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Stellar parallax clarification
Stellar Parallax Clarification. Created by Sal Khan.
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Correct me if I'm wrong, but why does this have to be an isosceles triangle?
Can't you just measure the offset angle of the star based on the position of the sun, then in six months, do it again to form (logically) one big triangle? Which you could then use the knowledge of the two degrees to figure out the third and then use trigonometry to figure out the distance that way? I think that would be a lot easier than first trying to figure out how to line it up at a 90deg angle from the sun.(19 votes)
You are correct, it would work, but the measurements with an isosceles triangle are relatively easy because two of the sides are the same length.(5 votes)
- I'm curious as to how an astronomer would track an individual star or object throughout the year to make that decision of maximum parallax. How does one identify a specific star to study from night to night when, at least to the layman, the vast majority of them seem very similar? Is there some way to "fingerprint" an individual star?(10 votes)
There are several ways to fingerprint a star, the first one is the relative position to the other farther away stars in the field. You could produce a diagram of the nearby stars and use it to approximate the displacement of the star you are looking at. Another hint is the relative magnitudes of the stars around. Yet another fingerprint is the spectrum, or the relation between colors among the stars, for example spectral lines which yield information about temperature and composition. Say for example your star is red and very bright you could notice a very bright star in the same field of view but displaced.(5 votes)
when dealing with such huge distances i'm curious how we know that we are at a right angle. and when finding the parallax of the star the example was 1.something arc seconds. what if the star is above the plane of our orbit? even just a minuscule amount like 1 or 2 arc seconds?(8 votes)
If one could observe, measure and record the same star everyday for a year, comparing the dates to greatest readings farthest apart should give you all you need to find your starting points for measuring the angles.(7 votes)
Is there any way we know where exactly we are in orbit at the time when this triangle becomes isosceles? I'm pretty sure they have some pretty crazy technology now to allow us to know these kinds of things, I was just wondering...(5 votes)
Check the date and you will know where we are in our orbit.(4 votes)
The sun's rays are refracted by the earth's atmosphere, so we don't see the sun rise and set on the horizon exactly when our position on the earth rotates into and out of the direct rays of sunlight. Given that the angle we are measuring is so small, doesn't the fact that we are not facing exactly where we think we are in relation to the base of the triangle established by the visible sun when it rises and sets on the horizon introduce an inaccuracy into this minuscule angular measurement?(6 votes)- Whether or not we are facing exactly where we think we should has no bearing on the accuracy of the measurement.(3 votes)
i don't get it. you're saying that every star out there can form an isosceles triangle? how is that possible?(3 votes)
Sure. Try drawing it. The earth goes around the sun. For every star, there is a triangle that has two corners somewhere in earth's orbit, and one corner at the star.(6 votes)
What if the star is moving away?(4 votes)- That is an excellent question, that is called radial velocity and it also gets measured as another component of the velocity. That one does not affect parallax but can be seen in the star spectra.(3 votes)
Could you not use the Law of Sines to figure out the dimensions of the scalene triangle? The distance of the base would be 2 AU, and you would already have the three angles of the triangle from your measurements. Then it would just take a little bit of trig to determine the rest of the side lengths.(4 votes)- I am just wandering where the value for the total change in angle, 1.5374 arcsecs came from. Is it a known value for the closest star to us or something else?(2 votes)
Yes, it is already measured by the scientists and there he uses it as a 'data given' to continue the calculation.(3 votes)
- Stars are only visible for half the year right? Would't the maximum shift be beyond the horizon? I feel like there is an important point regarding the "right at sunset/sunrise" and being offset in the W/E directions that I am missing. Can anyone help fill me in?(3 votes)
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.