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CHAPTER 3 COPERNICAN REVOLUTION 

hello and welcome to general astronomy lecture number three the Copernican revolution before we begin let's just take a look at this image this is an image of many many stars several thousand stars at least and very impressive in image of a dense region of stars but it makes this even more impressive is where that picture came from that entire image came from the point right here at the tip of the arrow all of those stars those many thousands of stars all that is within this tiny speck right here so just another image to give you some perspective on things that we are not quite alone in this vast universe at least with our stars I'm sure we'll find the life soon anyway back to the Copernican Revolution the Greeks and other ancient peoples developed many important scientific ideas but we now think of as science arose during the European Renaissance within half a century after the fall of Constantinople in 1453 polish scientist nicholas copernicus began the work that ultimately overturned the earth-centered Ptolemaic model also known as the geocentric model nicholas copernicus was born in torun poland on february 19 to 1473 his family was wealthy and he received an education in mathematics medicine and law he began studying astronomy though in his late teens by that time tables of planetary motion based on the Ptolemaic model had been noticeably inaccurate but few people were willing to undertake the difficult calculations required to revise those tables and his quest for a better better way to predict planetary positions Copernicus decided to try aristocracies Sun centered idea first proposed more than 1700 years earlier he had read a varistor Chris's work and recognized that much that recognized a much simpler explanation for apparent retrograde motion that backwards motion of planets in the sky was offered by a sun-centered system but he went far beyond aristocracy and working out mathematical details of the model through this process Copernicus discovered simple geometric relationships that allowed him to calculate each planets orbital period around the Sun as well as its relative distance from the Sun in terms of the Earth's on distance which we call the astronomical unit today the models success in providing a geometric layout for the solar system convinced him that the sun-centered model must be correct despite his own confidence in the model Copernicus was hesitant to publish his work during that his suggestion that the earth moved would be considered absurd however he discussed his system with other scholars including high-ranking officials of the Catholic Church who urged him to publish a book Copernicus saw the first printed copy of his book which translates to concerning the revolutions of the heavenly spheres on the day that he died May 24 1543 publication of the book spread the sun-centered idea widely and many scholars were drawn to his it's aesthetic advantages nevertheless the Copernican model gained relatively few converts over the next 50 years and for a good reason it didn't work that well the primary problem was that Copernicus had been what had been willing I'm sorry the primary problem was that while Copernicus had been willing to overturn Earth's central place in the cosmos he still held fast to the idea of the that the ancient peoples had that the heavenly motions must occur in perfect circles so he went past the idea of us being the center of everything but we still were thinking of perfect circles this isn't an incorrect assumption forced this incorrect assumption forced him to add numerous complexities to a system and complete including those circles upon circles much like those used by Ptolemy to get it to make decent predictions in the end his complete model was no more accurate and no less complex than the tool egg model and few people were willing to throw a thousands of years of tradition for a new model that works just as poorly as the old one so he was right in making the Sun the center of our solar system but still using perfect circles which we know today is not the case it added so many complexities that it really didn't make the model any better so imagine riding on a fast race horse as you pass a slowly walking pedestrian nearby he appears to move backwards relative to you even though he's still traveling in the same direction as you in your horse this sort of simple observation inspired aristocracy to formulate the heliocentric model in which all the planets including earth revolved around the Sun different planets take different lengths of time to complete in orbit so from time to time one planet will overtake another just as a fast-moving horse overtakes a person on foot when earth overtakes Mars for example Mars appears to move backward in the sky and that's what we call a retrograde motion so this figure here tries to explain that planets move at different speeds so here you'll see whatever it is this is Earth's orbit on the inside Mars is on the outside what happens is the earth actually catches up to Mars and then it starts to move faster and past Mars up so as we're passing Mars it appears to us to move backwards in the sky so you can see this tracing out one two three but then four five and six are moving backwards four continuing back to a west to east motion so this perfectly explains retrograde motion now not that whole circle on a circle thing we have the epicycles and the deference but we have this idea now that planets move at different speeds and overtake one another and that is the reason that we have retrograde motion so here's our first concept track you'll see these once in a while throughout our lectures what I'll do is ask you the question and then I'll pause for a couple seconds where you can pause the video and think about this and then whenever you're ready you can return and hear my so the first question we have in the heliocentric model could an imaginary observer on the surface of the Sun look out and see planets moving in this retrograde motion so in just a second when I say to pause the video think about it and then come back when you're ready so pause the video No all right so the answer is no a planet only appears to move in that backward retrograde motion if seen from another planet if the two planets were to move at different speeds and past one another an imaginary observer on the stationary Sun would only see planets moving in the same direction as they orbit the Sun so you wouldn't get retrograde motion so that should be the answer there we go okay Copernicus realized that because Mercury and Venus are always observed fairly near the Sun in the sky their orbits must be smaller than the Earth's planets in such orbits are called inferior planets and by the way we're going to go through lots of definitions here but you'll soon see a slide with an image showing all these things so for now you know try to follow along with the definitions but the image will be coming soon to help out and you can go back and forth between them if you need so all those planets since the smaller orbits to us are called inferior planets the other the other the other visible planets that being Mars Jupiter and Saturn are sometimes seen on the side of the celestial sphere opposite to the Sun when this happens earth must lie between the Sun and these planets and Copernicus concluded that the orbits of Mars Jupiter and Saturn must be larger than Earth orbit so these planets are called superior planets so we're going to go through a bunch of definitions now so let's see here when mercury or Venus is visible after sunset it is near what we call greatest Eastern elongation where elongation is the angle between the Sun and a planet is read from Earth so greatest Eastern elongation is when mercury or Venus is visible after sunset and its position is as far east of the Sun as possible so in this case it would appear above the western horizon after sunset and we would all often call it an evening the evening star as a result excuse me then we have greatest Western elongation the same idea at greatest Western elongation mercury or Venus is as far west of the Sun as it could possibly be it done rises before the Sun gracing the pre-dawn skies as a morning star in the east when mercury or Venus is at what we call inferior conjunction it is between us and the Sun so it's inferior planet so it's a planet with an orbit lower or smaller than ours so it's an inferior conjunction when it is between us and the Sun and it moves from the evening sky into the morning sky over weeks to months at superior conjunction a planet is on the opposite side of the Sun so it's moving back into the evening sky so inferior conjunction was one appliance between us and the Sun and then superior conjunction is when a planet is on the opposite side of the Sun to us a superior planet such as Mars whose orbit is larger than the Earth's is best seen in the night sky when is that what we call opposition at this point it is it in it I'm sorry at this point in its orbit the planet is in the part of the sky opposite the Sun and is highest in the sky at midnight this is also when the planet appears brightest because it is closest to us and one more I believe but when a superior planet like Mars is located behind the Sun at conjunction it is above the horizon during the daytime and thus is not well placed for nighttime viewing so these are all different terms that we give to locations of planets in our sky so here is the image I was talking about it is dense and all of those definitions are in here but it's a very good reference and you will need to know these things I can guarantee that so the heliocentric model explains why planets appear in different parts of the sky and different dates when and where in the sky a planet can be seen from Earth depends on the size of its orbit and its location on that orbit the inferior planets cycle between being visible on the west after sunset and in the east before sunrise so here's that image showing you all these different locations so conjunction happens whenever a planet is either if it's inferior between us and the Sun or superior on the opposite side of the Sun you have the greatest eastern and western elongations which is the farthest to the east or west that the planet will be relative to us in the Sun so you can see it makes have an angle here it will never be at a greater angle than this right it's either moving over here where it'll be a smaller angle or if you come down here it's also a smaller angle so that's the greatest elongation I mean that opposition is just when a planet is behind us relative to the Sun and this is when it rises or when it's viewed overhead at midnight and it's the best time to view it because it's closest to us right it's way closer here than a desire anywhere else in the orbit so that's a lot of terms to throw at you in the beginning here so again just just review the slides with the terms and then compare them to this image and you should have at least a basic idea of how this will work so let's look at our next concept check how many times is Mars at inferior conjunction during one orbit around the Sun so go back take a look at what inferior conjunction means take a look at that image and try to figure out how many times it would be at that configuration as it goes around the Sun once so pause the video now and come back when you're ready alright Mars has an orbit around the Sun that is larger than the Earth's orbit so as a result Mars never moves to a position between the Earth and the Sun so Mars is never at inferior conjunction alright so Copernicus found correspondence between the time a planet takes to complete one orbit that is its period so we call period at the time it takes to complete an orbit and the size of the orbit so now we're starting to finally put some mass into this and get some numbers out so there is a relationship between the size of the orbit and the time it takes to complete set orbit so determining this period of a planet that it takes to sorry there's a lot of stuff going on outside determining the period of a planet takes some care because Earth from which we must make the observations is also moving realizing this Copernicus was careful to distinguish between two different periods of each planet the synodic period is the time that elapses between two successive identical configurations as seen from Earth for example from one opposition to the next or from one conjunction to the next so synodic period is just the time between two equal configurations however the sidereal period is the true orbital period of a planet so the actual time that it takes for an planet to orbit the Sun so that is our sidereal period and so this table here just shows you the different periods for each planet from Mercury to Neptune and there's some interesting trends that we'll start to get into first you'll notice the true time sidereal period on the rate increases more and more as you go further out so there's that relationship between size of an orbits and how long it takes the synodic period is a bit different so we'll look into that in a bit so here is another concept check why is it that Jupiter sidereal period is longer than its synodic period so this is a tough one so think about this for a moment but I'll give you the answer in just a moment so pause the video and reference those slides so the question says why is Jupiter's sidereal period longer than its notic period so let's go back so here we see Cenac period is much lower than its side Ariel period right so why is that well Jupiter moves slowly and does not move very far in the time it takes for earth to pass jupiter by moving around the Sun and pass it again giving Jupiter a sonata period similar to the Earth's orbital period of one year however slow moving Jupiter takes more than a decade to move around the Sun back to its original position giving it a very large sidereal period so it takes a decade to go all the way around the Sun but relative to us because we move around the Sun so fast we come back to that position where we were pretty quickly so it has a really low synodic period so this stuff is a little bit tough to grasp I can't spend an entire lecture talking about it but you know review this stuff practice it a little bit I believe your book covers it even more so review it if you need to find a relationship between the sidereal period of a planet and the size of its orbit Copernicus still had to determine the relative distances of the planets from the Sun so we needed a distance measure well he devised a straightforward geometric method of determining the relative distances of the planets from the Sun using trigonometry his answers turned out to be remarkably close to modern values the distances are given in terms of astronomical units here on this table which is the average distance from Earth to the Sun however Copernicus did not know the precise value of the distance so he can only determine the relative sizes of the orbits of the planets so here you can see how remarkably close Copernicus was way back in the day I mean he's off by a 1/100 of an astronomical unit and of course as you get further away it's a little bit harder to measure but still I mean within great accuracy all things considered and notes we weren't able to see Uranus and Neptune back then so there's no values for that yet but remarkable accuracy for just using a bit of trigonometry to figure out the sizes of these orbits it's insane okay by comparing these two tables that I've shown you you can see the unifying relationship between planets orbits in the Copernican model the farther out a planet is from the Sun the longer it takes to travel around it in its orbit that is the longer its sidereal period right so I showed you that before so you can see here that the further auto planet is right there you're moving from Mercury to Neptune you're moving further away from the Sun well it takes longer and longer to go around the Sun it seems pretty obvious to us today but this is the first time it was ever noticed so this is for two reasons one the large larger the orbits the farther a planet must travel to complete its orbit right makes sense you have a greater distance to cover so it's going to take more time but also the larger the orbit the slower our planet moves so not only is it more distance to cover but it's also moving more slowly so for example mercury with its small orbits moves at an average speed of 47.9 kilometers a second or a hundred and seven thousand miles per hour but Saturn which is much further away travels around its large orbit much more slowly at an average speed of nine point six four climbers per second or twenty one point six thousand miles per hour the older Ptolemaic model offers no such simple relationships between the motions of different planets so this is the first time now that we're having some accuracy between the motions of planets is so what we'll do now is just continue a little bit further with some of the important people that led to these discoveries as well and we're taking it one step further through this Copernican revolution next up is Tico part of the difficulty faded faced by astronomers who sought to improve either the Ptolemaic or the Copernican system was a lack of quality data better data were provided by the Danish nobleman at Tikal Braja Seco became interested in astronomy as a young boy but his family discouraged this interest he therefore kept his passions secrets learning the constellations from a miniature model of a celestial sphere that he kept hidden in his home as he grew older Tikal was often arrogant about both his noble birth and his intellectual abilities at age 20 he fought a duel with another student over which of them was the better mathematician part of Tico's nose was cut off and he designed a replacement piece made of silver and gold in 1563 Tico decided to observe a widely anticipated alignment of Jupiter and Saturn to his surprise the alignment occurred nearly two days later than the date Copernicus had predicted resolving to improve the state of astronomical predictions he set about compiling careful observations of stellar and planetary positions in the sky Tico's fame grew after he observed what he called a nova meaning new star in 1572 by measuring its parallax and comparing it to the parallax of the moon he proved that the Nova was much farther away than the moon today we know that he saw a supernova the explosion of a distant star so parallax is a phenomenon in which the apparent position of an object changes because of the motion of the observer so this is something you can actually test out yourself so here's an example of this if we're on one side of the earth here on the left and we look at a nearby object well if you look at that object compared to the background it looks like it's somewhere over here in the sky but 12 hours later when we're on the other side of the earth and we look at that same nearby object well now it's going to look like it's to the left in the background stars so this apparent motion of an object is because of us moving is known as parallax so it hasn't actually moved necessarily we just have and we see it in a different location and you can actually test this out just by holding your hand in front of your face just hold your finger right in front of your face very close and look at it with one eye closed and then switch your eyes so close the other one and go back and forth quickly you look crazy doing it but your finger moves back and forth relative to the background objects in your room so that is an effect of parallax and that's exactly what we're talking about here so king frederick ii of denmark decided to sponsor Tico's ongoing work providing him with money to build an unparalleled observatory for naked eye observations over a period of three decades Tico and his assistants compiled naked eye observations accurate to within less than 1 arcminute so that's less than the thickness of a fingernail viewed at arm's length so if you hold the arm all the way out and look at the thickness of your nail that's how accurate his observations were just from naked eye observations no telescopes or anything because the telescope was invented shortly after his death Tico's data remains the best set of naked eye observations ever made despite the quality of his observations however Tico never succeeded in coming up with a satisfying explanation for these planetary motions all right so that's a good cutoff point from here I think we'll continue our discussion in our next lecture so thanks for watching and I'll see you there.