Stellar parallax clarification | Grade 11 | Physics | NCERT | Khan Academy (IN accent)

Added: 2026-06-03

[00:00:00]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 always the same or how do we know that we're always looking at an isosles triangle where this side is equal to this side. It worked out for the example I drew. But what if the star were over here or over here?

[00:00:24]Then if you draw the triangle at those same two points in the year, it's clearly no longer an isoclesles triangle. It looks more like a scaline triangle where all the sides are different. And in that case, the trigonometry we used wouldn't apply directly because we wouldn't have a nice right triangle. And that observation is absolutely correct. If you pick the same two calendar dates, say the middle of summer and the middle of winter, not every star will produce an isoclesles triangle with those exact positions.

[00:00:54]The key idea is this.

[00:00:57]You don't have to use those specific two dates. Instead, for any given star, you choose two points in Earth's orbit that are 6 months apart. And that maximize the apparent shift of the star from its central position. So if this is the sun and this is the distant star, you want to choose one position of Earth here and then 6 months later, Earth will be on the opposite side of its orbit over here.

[00:01:22]If you choose those two positions correctly, then the line from the sun to the star forms the symmetry axis between the two earth positions. In that case, the triangle formed by earth at position 1, earth 6 months later. The star is an isosles triangle. At those two positions, the apparent angular shift of the star is at a maximum in one direction at the first position and at a maximum in the opposite direction 6 months later.

[00:01:53]That's the important idea. You don't measure on arbitrary dates. You measure at the two points where the parallax displacement is maximized.

[00:02:02]When you do that, the geometry becomes symmetric again and the same right triangle trigonometry applies. So the comment was correct in noticing that not every pair of dates produces an isoclesles triangle.

[00:02:15]But for any star, you can always find two points in Earth's orbit 6 months apart that do produce that symmetric setup. And that's what makes the parallax method work.