<p>Quick Google reveals a couple simple analyses.  For <a href="https://socratic.org/questions/why-can-t-astronomers-use-parallax-to-measure-distances-to-other-galaxies" rel="nofollow noreferrer">example</a>, </p>

<blockquote>
  <p>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. <span class="math-container">$ p = \frac{1}{d} =
&gt; \frac{1}{7.6*10^5} parsec = 1.3 *10^{-6} arc-seconds $</span></p>
  
  <p>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.</p>
</blockquote>

CC BY-SA 4.0
2019-09-29T15:34:56.703Z
I 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
CC BY-SA 4.0
2019-05-01T13:47:01.640Z
2019-05-01T13:47:01.640Z
Carl Witthoft
<p>Per Wikipedia's <a href="https://en.wikipedia.org/wiki/Gaia_(spacecraft)#Objectives" rel="nofollow noreferrer">Gaia (spacecraft); Objectives</a> which I linked to in the question <a href="https://astronomy.stackexchange.com/q/30621/7982">What actually determines the angular uncertainty of the source of a detected gravitational wave?</a></p>

<blockquote>
  <ul>
  <li>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.</li>
  </ul>
</blockquote>

<p>20 (µas) is about <span class="math-container">$1 \times 10^{-10}$</span> radians. If the Earth's amplitude is 2 AU, then the farthest distance that could be <em>detected</em> is <span class="math-container">$2 \times 10^{10}$</span> AU. </p>

<p>If you want to measure to about 10% accuracy, then that distance is  <span class="math-container">$2 \times 10^{9}$</span> AU or about <s>3,000</s> 30,000 light years.</p>

<p>That sounds surprisingly far away!</p>

CC BY-SA 4.0
2019-05-01T16:39:44.553Z
But 20 microarcsec is not the most accurate parallax available.
ProfRob
CC BY-SA 4.0
2019-05-01T19:30:24.633Z
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
CC BY-SA 4.0
2019-05-01T22:34:35.230Z
@RobJeffries I'll try to investigate further then, thanks! I suppose I should look into VLBI as well.
uhoh
CC BY-SA 4.0
2019-05-02T10:02:01.957Z
Yes 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
CC BY-SA 4.0
2019-05-02T10:11:01.853Z
@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
CC BY-SA 4.0
2019-05-02T10:15:09.993Z
Parallax is based on a triangle with a base of 1 au.
ProfRob
CC BY-SA 4.0
2019-05-02T14:34:17.157Z
@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
CC BY-SA 4.0
2019-05-02T17:21:44.050Z
@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
CC BY-SA 4.0
2019-05-02T18:36:25.543Z
@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
CC BY-SA 4.0
2019-05-02T19:02:11.017Z
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
CC BY-SA 4.0
2019-05-02T22:49:11.043Z
@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
CC BY-SA 4.0
2019-05-02T22:59:40.017Z
@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
CC BY-SA 4.0
2019-05-02T23:00:13.997Z
@RobJeffries so I've asked [How can GAIA's accuracy for position, parallax, and annual proper motion for a given star all be the same number?](https://astronomy.stackexchange.com/q/31747/7982)
uhoh
CC BY-SA 4.0
2019-05-02T23:02:03.997Z
@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
CC BY-SA 4.0
2019-05-02T23:09:34.183Z
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
CC BY-SA 4.0
2019-05-02T23:19:53.417Z
@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
CC BY-SA 4.0
2019-05-02T23:21:58.457Z
@RobJeffries But this question could certainly have a better answer, based on a better source than Wikipedia.
uhoh
CC BY-SA 4.0
2019-05-01T15:14:14.940Z
2019-05-02T10:16:28.210Z
2019-05-02T10:16:28.210Z
uhoh
<p>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)?</p>

CC BY-SA 4.0
2019-05-01T10:50:21.560Z
Your first question is a dupe of [What's the farthest object as determined only by parallax?](https://astronomy.stackexchange.com/q/19666/5264).
pela
CC BY-SA 4.0
2019-05-01T10:52:10.493Z
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
CC BY-SA 4.0
2019-05-01T16:43:29.877Z
Unclear 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
CC BY-SA 4.0
2019-05-01T16:46:28.390Z
See also https://astronomy.stackexchange.com/questions/332/how-does-angular-resolution-of-a-telescope-translate-to-its-parallax-precision?rq=1
ProfRob
CC BY-SA 4.0
2020-05-26T15:06:44.873Z
FWIW, we don't even have a very accurate distance measurement for the well-known and relatively nearby star [Betelgeuse](https://en.wikipedia.org/wiki/Betelgeuse#Distance_measurements), which has parallax of around 4.51 ± 0.80 milliarc-seconds.
PM 2Ring
CC BY-SA 4.0
2020-05-26T16:10:22.263Z
@PM2Ring That is because it is too bright.
ProfRob
CC BY-SA 4.0
2020-05-26T16:22:10.590Z
@Rob True, and its variable brightness doesn't help either.
PM 2Ring
CC BY-SA 4.0
2020-05-27T02:58:31.510Z
@PM2Ring I've just asked [What will it finally take to accurately measure the distance to Betelgeuse?](https://astronomy.stackexchange.com/q/36365/7982)
uhoh
CC BY-SA 4.0
2020-05-27T02:58:38.470Z
@RobJeffries ditto
uhoh
<telescope><distances><parallax>
What is the maximum distance measurable with parallax?
technical_difficulty
# What is the maximum distance measurable with parallax?

(Asked by: username_0 on 2019-05-01)

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)?

**Tags:** telescope, distances, parallax
> **Comments:**
> **username_1**: Your first question is a dupe of [What's the farthest object as determined only by parallax?](https://astronomy.stackexchange.com/q/19666/5264).  
> **username_0**: 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.  
> **username_2**: Unclear 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.  
> **username_2**: See also https://astronomy.stackexchange.com/questions/332/how-does-angular-resolution-of-a-telescope-translate-to-its-parallax-precision?rq=1  
> **username_3**: FWIW, we don't even have a very accurate distance measurement for the well-known and relatively nearby star [Betelgeuse](https://en.wikipedia.org/wiki/Betelgeuse#Distance_measurements), which has parallax of around 4.51 ± 0.80 milliarc-seconds.  
> **username_2**: @PM2Ring That is because it is too bright.  
> **username_3**: @Rob True, and its variable brightness doesn't help either.  
> **username_4**: @PM2Ring I've just asked [What will it finally take to accurately measure the distance to Betelgeuse?](https://astronomy.stackexchange.com/q/36365/7982)  
> **username_4**: @RobJeffries ditto  

---

## 2 answers

### Answer by username_5 on 2019-05-01. Score: 1

Quick Google reveals a couple simple analyses. For [example](https://socratic.org/questions/why-can-t-astronomers-use-parallax-to-measure-distances-to-other-galaxies),

> 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.

> **Comments:**
> **username_6**: I 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.  

---

### Answer by username_4 on 2019-05-01. Score: 1

Per Wikipedia's [Gaia (spacecraft); Objectives](https://en.wikipedia.org/wiki/Gaia_(spacecraft)#Objectives) which I linked to in the question [What actually determines the angular uncertainty of the source of a detected gravitational wave?](https://astronomy.stackexchange.com/q/30621/7982)

> * 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!

> **Comments:**
> **username_2**: But 20 microarcsec is not the most accurate parallax available.  
> **username_5**: 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.  
> **username_4**: @RobJeffries I'll try to investigate further then, thanks! I suppose I should look into VLBI as well.  
> **username_2**: Yes 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.  
> **username_4**: @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.  
> **username_2**: Parallax is based on a triangle with a base of 1 au.  
> **username_5**: @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.  
> **username_2**: @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.  
> **username_5**: @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."  
> **username_2**: 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  
> **username_4**: @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.  
> **username_2**: @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.  
> **username_4**: @RobJeffries so I've asked [How can GAIA's accuracy for position, parallax, and annual proper motion for a given star all be the same number?](https://astronomy.stackexchange.com/q/31747/7982)  
> **username_4**: @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.  
> **username_2**: 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.  
> **username_4**: @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.  
> **username_4**: @RobJeffries But this question could certainly have a better answer, based on a better source than Wikipedia.  

---

