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Video transcript
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.