Parallax in observing stars

What I want to do in this video is explain 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, while you're looking out at a 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 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 in this direction right over here. And let's say the star that we care about is right over here. Obviously, clearly not drawn to 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 to simplify things, we're on the equator. And let's say that this star is roughly in the plane of our solar system. So we're sitting right here on the equator. And then right at dawn, 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 straight up. So if I look straight up right when the first light of the sun is reaching me, and 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. And then let me make it clear, this is a separate part of the diagram here. Maybe I'll do it over here. So if the night sky looks like this, the sun is just beginning to rise on the horizon. If I look straight up, I'm looking in this direction. So where would this star be relative to straight up? Well, straight up is going to be like that. The sun is, 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 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, just like that. So there's going to be some angle here. And this angle, whatever it is, 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 one side of the horizon to the other side of the horizon, you're essentially looking 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. What's going to happen? Six months, we're going to be on this side of the sun. We're assuming that our distance is relatively constant at one astronomical unit. Now what happens? Remember, 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, the sun is illuminating this side of the earth. The sun is going to be illuminating that side of 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. Let me do that in the same color. We look 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 if this is our field of vision six months later, now the sun is setting all the way to the right, on the right horizon. And if we look straight up, this star now is going to be to the right of straight up. So what just happened here? Well, it looks like relative to straight up-- and we're looking at the exact kind of position of the earth. We're making sure that we're picking times of year and times of day where straight up 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 let's say that 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 this star in the summer, it's going to be over here. Summer, it's going to be right over there. And 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 at a 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 as this angle there. You can see it's symmetric this way. Whatever this angle is going to be, and you could look at this. This is an isosceles triangle. 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 angle is going 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 number's reasonably good, you could measure just the total difference that it is around the center and then divide by two. But in the next video, what I want to do is if you are able to measure the apparent change in angle here, 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?