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Current time:0:00Total duration:2:22

I got a comment on the
video where we first introduced parallax,
especially relative to stars. Essentially asking,
how do we know that this angle and this
angle is always the same? Or how do we know
that we're always looking at an isosceles
triangle, where this side is equal to this side? It worked out for this example
that I drew right here. But what if the
star was over here? What if the star was over here. Then if you just
look at it this way. If you take at this point,
the triangle is no longer, it's clearly no longer,
an isosceles triangle. It looks more like a
scalene triangle, I guess, where all of the
sides are different. And so a lot of that
trigonometry won't apply. Because we won't be
able to assume that this is a right
triangle over here. And what I want to make
clear is that that is true. You would not be able
to pick these two points during the year. These two points in our
orbit six months apart, in order to do the same math
that we did in the last video. In order to calculate
this and still have an isosceles triangle,
what you want to do is pick two different
points six months apart. So you want to do is if
this is the sun, you want to pick two different
points six months apart, where it does form an
isosceles triangle. So if this is the distance
from the sun to this other star right over here,
you want to pick a point in Earth's orbit
around the sun here. And then another point in
the orbit six months later, which would put us
right over here. And if you do that, then we
are, now all of a sudden, we are looking at
two right triangles, if we pick those
periods correctly. And the best way to think about
whether this is a perpendicular angle, is you're going to try
to find the maximum parallax from center in each
of these time periods. Here it's going to be maximally
shifted in one direction. And then when you go to
this six months later, it's going to be maximally
shifted in the other direction. So to answer that question,
the observation is right. At exactly the middle of
summer in the middle of winter, all stars will not form
an isosceles triangle with the sun and the earth. But you could pick
other points in time around the year six
months apart where any star will form an
isosceles triangle. Hopefully you
found that helpful.