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i got a comment on the video where we first introduced parallax - especially relative to stars - essentially

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asking how do we know that this angle and this angle are all the same, or how do we know that we are

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always looking at an isosceles triangle where this side is equal to this side? it worked out for this

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example that i drew right here, but what if the star was over here, what if the star was over here?

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then if you just look at it this way, if you take it at this point, the triangle is no longer (clearly)

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an isosceles triangle. it looks more like a scalene triangle, i guess, where all the sides are different.

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and so a lot of that trigonometry would not apply, because we would not be able to assume that this is

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a right triangle over here. and what i want to make clear is that that is true. you would not be able

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to pick these two points during the year, these two points in our orbit, 6 months apart, in order to

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do the same math that we did in the last video. in order to calculate this and still have an isosceles

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triangle, what you want to do is pick two different points, 6 months apart. so what you want to do is

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this is the sun, you want to pick two different points 6 months apart, where it DOES form an isosceles

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triangle. so if this is the distance from the sun to this other star right over here, you want to pick

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a point in the earth's orbit around the sun here and then another point in the orbit 6 months later,

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which would put us right over here. and if you do that, then we are, now all of a sudden, looking at

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two right triangles, if we pick those periods correctly. and the best way to think about

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whether this is a perpendicular angle is we are going to try to find the maximum parallax from the center,

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in each of these time periods.

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here it's going to be maximally shifted in one direction, and then when you go this 6 months later,

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it's going to be maximally shifted in the other direction.

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so the answer to that question, the observation is right, at exactly the middle of the summer, or the

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middle of the winter, all the stars will not form an isosceles triangle with the sun and the earth. but you can

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pick other points in time around the year, 6 months apart, where any star will form an isosceles triangle.

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hopefully you found that helpful.