[ www.heliocentric.tv ] roughly seventy years after the

publication of Copernicus’s book concerning the revolutions Galileo’s

observations showed that the Ptolemaic system is incorrect and that the

Copernican system is probably correct as a description of physical reality

however let’s go back a few decades to see what at least a few scientists were

thinking even before Galileo’s groundbreaking observations and to see

what kind of refinements had been made to the Copernican model there was one

alternative that combined the features of both the heliocentric or sun-centered

system and the geocentric or earth centered system and this was suggested

by the Danish nobleman Tycho Brahe he sometimes pronounced eco I’m told that

in Danish it might be closer to 2 Co anyway I’ll say Tycho cuz that’s what

I’m used to he thought that perhaps the moon orbits

the earth but everything else orbits the Sun so Mercury Venus Mars Jupiter and

Saturn orbit the Sun and then the Sun together with all of the planets that

orbit it in turn orbits the earth so basically everything except the moon

orbits the Sun and then the Sun along with its orbiting planets orbits the

earth this is essentially a change of perspective from the Copernican system

instead of everything orbiting the Sun including the earth he has everything

orbiting the Sun except the earth but then all those things orbit the earth so

it’s just a change in perspective and without actually knowing that the earth

is moving you actually can’t tell the difference between this and the

Copernican system now now it turns out now we know that the earth is moving oh

I’ll show you ways that we know later on but at that time no one really knew that

the earth was moving it was just conjectured by Copernicus that it’s

moving and this system was in a sense equivalent just a

spective but this was not a very attractive idea to either side neither

the geocentric nor the heliocentric people were particularly pleased with

this combination of motions Tycho had an interesting life at the age of fourteen

he saw a partial solar eclipse from Denmark which happened to be total as

seen from Portugal and he was very impressed that astronomers had been able

to predict this so he wanted to dedicate his life to making ever more accurate

observations of the Moon Sun and planets especially the planets and namely Mars

in order to refine the predictive power of of physics and of these models he

wanted to know exactly when eclipses and other things would occur

he was quite bright but also a rather at argumentative fellow he thought pretty

highly of himself and at the age of 20 he had a duel with a fellow student not

over a woman but over who was the better mathematician of the two he lost his

nose during that duel and thereafter wore a gold and silver amalgam and

indeed on his tombstone where there’s a relief of of Tycho’s face you can see a

line here which is supposedly the demarcation between his metal nose and

his flesh and bones Tycho discovered a supernova an exploding star in the year

1570 – now he didn’t know the physical nature of the star that it was a star at

the cataclysmic end of its life going boom and creating elements and all the

great stuff I’ll tell you about later but he but he saw that the star had

brightened to naked-eye visibility in fact it was visible during the day and

it remained visible as it faded for eighteen months and this was an

astonishing thing because Europe was just emerging from the Middle Ages and

people thought that the heavens were immutable even though the ancient Greeks

had seen you know exploding stars and other things nevertheless the idea was

that the heavens are immutable and unchanging and so Tycho’s observation

went a long way toward dispelling that belief and he

gained favor with the king and was given a rather large amount of money with

which to set up an observatory you ran a Borg on the island of Hien h ven and he

was given funds to conduct all sorts of studies and stuff so he he became quite

quite the guy and had these lavish parties and social gatherings in his

castle indeed he was thought to have had something like 1% of Denmark’s entire

wealth at one point in the 1580s so he had these great parties and lots of

social gatherings but he drank a lot and and was egotistical and argumentative

and actually kind of annoyed a lot of people he had some other interesting

characteristics he had a dwarf named JEP who was his court jester and Tycho

actually thought that JEP was clairvoyant and he kept JEP under the

dinner table and fed him scraps of food and stuff so anyway but Tycho is kind of

a weird guy but at this Observatory he made fantastic observations of the

planets he didn’t have a telescope but he had other instruments with which he

could measure the altitude of a planet above the horizon and its angular

distance from other stars and things like that so he amassed this wide and

broad body of observations which later I will discuss were analyzed by Kepler a

superb mathematician well a new king came to power in 1588 and Tycho’s

influence waned and eventually his funds were cut off and finally he he decided

to to leave Denmark I mean he had basically annoyed the king and was

really an arrogant guy and everything so he he said okay I’m done with Denmark

and he settled in 1599 in prague at the invitation of the holy roman emperor

rudolf ii in 1601 Tycho drank too much at a dinner and neglected to go

frequently enough to the bathroom so he suffered from a urinary infection and

two weeks later died of it at a rather young age more recent research suggests

that his actual cause of death was mercury poisoning whether mercury he

had taken himself to fight his urinary infection or deliberately poisoned

perhaps even by his mathematician Kepler and Kepler was rather annoyed with with

Tycho because Tycho had hired him to analyze the data yet only gave small

parcels of data at a time he wouldn’t give Kepler this huge set of

observations and so Kepler felt frustrated he couldn’t really discern

what was going on from fragments of data so Kepler in a sense was happy when

Tycho died because he was able to get his hands on a data after a bunch of

battles with Tycho’s relatives who wanted to confiscate the the data but

Kepler managed to manage to get away with it so you then analyzed the data so

here’s Kepler you had a lot of interesting ideas he thought that the

planets are on these spheres that circumscribe the five perfect Platonic

solids and stuff and he spent years trying to prove this and it just didn’t

work out because turns out it’s not true but in any case he analyzed Tycho’s data

and he refined the Copernican model with three important empirical laws now they

were empirical in that Kepler had no physical explanation for them he just

found that quantitatively they appeared to be true but he didn’t know why they

were true that will come with Newton the first law that he figured out in the

year 1604 is that the planetary orbits are ellipses not circles and the Sun is

not at the center of the ellipse but rather is at one focus of the ellipse

now there are two foci and there’s nothing at the other focus in Kepler’s

system the Sun is at one focus nothing as of at the other focus here you can

see in this diagram that an ellipse is defined to be the set of points such

that the sum of the distances from two other points the foci is a constant so

distance one let’s call it distance to is B and ellipse is the set

of points such that a plus B is equal to a constant and it’s easy to draw an

ellipse using this in mind by taking a cardboard sheet like this putting a loop

of string around it you pull the string tight with the span and then draw the

ellipse around the two tax keeping the pen in such a way that the string is

tight and the sum of the distances is clearly a constant there we go there’s

an ellipse anyway that gives you an ellipse Kepler’s first law then says

that the Sun is at one focus and the earth and indeed other planets orbit the

Sun along an elliptical not a circular trajectory with the Sun at one focus

nothing at the other focus may be Kepler’s ghost or something like that

let’s discuss ellipses in a little bit more detail here’s an ellipse with the

two foci marked the long axis is known as the major axis the short axis is the

minor axis half of the major axis is just the semi-major axis and similarly

for the semi semi minor axis here’s a set of ellipses having different

eccentricity but the same major axis now the eccentricity is defined to be the

distance between the foci divided by the length of the major axis so in all these

cases that major axis has the same length but as I put the foci farther and

farther apart the ellipse becomes more and more highly eccentric here it’s a

very highly eccentric ellipse here it’s an eccentricity of only 0.3 so it looks

more circular it turns out that most of the planets

have orbits that are nearly circular that ellipses have only a very small

eccentricity and this as I briefly mentioned in lecture 13 is the reason

that Copernicus’s system with circular orbits worked quite well recall that

Copernicus had circular orbits like that of Mars but whose was a little bit

offset from the Sun well a circle whose Center is offset from the Sun looks

almost identical to an ellipse with a small eccentricity the dots the circle

the dashed line is the ellipse you see that they are nearly the same and so

Copernicus a system worked so well because though the planetary orbits

really are elliptical not circular the ellipses are nearly circular the

eccentricities are very low the second law that Kepler came up with is that a

line between the Sun and a planet sweeps out equal areas in equal times let me

show you what I mean here’s the Sun with the elliptical orbit of a planet

surrounding it what we’re saying is that in going from position 1 to position 2

along its orbit the line between the planet and the Sun sweeps out a pie

shaped area like this that area is the same as the area swept up elsewhere in

the orbit when the planet goes from position 3 to position for as long as

the time interval it took to go from 3 to 4 was exactly the same as the time

interval from 1 to 2 equal areas in equal times let’s look at a whole bunch

of sectors here all of these sectors have equal areas and so if you make T

one which spans two of these sectors equal to t2

Kepler’s law his second law tells you that the planet travels a lot less of a

distance way out here far from the Sun than it does close to the Sun now here

the the elliptical orbit has been greatly exaggerated but if the planet

had such an eccentric orbit it would travel more slowly out here far from the

Sun then when it’s close to the Sun because the area it sweeps out is the

same in each case and when it’s close to the Sun it has to move more in order to

sweep out an area equal to that swept out in this long skinny triangle so I’ve

set up here a planet whose orbit has an eccentricity of 0.6 and it’s orbiting

the Sun and what’s let’s watch it move it moves slowly when it’s far from the

Sun and more quickly when it’s near the Sun slow fast that kind of a thing okay

it changes its speed and quantitatively you can figured out by how much by using

Kepler’s second law if we go back and make the eccentricity zero you will

notice that the speed of the orbit is unchanging with time but it changes the

more eccentric the trajectory is this applies most visibly to comets

such as this one in particular comets like Halley’s Comet have periodic orbits

that is they come around the Sun every once in a while as is shown here some

comets come in from very far away and sweep past the Sun only once but the

so-called periodic comets sweep past the Sun of a few decades or so and they

spend most of their time way out here far from the Sun and then they zip past

it so they go zoom zum-zum like that and they spend almost

all their time way far from the Sun here’s the orbit of Comet Hallie in fact

in 1948 it was way out here by 1977 that had come closer than 1983 then 85 and

then it’s swung past the Sun in 1986 zoomed past it very quickly and then

started slowing down and spending most of its time way out in the far reaches

of the solar system generally between Neptune’s orbit and Pluto’s orbit the

third law that Kepler came up with was much later in time in 1618 and that he

called his harmonic law and it says that the square of the orbital period of a

planet around the Sun is proportional to the cube of its average distance or more

precisely the cube of the semi-major axis of the ellipse they turn out to be

mathematically about the same thing so the planets farther out have longer

orbital periods that was already known before Kepler’s time but quantitatively

Kepler showed that the square of the orbital period is proportional to the

cube of the semi-major axis so you can write that P squared equals some

constant K times R cubed where R is the semi-major axis Kepler was ecstatic

about this law he called it his harmonic law because he was looking for the music

of the spheres he had a real musical talent and he was trying to find harmony

among the spheres and some sort of musical notes out there and this comes

the closest to that because musical notes are arranged in harmonic ways that

are not precisely like this but have some similarities so let’s write down

this equation P proportional to or P squared proportional to R cubed or you

can write it P squared equals K some constant times R cubed now it’s

convenient to use units based on the Earth’s orbit for example I

can write that the square of the orbital period of some planet is equal to the

constant K times the cube of the planets semi-major axis I can write that same

equation for the earth the square of the Earth’s orbital period is some constant

multiplied by the cube of Earth’s distance from the Sun if I then divide

one equation by the other the constant K cancels out because it’s a constant and

so we get that the orbital period of the planet divided by the Earth’s orbital

period that quantity squared is equal to not just proportional to but now equal

to the distance of the planet from the Sun divided by the distance of the Earth

from the Sun that kinetic quantity cubed so we know that the Earth’s orbital

period is one year that’s a familiar unit and the Earth’s distance from the

Sun is just some number it happens to be 93 million miles 150 million kilometres

I’ll talk in the next lecture on how that’s determined we can write 150

kilometres as 1.5 times 10 to the 8th kilometers the 10 to the 8th just tells

you how many decimal points you should move over to get the number that you’re

trying to write down you should move over eight decimal points one two three

four five six seven eight if you write that out you would get 150 million but

it’s kind of cumbersome to keep track of all those zeroes and write them all down

you might miss some so we use scientific or exponential notation of this kind if

you’re using a calculator this would show up on your calculator as 1.5 e8

okay I think most people are familiar with this kind of notation because we

all use calculators anyway that’s called an astronomical unit you can figure out

what it is through measurements so we know that the earth orbits in one year

at a distance of one astronomical unit if we then say that oh I’ve measured the

orbital period of Mars to be one point eight eight years

one can do that just look at Mars and see how long it takes to go all the way

around the Sun turns out to be one point eight eight years if you plug in one

point eight eight here take its square and then ask yourself what number when

cubed gives you the same number that is the square of one point eight eight you

find that that number is one point five two or one point five two astronomical

units that is 52% greater than the distance of the Earth from the Sun so

using ratios like this as is very useful so Mars is about 52% farther from the

Sun than Earth is and you can figure that out using Kepler’s third law only

by measuring the orbital period of Mars okay well let’s set up another animation

here where for simplicity I’ll just have circular orbits initially this one is

close to the Sun the planet is really zipping around quickly if I now stop the

animation and I put the planet farther away say 2.5 units from the Sun instead

of 1 you can see that the orbit the orbital velocity is much slower and

quantitatively what Kepler said was that the square of the orbital period is

proportional to the cube of the distance this also applies to objects orbiting

the Earth and in particular there are lots of satellites orbiting the Earth a

satellite just above the Earth’s surface goes about 230 degrees in one hour that

is about 2/3 of the full circle as the earth itself rotates about 15 degrees

per hour so the space shuttle and other near-earth satellites orbit in about an

hour and a half it turns out a satellite orbit at 3 and 1/4 Earth radii traverses

42 degrees in one hour but if you put the satellite at six-and-a-half Earth

radii then it traverses 15 degrees in one hour in other words it traverses the

angular distance as the Earth’s rotating surface and that means that this

satellite will appear stationary above a particular point on the Earth’s surface

this is the idea behind geostationary orbits here’s one shown right here if

you have a satellite above a communications tower it will remain

above that communications tower all the time if it’s orbiting at a distance of

six-and-a-half Earth radii from the middle of the earth if you put it too

close to the earth it orbits more quickly than the rotating earth and so

the same satellite antenna won’t always be in communication with the satellite

that’s okay it just happens to be a different kind of communication

satellite if you put the orbit too far from the earth then you notice that the

earth is rotating more quickly than the satellite is orbiting and once again it

does not remain hovering above one and only one communication station so

geostationary satellites are important for a number of forms of communication

and weather you know monitoring the weather at any particular location or

something like that ok well the stage was now set for Isaac Newton later Sir

Isaac Newton a brilliant but rather eccentric English physicist who made

many magnificent contributions to the development of physics and astronomy and

especially his three laws of motion and his law of universal gravitation Newton

lived from 1642 to 1727 and he he is what I would call not an ordinary genius

I mean they’re lots of ordinary geniuses wandering around on college campuses and

businesses and wherever you get people who are very talented they know what to

do they do it well they do it efficiently they’re smart people but

then there are some people who live in a completely different plane of existence

and this happens in all fields Mozart and Michelangelo and the Vinci well for

physics it was Newton Newton lived in a different plane of existence and

fought in ways that most of us even those of us who happen to be ordinary

geniuses cannot comprehend Newton’s life was interesting in 1661 he went to

Cambridge University but in 1665 he had to flee Cambridge due

to the plague and he went to the countryside and that was his most

fertile time he was just in his early 20s and he developed the calculus a form

of mathematics he developed his laws of motion the law of universal gravitation

everything it was just incredible what he did while away from college you know

on his summer vacations sort of you know his vacation from the plague in 1668 he

invented a form of telescope the Newtonian telescope and the next year

became the exalted Lucasian Professor of mathematics at Cambridge University he

finally published his work in the Principia being urged by his friend

Edmund Halley to do so and partially funded by Hallie just six years later

however he had a nervous breakdown but he got out of it and then became a

warden of the mint where he took extreme pleasure in in punishing counterfeiters

he apparently was had a sort of a cool bent to him he published his work on

optics in 1704 and then the next year was knighted not mostly for his

scientific studies but rather for his government service in the Principia he

described his three laws of motion the first is that if there are no forces

acting on a body then that body’s speed and direction remain constant now

usually we think of rest as being the natural state of things and indeed

Aristotle thought that a force was needed to keep a body in motion when you

throw something and you have it dragged all across the table it comes to rest

and so people thought that rest was the natural state of objects Newton said no

motion is just as good as rest and that motion is uniform along a straight line

in a given direction as long as there are no forces acting upon the body but

rest and motion are equally natural if there

are no external forces so you could have a hockey puck for example going along

some clean very smooth ice eventually we know it’ll come to rest due to friction

but if you didn’t have the friction it would keep on going the second law known

as F equals MA is just that the force is equal to the mass times the acceleration

now acceleration is a change either in speed or in direction if I’m moving in a

circle but at a constant speed I am accelerating you can tell that when

you turn in a car on the curve you saw your body sort of knows that the turn is

being made you’re being accelerated so Newton said that accelerations are due

to forces and for a given force the acceleration is less for a massive body

than for a low-mass body because after all acceleration equals force over m so

if the force is given then a large body is accelerated by that force less than a

small body so if I kick a small ball I can get it to really go hauling but if I

try to kick a truck you know it won’t really move very much because the mass

of the truck is so much bigger than that of the ball

the third law often known as the law that says for every action there is an

equal and opposite reaction well what what he was really saying was that when

two bodies interact they exert equal and opposite forces on each other the forces

come in pairs if I push on the wall its pushing back on me okay if I hop from

this step down toward the earth the earth is indeed pulling on me but I’m

pulling on the earth as well and my measly mass pulls on the earth just as

much as the earth pulled on me the forces are equal and opposite so then

why do I fall why doesn’t the earth come up toward me ah let’s go back to the

second law the Earth’s mass far exceeds my maths and so for a given force the

earth is accelerated much much less than I am but the forces are equal and

opposite a good example of this is in rocket propulsion when the fuel burns

and a jet of gas comes shooting out of the end it’s not that the gas is pushing

on the earth and that somehow it propels the rocket upward you can have a rocket

way out in outer space and the gas propels the rocket forward because the

gas going outward has to be balanced by a force on the rocket pushing it forward overall the system has no net forces

acting on it from outside but the internal forces have to be paired the

outward push of the gas has is balanced by the inward that is balanced by the

forward motion of the rocket these laws and the subsequent law of universal

gravitation unified many seemingly disparate areas of physics into one

simple unified whole and this is one of the great goals of science to explain a

lot of different phenomena through a small number of fundamental ideas Newton

went a long way in achieving that goal

Alex > Neil

Well I never, I didn’t know people wore a metal nose when they lost their own. 👍🍻🐒

Keep this series up!

Hey… how bout you also broadcast the silly 1950s series playing on the lower left.

To many big words flattards want understand

Very informative keep these types of videos up

Thank you for sharing

This is probably working off old information. It's now known that mercury poisoning was not the cause of death.

ARE YOU BLIND?