alright so looks good people are picking me up okay so today we're gonna finish up the history of astronomy section here and again almost everything that I'm talking about it comes from Chapter three except for the very last person that we're going to talk about but I'll point that out when we get to it and up until this point in the history for a long long time for hundreds of years hundreds of years hundreds of years people thought that the earth was at the center of the solar system and then Copernicus came along not this is in Copernicus but we saw him last time Copernicus uh brought back well he came up with the heliocentric model not necessarily the very first person ever to come up with it but he was the one who brought it into the Renaissance right and he had the Sun in the center and all of the planets orbiting the Sun in perfect circles okay now after that after he published that people were not super thrilled about it so they tried to do a lot of work to try to prove him wrong and remember the last person that we talked about was this guy right here Kepler okay and that's who were gonna talk about first today because he took the best star charts that existed at the time and he helped to make them and he showed that they really matched up a lot more closely with Copernicus than the old wrong Earth centered idea so the solar system is heliocentric not geocentric but just like the ancient Greeks saw whenever you make better star charts you might find that the idea is not perfect and has to be tweaked a little bit so it turns out that what Copernicus said was mostly right but it wasn't perfectly right okay and so what Kepler did is he realized he could explain exactly how orbits work using only three laws all right and so that's what we're gonna be talking about right here well talk about Kepler's Three Laws of orbits okay Kepler's three laws of orbits now in your book these are probably called Kepler's three laws of planetary motion but it turns out Kepler didn't know this but these laws work for all orbits so they work for the moon around the around the Earth they work for satellites around the earth if I took your body and threw you into space you'd orbit around the earth using these same laws okay so real quick let me get this going let's talk about these laws so Kepler's first law oops it's coming there we go nope there we go okay here we go Kepler's first law and with these laws when I when we have them stated here don't worry if they don't make a lot of sense just from reading them we'll make them make sense so Kepler's three laws of orbits okay first law the orbit of each planet around the Sun is an ellipse with the Sun at one focus okay the orbit of each planet around the Sun is an ellipse with the Sun at one focus okay so let's work through this and figure out what everything is trying to say okay so check this out what is he changing first up does anybody know what an ellipse is do you guys know what this is does anybody know what an ellipse is it's uh it's a kind of shape what is it what basic kind of shape is an ellipse it's a easier less fancy word for it yeah it's an oval it's an oval right so one thing that Kepler is changing here is the shape of the orbit remember what shape did Copernicus say these orbits were perfect circles and Kepler's saying no it turns out the data says it's almost a circle but it's actually a little bit stretched out it's more shaped like an oval okay and I'll explain a little bit more about what that is right now actually okay so can any of you people out there any of you guys draw a perfect circle just freehand can any of you draw just a perfect free like if I asked you like right now to save your life you need to draw a perfect circle how many of you would survive that situation not that many of you right I would die too right I mean you saw my circles right here that's my circles right that's the best that I can do freehand but I could save all of our lives if I gave each one of you a thumbtack and a piece of string okay if you if you had a thumbtack and a piece of string every one of us could draw a perfect circle okay now how do you do that you might have done this in school at some point if you put the thumbtack in the paper and tie the string to the thumbtack and your pencil and pull it tight you could just swing it around and you draw a circle right now in that case if you drew a circle like that by swinging it around a thumbtack by swinging your pencil around a thumbtack don't overthink this where would the thumbtack be in the circle where exactly with the thumbtack be inside of that circle yeah it would be exactly at the center right so this is what I'm getting that right here if you put a thumbtack in your page tie it to your pencil pull it tight you're going to draw a perfect circle there and so that is how Copernicus thought the the orbits of the planets worked with the Sun right here at the thumbtack and then like your pencils kind of like a planet orbiting around the thumbtack and by the way this right here this distance from the center to the edge that's called a radius you probably learned about that in school at some point keep that in mind let's move on to a to an ellipse now if you want to draw a perfect ellipse it's going to be very similar to drawing a perfect circle the only difference is instead of having one thumbtack you're gonna have two thumbtacks okay two thumbtacks so let's say instead of putting a thumbtack here you put one thumbtack here and one thumbtack here so there's got two thumbtacks okay and instead of just tying your pencil to one of them you tie your pencil in a triangle around both of them okay so like your pencils tie it around your two thumbtacks making a triangle of string now if you pulled that tight and drew a shape around both thumbtacks because the two thumbtacks are spread out they're gonna stretch your shape out so instead of drawing a perfect circle instead you're gonna end up drawing an oval right so instead of this you're gonna get this don't worry about all the words all over it right now but yeah so instead of again instead of this with one thumbtack with two thumbtacks you're gonna get an ellipse okay so Kepler is saying that the shape of the orbits are actually stretched out a little bit like this so the orbits are not perfect circles he's changed the shape all right and now these thumbtacks they're not at the center anymore they're not at the center they're off to the sides at two places that they're that are each called a focus okay so these two places right here here and here to either side of the center inside of the of the oval are each called a focus and the reason I'm pointing that out is that if we go back to the the first law Kepler's saying that the Sun is at one focus so according to Kepler is the Sun perfectly at the center of the orbits of the planets is the Sun perfectly at the center of the Earth's orbit yes or no according to Kepler here no so basically the planets are orbiting the Sun but because the orbits of the planets are a little bit stretched out the Sun is not perfectly at the center and that's what Kepler's law is saying right here oh and by the way I should say Kepler's laws are correct okay so we finally at this point we're getting to stuff that we still use when we put astronauts into orbits we use Kepler's laws to make sure they stay alive okay so this is true the Sun is not perfectly at the center okay so right here if the Sun is right there let's say it's at this focus imagine the sun's right there a planet would sweep around this orbit okay now check this out check this out um excuse me uh with that in mind does a planet always stay the exact same distance away from the Sun okay does they plan it always keep the exact same distance away from the Sun no so some points during the year we're closer to the Sun and some points during the year we're further away from the Sun by the way the law didn't say anything about the other focus so it turns out that there's nothing at the other focus okay so the Sun is at one focus and there's nothing at the other one so the planet will be closer to the to the Sun sometimes and farther away at other times okay now there's a couple of other little things I need to mention here before we move on to law number two there's one important term in this picture other than focus and that is this distance right here it's called the semi-major axis okay it's called the semi-major axis and that distance is this distance right here okay it starts at the center goes through one focus and then goes all the way to the edge of the ellipse so this is the semi-major axis right here from the center through one of the focuses to the edge okay why is that particular distance important it turns out just like you guys said since the planet doesn't always have to or doesn't always stay the exact same distance from the Sun sometimes it's small and sometimes it's large in order to talk about the size of an orbit we usually just say the average distance between a planet and the Sun okay because sometimes it's small sometimes it's large but the average would be somewhere in between it turns out with the way that ellipses work the semi-major axis right here so this distance right there is mathematically exactly the the average distance for that planet so if you took all of the possible distances a planet could have and average them up the semi-major axis is the average distance that a planet is away from the Sun okay and because that's so important again if we want to talk about how big an orbit is we just say how big the semi-major axis is okay and by the way it's important enough that it's represented with just a lowercase a so anytime you see just a lowercase a that's the semi-major axis okay now all right a couple more things I need to say are all ellipses are all ovals are all ellipses this exact shape no okay all ellipses are not this exact shape okay some are more stretched out and some are more circular right so let me just show you a picture of a few of them right here here we go here's three ellipses one two three and you can see as you go down the page you get more stretched out if you want to talk about how stretch out and orbit is you mention it's s intricity okay right there an S in the essent Rissa T is how stretched out in orbit is okay so if you want to say how big an orbit is you talk about its semi-major axis or average distance from the Sun but if you want to talk about how stretched out that orbit is it's the essent Rissa T the higher the centricity the more stretched out the orbit is okay and check this out check this out here we go s intricity is always a number between zero and one so a number closer to zero looks closer to this shape and a number closer to one would be even more stretched out than this okay so here's my first question what do you notice about this ellipse what do you notice about this with s intricity zero what's going on with this guy what what is this right here what's that guy yeah that's a circle okay so that circle right there is an ellipse all right a perfect circle is an ellipse it's just a special case it's the least stretched ellipse so that means Copernicus wasn't way off he just had the wrong s centricity okay so where are the FO side on this circle where are the foci where are the focuses technically you're not supposed to say focuses to focuses are called fossa when you talk about them together that's the plural but where are the folks I for this thing they're in the middle there's two of them but they're on top of each other that's why it looks like there's one so if you see here as the circle gets more stretched out as the ellipse gets more stretched out the foci go farther and farther apart so the more stretched out your orbit is the further away from the center of the orbit the Sun is okay so here's the last thing about law number one if we look here Copernicus thought it was this Kepler's saying it's actually a not a perfect circle are the orbits of the planets in our solar system closer to an S intricity of zero or closer to an S intricity of one so are we more shaped close it we are in a lip so we're not perfectly this but are we close to this or are we close to one yeah keep in mind remember when when Copernicus looked at the data he mistakenly thought the orbits were this so if the orbits were actually super stretched out like this nobody would look at orbit like this and think they were seeing a circle right so it turns out that in order to mistake it as a circle the S intricity must be pretty close to zero okay so sometimes orbits are drawn really stretched out like this but they're actually so close to being a perfect circle with an essence that's why you can get away with drawing them as circles and and nobody really bats an eye at it okay so the essen tricity of the planets is close to this there are things in our solar system with orbits really stretched out like this okay but our planet definitely isn't like that a thing that would have an orbit like let me know what kind of things have orbits really stretched out like this and probably not it's comet's comets have orbits that are super stretched out like this and that's actually what makes comments look the way they do we'll talk more about that later now check this out okay so that's law number one what did Kepler change in law number one he changed the orbits from circles to ellipses and he changed the location of the Sun from the center to a focus a little bit off to the side boom all right law number two oh actually before we move on to one number two there is one last thing I want to say okay here's a picture of an of a planet going around the Sun there's special names for the place on the orbit that's absolutely the closest place on the orbit and the place on the orbit that's absolutely farthest from the Sun as well okay so right here perihelion is what we called the absolute close place on the orbit ok perihelion is the closest place on the orbit to the Sun and aphelion not aphelion but aphelion is the place farthest from the Sun so does anybody remember what what is he Leon probably mean what is he Leo right here mean what's he Leo what's that is stand for right there the Sun that's right Helio stands for the Sun so in this case aphelion just means far from the Sun and perihelion just means close to the Sun ok