Lecture2 part3 video

Summary

This lecture segment delves into the European Enlightenment period, focusing on the 15th to 17th centuries' astronomical advancements. It highlights Copernicus's heliocentric model, which challenged Ptolemy's geocentric system. Despite initial inaccuracies, Copernicus's ideas laid the groundwork for Kepler's three laws of planetary motion, derived from Brahe's precise astronomical data. These laws—planets orbit in ellipses with the Sun at a focus, sweep equal areas in equal times, and relate a planet's orbital period squared to its average distance from the Sun cubed—revolutionized astronomy and are still fundamental today.

Takeaways

• 📚 The period between 1415 and 1600 in Europe is known as the Enlightenment, characterized by a resurgence of interest in motion, physics, and astronomy.
• 🌟 Nicholas Copernicus, born in 1473, was influenced by the Greek educational system and proposed a heliocentric model of the solar system, simplifying the explanation of planetary epicycles.
• 🔍 Copernicus's model suggested that the Earth and other planets orbit the Sun, which helped to explain the apparent retrograde motion of planets.
• 🚫 Copernicus published his work on his deathbed due to the Catholic Church's opposition to the idea that the Earth was not the center of the universe.
• 🌌 Despite its simplicity, Copernicus's model was not more accurate than Ptolemy's geocentric model and could not explain the lack of observable parallax.
• 🤔 The concept of gravity, which explains why objects on Earth do not fall off as it moves, was not yet understood during Copernicus's time.
• 👑 Tycho Brahe, a nobleman and astronomer, made precise measurements of celestial bodies, challenging the Greek ideal of a perfect and unchanging universe.
• 📊 Brahe's observations of supernovae and comets confirmed that these phenomena occurred beyond the Moon, contradicting the Greek belief in an unchanging heavens.
• 📚 After Brahe's death, his assistant, Johannes Kepler, used the collected data to refine the heliocentric model and formulate his three laws of planetary motion.
• 📐 Kepler's laws describe that planetary orbits are elliptical with the Sun at one focus, planets sweep out equal areas in equal times, and the square of a planet's orbital period is proportional to the cube of its average distance from the Sun.

Q & A

What significant period in European history is discussed in the script?

The script discusses the Enlightenment period in Europe, which occurred between the 14th and 17th centuries, approximately six to seven hundred years ago.

Who is Nicholas Copernicus and what is his contribution to astronomy?

Nicholas Copernicus was a Renaissance-era mathematician and astronomer who proposed the heliocentric model, which placed the Sun at the center of the solar system, as opposed to the Earth.

What is Occam's razor, as mentioned in the script?

Occam's razor is a problem-solving principle that suggests simpler explanations are more likely to be correct than complicated ones, which Copernicus applied to his astronomical theories.

Why was Copernicus's model of the solar system initially controversial?

Copernicus's model was controversial because it contradicted the then-accepted geocentric model and the teachings of the Catholic Church, which declared the Earth to be the center of the universe.

What was the main issue with Copernicus's model of the solar system?

Copernicus's model assumed that planets orbited the Sun in perfect circles and at constant speeds, which was not accurate and made his model less reliable than it could have been.

Who was Tycho Brahe and what was his contribution to astronomy?

Tycho Brahe was a Danish astronomer known for his accurate and comprehensive astronomical observations. He challenged the Greek ideal of a perfect and unchanging universe by observing supernovae and comets.

What did Tycho Brahe's observations of supernovae and comets indicate about the nature of the universe?

Tycho Brahe's observations indicated that supernovae and comets were celestial events occurring beyond the Moon, contradicting the Greek belief in an unchanging and perfect heavens.

Who was Johann Kepler and what did he contribute to the understanding of planetary motion?

Johann Kepler was a mathematician and astronomer who, using Tycho Brahe's data, formulated the three laws of planetary motion, which described the elliptical orbits of planets and their varying speeds.

What are Kepler's three laws of planetary motion?

Kepler's first law states that planets orbit the Sun in elliptical orbits with the Sun at one focus. His second law, also known as the law of equal areas, states that a line connecting a planet to the Sun sweeps out equal areas in equal times. The third law, or the harmonic law, relates a planet's orbital period squared to the cube of its average distance from the Sun.

How did Kepler's laws of planetary motion change the understanding of the solar system?

Kepler's laws provided a mathematically sound description of planetary motion that was more accurate than previous models. They showed that planets move in elliptical orbits and at varying speeds, which was a significant departure from the circular orbits and constant speeds assumed by earlier models.

What was the significance of the period of astronomy discussed in the script for the development of modern science?

The period discussed in the script was significant for the development of modern science as it marked a time when scientific inquiry was based on empirical evidence and mathematical principles, leading to the establishment of the scientific method and the advancement of astronomy and physics.

Outlines

00:00

🌟 The Enlightenment and Copernicus' Heliocentric Model

This paragraph discusses the period of the Enlightenment in Europe, around 1400-1600, which was a time of significant advancements in motion physics and astronomy. It highlights the role of universities and the Greek educational system in fostering scientific thought. Nicholas Copernicus, born in 1473, is introduced as a key figure who challenged the complex Ptolemaic model of the universe with a simpler heliocentric model, placing the Sun at the center of the solar system. Despite the risk of heresy due to the Catholic Church's geocentric views, Copernicus published his findings posthumously. His model, though simpler, was not more accurate than Ptolemy's and retained some Greek ideals, such as circular orbits and constant planetary speeds, which were later disproved.

05:01

🔭 Tycho Brahe's Accurate Observations and Geocentric Model

The second paragraph introduces Tycho Brahe, a nobleman and astronomer who made precise measurements of celestial bodies using an advanced observatory without telescopes. His observations challenged the Greek notion of an unchanging, perfect universe by documenting supernovae and comets, proving they were celestial events. Brahe's geocentric model, which he proposed due to the lack of observed parallax, was an attempt to reconcile his accurate data with the then-prevailing beliefs. His work laid the foundation for future astronomical advancements, and his death in 1601 marked the end of an era in observational astronomy.

10:05

📚 Kepler's Laws of Planetary Motion

The third paragraph focuses on Johannes Kepler, who inherited Tycho Brahe's extensive astronomical data. Kepler used this data to refine the heliocentric model, developing his three laws of planetary motion. His first law stated that planets orbit the Sun in elliptical paths, with the Sun at one focus. The second law, or the law of equal areas, described how a planet sweeps out equal areas in equal times, indicating variable speeds in its orbit. The third law, relating a planet's orbital period squared to the cube of its average distance from the Sun, revealed the relationship between a planet's distance from the Sun and its orbital period. These laws provided a more accurate model of the solar system and are still fundamental in astronomy today.

15:08

🚀 The Impact of Kepler's Laws on Modern Astronomy

The final paragraph emphasizes the enduring significance of Kepler's laws in modern astronomy. It points out that while Kepler did not understand the underlying reason for the laws' accuracy, the principles of gravity later explained why they worked. The paragraph also notes that this period of scientific advancement was crucial for the development of modern science, building upon Greek knowledge but marking a significant leap forward. The lecture concludes with a teaser for the next part, which will delve into the role of gravity in explaining Kepler's laws.

Keywords

💡Enlightenment

The Enlightenment refers to an intellectual and philosophical movement that dominated the world of ideas in Europe during the 17th and 18th centuries. It emphasized reason, individualism, and skepticism, and often opposed traditional doctrines. In the context of the video, the Enlightenment is used to describe the period around 1400-1600 when there was a renewed interest in studying motion, physics, and astronomy, marking a significant shift from the previous Dark Ages.

💡Nicholas Copernicus

Nicholas Copernicus was a Renaissance-era mathematician and astronomer known for his heliocentric model of the universe, which placed the Sun, not the Earth, at the center. His work is foundational to modern astronomy and is a central theme in the video, as it represents a paradigm shift from the Ptolemaic model and laid the groundwork for future astronomical discoveries.

💡Occam's Razor

Occam's Razor is a problem-solving principle that suggests the simplest explanation or solution is usually the best. In the video, Copernicus is said to have applied this principle to astronomy, favoring a simpler model of the solar system with the Sun at the center over the complex Ptolemaic model with its epicycles.

💡Epicycles

Epicycles are small circular orbits that a celestial body was thought to make on top of its larger orbit around the Earth, as per the Ptolemaic system. The video discusses how Copernicus' heliocentric model provided a simpler explanation for the observed motion of planets, including the apparent retrograde motion of Mars, without needing to invoke epicycles.

💡Heliocentric Model

The heliocentric model is a description of the solar system with the Sun at the center and the planets, including Earth, orbiting around it. The video explains how Copernicus' heliocentric model was a significant advancement over the geocentric model, which placed Earth at the center, and how it helped explain the observed planetary motions.

💡Tycho Brahe

Tycho Brahe was a Danish astronomer known for his accurate and comprehensive astronomical observations. In the video, he is highlighted for his meticulous measurements of celestial bodies, which he conducted without the aid of a telescope, and for his contributions to the understanding of comets and supernovae, challenging the Greek ideal of a perfect and unchanging universe.

💡Johan Kepler

Johan Kepler was a German mathematician, astronomer, and astrologer who formulated the three laws of planetary motion. The video discusses how Kepler built upon Copernicus' work and Tycho Brahe's data to develop a more accurate model of the solar system, which included the discovery that planetary orbits are elliptical, not circular.

💡Kepler's Laws of Planetary Motion

Kepler's Laws describe the motion of planets around the Sun. The video explains the three laws: 1) Planets move in elliptical orbits with the Sun at one focus, 2) A line connecting a planet to the Sun sweeps out equal areas in equal times, indicating varying speeds at different parts of the orbit, and 3) The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit, relating a planet's distance from the Sun to its orbital period.

💡Supernovae

Supernovae are massive explosions that mark the end of a star's life and briefly outshine entire galaxies. In the video, Tycho Brahe's observation of a supernova challenged the Greek belief in an unchanging heavens, as it provided evidence of change within what was considered the perfect realm of the cosmos.

💡Comets

Comets are small celestial bodies composed of ice, dust, and rocky material that form a temporary atmosphere and tail when they approach the Sun. The video mentions how Brahe's observations of comets also contradicted the Greek view of a perfect universe, as they too were shown to be part of the heavens, contrary to previous beliefs.

💡Parallax

Parallax is the apparent shift of an object's position relative to distant objects, and it's used to measure distances in astronomy. The video discusses how the lack of observable parallax for stars was a challenge for heliocentric models, as it suggested that the stars were much farther away than previously thought, which was a problem for geocentric models as well.

Highlights

The Enlightenment period in Europe (1415-1600s) saw a resurgence of interest in motion, physics, and astronomy.

Nicholas Copernicus, born in 1473, benefited from the new university system and studied astronomy within the Greek educational framework.

Copernicus applied Occam's razor, favoring simpler explanations, and questioned the complex Ptolemaic model of the universe.

He reintroduced the heliocentric model, placing the Sun at the center of the solar system, which offered a simpler explanation for planetary motion.

Copernicus published his model on his deathbed due to the Catholic Church's opposition to the idea of a non-geocentric universe.

Copernicus's model explained the apparent retrograde motion of planets without the need for epicycles.

Despite its simplicity, Copernicus's model was not more accurate than Ptolemy's due to his adherence to circular orbits and constant orbital speeds.

The lack of observable parallax continued to challenge the heliocentric model, conflicting with the common-sense notion of a stationary Earth.

Tycho Brahe, born into nobility, made precise astronomical measurements that would later challenge the Greek ideal of a perfect and unchanging universe.

Brahe's observations of supernovae and comets demonstrated that these celestial events occurred beyond the Moon, contrary to Greek beliefs.

Brahe proposed a geocentric model, despite not being able to observe parallax, due to the high accuracy of his measurements.

Johannes Kepler inherited Brahe's data and refined the heliocentric model, formulating his three laws of planetary motion.

Kepler's first law stated that planetary orbits are elliptical, with the Sun at one focus, contradicting the circular orbits of Greek philosophy.

His second law described how a planet sweeps out equal areas in equal times, indicating variable speeds in its orbit.

Kepler's third law, known as the harmonic law, related a planet's orbital period squared to its average distance from the Sun cubed.

These laws are still used in astronomy today and were pivotal in the development of modern scientific methods.

The period of the 15th to 17th centuries was crucial for the advancement of astronomy and the establishment of empirical scientific practices.

Transcripts

hello everyone welcome to part three our

discussion of the rise of astronomy now

in today's part of this lecture we're

going to talk about what was going on in

Europe in the 1415 and 1600s this is

about six seven hundred years ago and

what what's happening there was very

interesting it's a period of time I call

the Enlightenment and during this period

of time lots of people were studying

motion physics and astronomy this is a

period just after the end of the Dark

Ages when Europe consolidated into a

bunch of larger nation-states and we

started to have the beginnings again of

Greek style educational systems and

universities now Nicholas Copernicus is

one of the people who benefits from this

new university system he's born in 1473

Nicholas Copernicus study astronomy and

was trained in the Greek system of

education they were still using that at

this point in well honestly we still

kind of used the Greek educational

system today so in any case now

Copernicus understood what we now call

today Occam's razor which is the idea

that really complicated explanations for

things are not as good as simple

explanation for things now this is not

always the case but in science it's

something that in general is an ideal

now

Copernicus knew that Ptolemies model had

problems it was very complicated and

needed to be rebooted every once in a

while

in order to continue to work and he also

knew that because it was so complicated

especially in its explanation about

epicycles he thought there was a simpler

idea and he actually reconsidered the

idea of era star

cos that the Sun was the center of the

solar system and when he did this he

realized something about the solar

system that actually explained epicycles

very very simple okay the idea is this

Kepler or Copernicus rather Copernicus

ended up publishing his data on his

deathbed he publishes his work on his

deathbed because of the time the

Catholic Church was very important in

northern Europe and the church decreed

the earth was the center of the universe

and so saying that the earth was not was

actually heresy but in any case he

published a model and in his model the

Sun was the center and the earth went

around the Sun and the reason why we see

epicycles why it appears for instance

Mars changes positions relative to the

background stars just has to do with our

position relative to Mars as the earth

goes around the Sun so here our point of

view Mars looks like it's right here but

one month later Mars looks like it's

here from our point of view now find

Mars is moving west to east but then one

month later we are here and Mars from

our point of view appears to be here so

it's moving in the opposite direction

relative to the background stars again

it's not because Mars is going through

little loops in the sky is just because

we're lapping Mars this explanation is

very very simple

however Poorna kiss was educated in the

Greek system and because of that he his

model was actually based on some Greek

ideas like he believed that the planet's

orbit of the Sun in perfect circles

that's a very Greek idea turns out not

to be the case and because of this he

also assumed that the the orbital speeds

of plants were constant

change speed that also turns out not to

be the case because of this his model

didn't work any more accurately than

Ptolemies model now furthermore his

model could not explain the fact that

you could not see parallax people were

still worried about this you can't see

parallax well this problem becomes less

of an issue over time because as we'll

talk about in the next lecture people

begin to realize that the universe is

much much bigger than they thought

especially when the telescope is

invented telescope at this point still

not invented telescope is not invented

until the early 1600s furthermore his

ideas conflicted with what we call

common sense the Aristotle in common

sense now this is a little complicated

but the idea is this if the earth is

moving why would it not leave like for

instance the moon behind if the earth

goes around the Sun and the moon was

around the earth well why isn't the

earth leave the moon behind when it

moves or even more basic than that when

the earth moves why does it not leave us

behind I mean you can imagine like a a

cart you know with wheels okay you stack

something on that cart and then you push

the cart forward well unless the thing

is tied down the thing is gonna fall off

the Greeks know about that

we know by that today why is it that the

earth can move and we just don't fall

off the earth well we know the answer

today the answer is gravity they didn't

have that idea then and so the effect

the idea that the earth moves conflicted

with this idea of common sense

now the Poorna cos dies and a few years

later a guy named Tycho Brahe hey or

Tycho Brahe is born now Tycho Brahe is

born rich and into nobility and he's

really interested in

I mean and mathematics and he has

because he's born into nobility he is

the nephew of the Emperor of a Empire

that is now what you might think of as

like Denmark the Netherlands northern

Europe and he was named the Imperial

astronomer by the Emperor he was so

interested in astronomy and he was given

an observatory now an observatory at

that time did not have telescopes what

he had built was a giant arch that giant

arch had a wooden tube that you could

look through so you would stand down

here that's all person and he would look

through this tube and he would point it

at a star in the sky or a planet in the

sky okay and you could measure how high

above the ground That star was and the

whole thing was on a giant lazy susan

that would spin around and so you could

tell the direction north south east west

of that star and he made a meticulous

measurements of planets and stars in the

sky also other things

now he did his measurements he didn't do

himself obviously he had people who work

for him who made the measurements but

over 20 years they collected this

measurement in his data and it was more

accurate this was the most accurate

astronomical device ever built at the

time so the positions he was measuring

were super accurate now he also does

other things so for example he pokes

holes in the Greek ideal of the universe

he does something he measures the

positions of supernovae and a comet in

the sky now a supernova is a star that

explodes from our point of view a new

star appears in the sky for a little bit

and then disappears a comet is a ball of

ice that orbits the Sun when it gets

close to the Sun it grows a tail now the

Greeks would have said that these

supernovae and these comets

they are not in the heavens they are

actually in the upper part of the sky

because the Greeks believed the heavens

were perfect and therefore unchanging

but Braja is able a Brock is able to

make observations with his accurate

device and various places in Europe it

was able to prove that whatever these

things were these supernovae these

comets whatever they were they were

further from the earth they were further

away from the earth and the moon was

they were definitely in the heavens so

poking holes okay into the Greek ideal

of what the universe looked like

furthermore he proposes a geocentric

model because again he still cannot

observe parallax and that's still a huge

thing he proposes a weird a geocentric

model we're not gonna get into it

because Tycho Brahe dies relatively

young in 1601 now at the time he had an

assistant named Johan Kepler and when

Brock dies Johan Kepler gets his data

those twenty years of data but the

positions of objects in the sky

specifically planets and using this data

Kepler takes Copernicus's model this

model where the Sun is the center of the

solar system and the planets orbit

around the Sun he takes the model he

changes it he comes up with what he

calls the three laws of planetary motion

he changes the model and makes it work

it makes it work perfectly so how does

he changed the model well first of all

Tipler realizes based on brahs data data

is that orbits are not actually circles

they're ellipses so when ellipse looks

like this it's basically a squished

circle where instead of having I got a

circle is a circle and it has one focus

the middle an ellipse as two foci

is a squished circle where if you add

the distance from one focus to the edge

then back to the other focus that

distance is the same no matter how you

measure it so if I went from here to

here to here or from here to here to

here at the same overall distance so

it's similar to a circle in fact if you

take these two foci and put them on top

of each other right there in the middle

well that is a circle so a circle was a

special case of an ellipse and what

Kepler's first law of planetary motion

says is that all orbits are ellipses and

the Sun is at one focus of that ellipse

so all planets orbit around the Sun in

an elliptical orbit and the Sun is one

focus of that ellipse now that is the

first of three laws Kepler's second law

says this if you imagine so you have a

planet okay imagine you draw a line

between the Sun and that planet as the

planet goes around the Sun it is going

to sweep out a certain amount of area

now if two months go by and the planet

has swept out this much area well what

Kepler's second law says is that in any

other two-month period any other tooth

period the planet will sweep out the

same amount of area so if this is two

months then this amount of area is the

same as that amount of area now if you

think about it if planets orbiting the

ellipses well the planets over here it's

closer to the Sun so it's a shorter

wedge which means that the same area

means it has a longer sweep here on the

right-hand side it's a longer wedge

which means it's the same amount of area

you're getting a shorter sweep but both

of these are 2 months and what that

means is that here the planet is closer

to the Sun it's moving

faster then when it's out here further

away from the Sun okay here close to the

Sun it moves further in the same amount

of time as it moves from here to here

when it's furthest from the Sun so

planetary velocities are not constant to

change over time now we understand why

today we understand why this has to do

with gravity so imagine you take a ball

you throw it up into the air well it

goes up in the air it slows down and

then it comes back down towards the

Earth that's exactly what's happening

here right here the planet is moving

it's moving away from the Sun it's like

the ball being thrown up into the air

because of gravity it's slowing down

until it gets as far away from the Sun

it's gonna get it's as slowest and then

it falls back towards the Sun speeds up

so it's fastest here where it's closest

to the Sun and slowest here where it's

furthest from the Sun okay just gravity

that's Kepler's second law

now where's third law says at the period

how long it takes for a plan to go once

around the Sun measured in years so for

the Earth of just one one year okay for

Mars is about one and a half for Venus

it's about 0.7 for Jupiter it's just

under 12 years the period squared is

equal to the distance how far that

planet is from the Sun measured an au

cubed now au is the average distance

from the earth to the Sun for the earth

is just one okay for Mars it's a bit

more than one for Jupiter it's almost

five for Saturn it's ten almost ten so

period squared and distance cubed now

for the earth this is just one equals 1

because 1 squared is 1 1 cubed is 1 but

for Jupiter a period or distance

distance is almost 5 and period because

of that if you do the squared and cubed

here

the period for Jupiter is almost but not

quite ten years okay so the further

planet is from the Sun the longer it

takes to go once around the Sun now this

because it's squared and cubed I mean

obviously if a planet is further from

the Sun so if you have a Sun the planet

here the planets further away well yeah

it's gonna take longer if it's the

longer orbit but because of the squared

and the cubed but this actually tells

you is not only do planets further from

the Sun not only do they have further to

go once around the Sun but they're

actually moving slower than plants

closer to the Sun so mercury goes around

the Sun faster than Venus does and if

Venus goes round faster than the earth

the earth goes round faster than Mars

and keep going out okay so not only do

they have further to go the further they

are from the Sun they're also moving

slower so planets like Neptune it's 40

times further from the Earth or from the

Sun than the earth is and it takes like

a hundred and eighty years for Neptune

to go once I know even more than maybe

then ferment them to go once around the

Earth or once around the Sun and the

further it is away the longer it has to

go and the slower it's traveling okay so

that's Kepler's third law a P squared

equals a cubed okay missus sometimes own

as the harmonic law okay but that's the

third law so we have orbits are ellipses

that's the first law okay second law

says that the orbital speed of a planet

as it goes around the Sun depends on how

far away from the Sun it is so when it's

closer to the Sun it's moving faster

then it was further away and the third

law says that the planets overall

distance from the Sun is related to how

long it takes to go once around the Sun

and that planets that are further from

the Sun on average will move slow

than plants that are closer to the Sun

and I want to make it clear these laws

are still in youth today because they

work now Kepler did not understand why

they worked today we do the reason why

these laws work has to do with gravity

and and the next part of this lecture

we'll talk a little bit about that

and but these laws are super important

for astronomy again they're still used

today and this period of astronomy was

really huge and not only pushing forward

astronomy but also science in general

okay this period of time is when what we

now think of as really modern the

science was truly developed it was based

on what the Greeks were doing but this

is where it really gets developed okay

stay tuned for the next part of this

lecture