Parallax in observing stars

what I want to do in this video is explain what parallax what parallax actually is and then try to visualize what the parallax would be like in the context of observing relatively nearby stars and then in the next video we're going to think about how we can use the parallax of nearby stars to figure out how far they actually are away from us so parallax really is just the apparent change in position of something based on a different line of sight so when you see that if you just look at if you just while you're looking at out of the car you're going to see that depending on how far different things are from you it looks like they're moving relative to each other right now I'm looking at my computer monitor and if I move my head around or shake my head around it looks like the wall behind the computer monitor is moving relative to the computer monitor we've all experienced this but let's think about what parallax means when looking at stars so let me draw let me draw the Sun here and obviously none of this is drawn to scale so let me draw the Sun here and let me draw the earth at some point in its orbit around the Sun and we're going to pretend like we're looking from above the solar system so the earth will be rotating the earth will be rotating in this direction right over here and let's say the star that we care about the star that we care about is right over here the star that we care about is right over here obviously not clearly not draw on the scale and what we're going to do is we're going to wait to the point in the year so the point in our orbit around the Earth so that right at dawn so we're sitting right here on the surface of the earth and just to simplify things we're on the equator and let's say that this is the Stars roughly in the plane of our solar system so we're sitting right here we're sitting right here on the equator and then right at dawn right when the first light of the Sun right when the first light of the Sun begins to reach me remember right now the Sun is lighting up this side of the earth so right when the first light of the Sun is reaching me I'm looking I'm looking straight up so if I look straight up right when the first light of the Sun is reaching me and I look straight up I look straight up like that I will be looking in that direction now so let's say that that direction that I'm looking at is this direction right over here so let's say this and then let me make it clear this is a separate part of the diagram here this isn't the diagram of the maybe I should do it maybe I'll do it over here so if I'm looking at if the night sky looks like this the night sky looks like this the Sun is just beginning to rise on the horizon if I look straight up if I look straight up I'm looking in this direction so where would this star be relative to straight up well straight ups going to be like that the Sun is right if the Sun is right the way I drew it right here right to my left straight up is just like that the Sun is just coming over the horizon this star right here the apparent position of this star relative to straight up is going to be at some angle at some angle to the left of straight up it's going to be right over there and obviously the star won't be that big relative to your entire field of vision but you get the idea maybe I'll draw it a little bit smaller than light by just like that so there's going to be some angle here and this angle whatever it is I don't know let's just call it let's just call it theta that's going to be the same angle as this and when I talk about the angle I'm talking about if you measure from a one side of the horizon to the other side of the horizon you're essentially looking around halfway around the earth that would be 180 degrees so you could literally measure what this angle is right over here now let's say we waited six months six months what's going to happen six months we're going to be on this side of the we're going to be on this side of the Sun our distance we're assuming that our distance is relatively constant at one astronomical unit now what happens if we wait remember the Sun the earth is rotating the earth is rotating like this so if we wait right at sunset right when the last glimpse of the Sun has just gone away because you can remember right now right now the Sun is illuminating this side of the earth the Sun is going to be illuminating that's how the earth so if we're sitting right at the equator right over there right when the Sun is just setting we look straight up right when the Sun is just setting we look straight up let me do that in the same color we look the straight up so six months later when we look straight up where is the star relative to straight up well now the star will be to the right it'll be in the direction so let me be and this is our field of vision if this is our field of vision six months later now the Sun is setting now the Sun is setting all the way to the right on the right horizon and if we look straight up this star now this star now is going to be to the right is going to be to the right of straight up so what just happened here well it looks like relative to straight up and where we're looking at the exact kind of position of the earth looking we're looking in the same straight we're making sure that we're picking times of years and times a day we're straight up is is the same direction we're looking in the same direction of the universe it looks like the position of that star has actually shifted and if this was let's say that this is let's say this is the middle of summer and that this is the middle of winter doesn't have to be it could be any other two points in time six months apart then when we look at the this star in the summer it's going to be over here summer it's going to be right over there when we look at the star in the winter it is going to be over here and in general for any star especially stars that are in the same plane as the solar system you can find two points in the year where that star is that I'm kind of a maximum distance from center and those are the two distances those are the two times of year that you'll want to care the most about because it'll be most interesting to measure this angle and I want to be clear this angle here is going to be the same thing it's going to be the same thing as this angle there you can see it's symmetric this way I mean this is a whatever this angle is going to be and you could look at this this is kind of a this is an equilateral triangle now sorry this is this is an isosceles triangle whatever whatever this distance is from here to here is going to be the same as this distance from here to here and so this angle is going to be equal to that angle and that angles to be equal to that angle what I want to do in the next video is think about if we're able to precisely measure these angles either one of them or both of them and let me be clear if this angle in the night sky is Theta and this angle right here is Theta the difference over here is two theta so one option if you want to kind of make sure that your numbers reasonably good you can measure just the total difference that it is around the center and then divide by two but in the next video what I do is if you are able to measure the change in a parent or the apparent change in angle here if you were to if you were to be able to measure that how would you be able to use that information to actually figure out the distance to this star