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?