but it was an ambitious attempt

nonetheless and that's why i wanted to

mention it in the end

so this was it for today if you want to

know more about

world history then get a copy of my book

the great world history book

see you next time so in order to better

understand that strange retrograde

motion of the planet that complex motion

that you see right here

i created a javascript model uh i did

this

the easy way i first created the

copernican model with the sun in the

center

and then all the planets revolving

around this i used the real values of

the planets so the real velocity

velocity the real distances and so on

and then i made what is called a

coordinate transformation

where i use simple mathematics to view

what

this motion looks like as seen from the

earth and that's just

a few lines of mathematics and then you

immediately get from this

to this insanely complicated picture

well let's first look at the inner

planet so you better understand

what's going on in those lectures so

let's look at

let's look at mercury first let's slow

it down here

as mentioned before we can easily see

that mercury is rotating around the sun

while ptolemy didn't know that he

thought that mercury was rotating

somewhere

here but this is very clear evidence of

the heliocentric model

right there it is revolving not around

the earth

but it's revolving around the sun

the same goes for venus so here we see

mercury and venus the two inner planets

both circling around the sun it takes a

slightly bigger orbit you can see it

creates

beautiful patterns and the pattern of

venus is

especially beautiful as it creates a

four-pointed

flower that we'll see in a moment so

here we have the fourth

side and then we get the last one right

here

so here we see that four five pointed

flower

it's it's pretty incredible um

a good idea for uh for a tattoo in fact

so let's now look at the outer planets

here we have

jupiter and saturn we also have mars but

mars is a bit more complicated

to to understand but in the end it works

in the same way

so what do we see here we see that the

motion

the retrograde motion of jupiter and

saturn perfectly mimics

the motion of the sun and that is

because of course we actually have to

view this motion

as seen from the sun this is the actual

motion

of those two planets right here

and the fact that they move so similarly

with the same

rotational period in the same direction

is also

evidence for that heliocentric model

see you next time