What is the furthest star or celestial object whose distance has been calculated with parallax and how does it compare to the theoretical limit using today's telescopes? And how exactly does telescope aperture relate to the maximum distance measurable (other than the bigger the aperture the bigger the distance)?
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Your first question is a dupe of What's the farthest object as determined only by parallax?. – pela May 01 '19 at 10:50
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The question is primarily about the technical limitations of that method and the theoretical limit - I hope that's enough of a difference for it not to be considered a dupe. – technical_difficulty May 01 '19 at 10:52
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1Unclear what you mean. The best parallax precisions are discussed in answers to that question. There is no obvious "theoretical limit" to how accurately you can measure the position of an object, only technical and engineering limits that are continually being improved. We are already beyond limits where the bending of light by GR by the Sun and solar system objects must be taken account of. – ProfRob May 01 '19 at 16:43
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See also https://astronomy.stackexchange.com/questions/332/how-does-angular-resolution-of-a-telescope-translate-to-its-parallax-precision?rq=1 – ProfRob May 01 '19 at 16:46
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1FWIW, we don't even have a very accurate distance measurement for the well-known and relatively nearby star Betelgeuse, which has parallax of around 4.51 ± 0.80 milliarc-seconds. – PM 2Ring May 26 '20 at 15:06
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1@PM2Ring That is because it is too bright. – ProfRob May 26 '20 at 16:10
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1@Rob True, and its variable brightness doesn't help either. – PM 2Ring May 26 '20 at 16:22
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@PM2Ring I've just asked What will it finally take to accurately measure the distance to Betelgeuse? – uhoh May 27 '20 at 02:58
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@RobJeffries ditto – uhoh May 27 '20 at 02:58
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Quick Google reveals a couple simple analyses. For example,
The Andromeda Galaxy, M31, is the nearest major galaxy to the Milky Way. The distance to M31 has been measured using other techniques to be 2.5⋅10^6 light years , or 7.6⋅10^5 parsecs. Using the slightly modified parallax formula, we can find the necessary parallax angle to measure the distance to Andromeda. $ p = \frac{1}{d} = > \frac{1}{7.6*10^5} parsec = 1.3 *10^{-6} arc-seconds $
This is an incredibly small angle. For comparison, the resolution of the Hubble Space Telescope is 0.05 arc-seconds, so even Hubble would not be able to detect the necessary angular shift of the nearest galaxy to effectively use parallax as a measure of its distance.
Carl Witthoft
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1I think, measuring parallax does not need to measure the absolute angular position of the object on the sky. If there is an enough strong another source behind it, but enough far away, only their angle is also enough. This would enable for more better measurements. – peterh Sep 29 '19 at 15:34
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Per Wikipedia's Gaia (spacecraft); Objectives which I linked to in the question What actually determines the angular uncertainty of the source of a detected gravitational wave?
- Determine the position, parallax, and annual proper motion of 1 billion stars with an accuracy of about 20 microarcseconds (µas) at 15 mag, and 200 µas at 20 mag.
20 (µas) is about $1 \times 10^{-10}$ radians. If the Earth's amplitude is 2 AU, then the farthest distance that could be detected is $2 \times 10^{10}$ AU.
If you want to measure to about 10% accuracy, then that distance is $2 \times 10^{9}$ AU or about 3,000 30,000 light years.
That sounds surprisingly far away!
uhoh
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3000 ly is a long way compared with going to the chemist down the road, but is a fraction of the size of even our puny galaxy. – Carl Witthoft May 01 '19 at 19:30
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@RobJeffries I'll try to investigate further then, thanks! I suppose I should look into VLBI as well. – uhoh May 01 '19 at 22:34
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1Yes VLBI is the record holder I think - as discussed in the closely linked question. In your answer, I note that a 200 $\mu$as parallax would be measured with 10% precsion. This corresponds to a distance of 5000 pc or $\sim$ 15,000 light years. – ProfRob May 02 '19 at 10:02
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@RobJeffries thanks for the hint, I'll follow up on that, but if you have something handy please feel free to post it. I know that parsec's are related to parallax. I checked my math and I was missing a zero, it's 30,000 ly not 3,000. I think you get 15,000 based on a 1 AU displacement (definition of parsec/parallax), I was using the literal amplitude of Earth's motion as 2 AU and calculating the amplitude of the apparent displacement. – uhoh May 02 '19 at 10:11
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@RobJeffries but not with a single telescope. If we had two, one on Mars and one on Earth, we could do some great things with parallactic observations. – Carl Witthoft May 02 '19 at 14:34
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1@CarlWitthoft Stellar parallax is the angle in a triangle with a base of 1 au. That is what the parallax (and parallax precision) reported by Gaia is defined as. – ProfRob May 02 '19 at 17:21
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@Rob, '"Stellar parallax" is the name of the operation; the choice of a baseline 1AU long is standard, but that baseline value is not called "stellar parallax." – Carl Witthoft May 02 '19 at 18:36
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I haven't a clue what you are arguing about. The parallaxes reported by Gaia are inverted to give the distance in parsecs. The parallax angle is defined as having a 1au baseline. Gaia does not orbit 1au from the Sun. @CarlWitthoft – ProfRob May 02 '19 at 19:02
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@RobJeffries let's be careful here. The question doesn't ask "What is the parallax of..." It only asks about using parallax as a technique. My answer doesn't use the word parallax at all. My block quote says that 20 µas applies to three different measurements at the same time "position, parallax, and annual proper motion" which probably should have different numbers and not be lumped together. I've used the first one position for my calculation. You're using the second. I appreciate the tutorial about parallax as a unit, but I'm not using that unit here, I'm using position. – uhoh May 02 '19 at 22:49
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@uhoh The measurement of a position does not yield a parallax. Your answer and calculation is not correct. When your source says the parallax uncertainty is 20 microarcsec, that is precisely what it means. – ProfRob May 02 '19 at 22:59
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@RobJeffries But my source says the resolution for position is 20 microarcsec too. The question doesn't ask "What is the parallax of..." It only asks about using parallax as a technique. I don't talk about parallax at all in my answer. I assume two position measurements 6 months apart, with a baseline of ~2 AU. Of course you need a few more to subtract out proper motion, so say four measurements over 18 months. – uhoh May 02 '19 at 23:02
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You talk about the parallax precision. At it's most basic, a parallax requires measuring the difference between two positions, which has a larger uncertainty than that in one position measurement. Further: the position uncertainty quoted is not that of an individual measurement at one epoch. It is the result of fitting a 5-parameter model to a set of position measurements. – ProfRob May 02 '19 at 23:09
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@RobJeffries If we are going to go full-astrometric on the question "What is the maximum distance measurable with parallax?" we'd have to close as "unclear what you are asking" because there is no such thing as a single maximum distance measurable with parallax. I gave a ballpark answer 300,000 ly for a distance detectably different than infinity, 30,000 ly for a 10% error. I didn't specify a number of measurements or span of epochs. If we could run GAIA non-stop for 100 years without changing it's rotation axis, so that it measured the same stars continuously for a century, it can be better. – uhoh May 02 '19 at 23:19
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1@RobJeffries But this question could certainly have a better answer, based on a better source than Wikipedia. – uhoh May 02 '19 at 23:21