Lecture2 part3 video
Summary
TLDRThis 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 lawsβplanets 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 cubedβrevolutionized astronomy and are still fundamental today.
Takeaways
- π The period between 1415 and 1600 in Europe is known as the Enlightenment, characterized by a resurgence of interest in motion, physics, and astronomy.
- π 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.
- π Copernicus's model suggested that the Earth and other planets orbit the Sun, which helped to explain the apparent retrograde motion of planets.
- π« 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.
- π Despite its simplicity, Copernicus's model was not more accurate than Ptolemy's geocentric model and could not explain the lack of observable parallax.
- π€ 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.
- π Tycho Brahe, a nobleman and astronomer, made precise measurements of celestial bodies, challenging the Greek ideal of a perfect and unchanging universe.
- π Brahe's observations of supernovae and comets confirmed that these phenomena occurred beyond the Moon, contradicting the Greek belief in an unchanging heavens.
- π 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.
- π 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
π 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.
π 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.
π 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.
π 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.
Mindmap
Keywords
π‘Enlightenment
π‘Nicholas Copernicus
π‘Occam's Razor
π‘Epicycles
π‘Heliocentric Model
π‘Tycho Brahe
π‘Johan Kepler
π‘Kepler's Laws of Planetary Motion
π‘Supernovae
π‘Comets
π‘Parallax
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
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