Ptolemy's Almagest
Summary
TLDRIn 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 Despite his accurate predictions, Ptolemy's model was eventually superseded by Copernicus's heliocentric theory.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
- π Ptolemy's 'Almagest' is one of the most influential scientific texts in history, detailing his geocentric model of the universe.
- π Ptolemy believed the Earth was at the center of a spherical universe, with celestial bodies moving in complex, predictable patterns.
- π Ptolemy's geocentric model was remarkably accurate in predicting the motions of celestial bodies and dominated for over 1200 years.
- π Ptolemy's model included the use of epicycles to explain the retrograde motion of planets, a concept later refined by Copernicus's heliocentric model.
- π The 'Almagest' is filled with extensive astronomical tables and mathematical diagrams illustrating the complex motions of the celestial bodies.
- π Ptolemy provided evidence for a spherical Earth, including the observation that not all observers see the same stars at the same time.
- π Ptolemy recognized the Earth's tilt and its effect on the changing visibility of stars and the length of daylight throughout the year.
- π He explained the changing position of the Sun's apparent path across the sky, leading to the understanding of solstices and equinoxes.
- π Ptolemy's work was deeply rooted in Greek philosophy, particularly the belief in the divine order and symmetry found in mathematics.
- π 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
π 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.
π 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.
π 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.
π 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.
π 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.
Mindmap
Keywords
π‘Ptolemy
π‘Almagest
π‘Geocentric model
π‘Heliocentric model
π‘Astronomia
π‘Epicycles
π‘Retrograde motion
π‘Precession
π‘Zodiac
π‘Equinox
π‘Solstice
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
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