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 are all the same, or how do we know that we are
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 it at this point, the triangle is no longer (clearly)
an isosceles triangle. it looks more like a scalene triangle, i guess, where all the sides are different.
and so a lot of that trigonometry would not apply, because we would not 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, 6 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, 6 months apart. so what you want to do is
this is the sun, you want to pick two different points 6 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 the earth's orbit around the sun here and then another point in the orbit 6 months later,
which would put us right over here. and if you do that, then we are, now all of a sudden, 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 we are going to try to find the maximum parallax from the center,
in each of these time periods.
here it's going to be maximally shifted in one direction, and then when you go this 6 months later,
it's going to be maximally shifted in the other direction.
so the answer to that question, the observation is right, at exactly the middle of the summer, or the
middle of the winter, all the stars will not form an isosceles triangle with the sun and the earth. but you can
pick other points in time around the year, 6 months apart, where any star will form an isosceles triangle.
hopefully you found that helpful.

Stellar Parallax Clarification

Stellar Parallax Clarification