<blockquote>
  <p>The widely known phenomenon termed gravitational lensing is believed
  to curve space, thereby affecting the path followed by light and other
  electromagnetic waves.</p>
</blockquote>

<p>and gravitational waves! In fact, the paths followed by light and other massless particles (for the lack of a better word) are called <em>null geodesics</em> and they have in common that $$\mathrm ds^2 = 0, $$ i.e. the 4-distance they experience is zero.</p>

<blockquote>
  <p>This effect is associated principally with galaxies and galaxy
  clusters, as it requires considerable mass. But in theory any star or
  star cluster, or black hole, can have this effect to some degree.</p>
</blockquote>

<p>One could argue that the Shapiro delay is of the same nature, only temporal rather than spatial. You can observe the Shapiro delay from the sun using radar probes!</p>

<blockquote>
  <p>What can we tell for sure about the position of external galaxies, if
  we are uncertain that their light is actually coming to us along a
  straight path: </p>
</blockquote>

<p>It is by definition! The path that light takes <em>is</em> straight, even if it seems bent to us in 3-dimensional space. Therefore, galaxies appear where they are because that's where they are. It's just that we project our idea of Euclidean (i.e. unbent) space onto the sky!</p>

<p>I know what you want to ask though: How can we be sure that the sky isn't curved in some insane way somewhere and we're actually looking somewhere else? We <em>do</em> assume that on the whole, space is Euclidean. </p>

<p>Well, on the small scale this might be the case: We might be looking at stuff whilst it is "really" somewhere else (note that it is really there, the "really somewhere else part" is just us imposing our coordinates on the sky!!).</p>

<p>But we know beyond reasonable doubt that the Universe, as a whole, is more or less Euclidean. At least up to redshift z~1000, i.e. about 300,000 years after the Big Bang. We can observe the Cosmic Microwave Background, and it tells us something about the curvature in the sky. We know that there's structures there which have a certain angular size, as we know that they had 300,000 years to form and we know the speed at which they formed. So we can predict their typical size, and it turns out that the angle under which they appear would be bigger if the universe were oblate/hyperbolic and smaller if the universe were closed. They are just right for a flat universe. So we know that on big scales, space is indeed Euclidean. It might not be the case for individual stars, galaxies, etc. but on average, it works. And cosmology / gravitational lensing usually works with averages and statistics.</p>

<blockquote>
  <p>Can a galaxy appear to be in more than one place in the sky?</p>
</blockquote>

<p>Totally. There's a plethora of cases of <a href="http://www.roe.ac.uk/~heymans/website_images/148928main_image_feature_575_ys_4.jpg" rel="nofollow noreferrer">multi image lens-source systems</a>. You can usually sort them out by looking at their spectra and checking their time-variability.</p>

CC BY-SA 3.0
2017-01-19T21:16:10.370Z
Actually what I wanted to ask is whether the potential for objects to appear in more than one location has any implications for (the tendency of astronomers to "know") how many galaxies exist in the universe - such as the recent analysis of Hubble deep field images at Nottingham, which led to yet another upwards revision of the total. What is the likely margin for error, if a percentage of the objects have accidentally been counted twice? In one of the example images, one object appeared to be five separate objects.
Ed999
CC BY-SA 3.0
2017-01-20T09:05:03.400Z
Oh for sure, but this isn't due to multiple imaging of galaxies (because it's a super rare occasion for a galaxy to be positioned 'just right'). However, because lensing can magnify your image, you can look farther than you'd expect, and you count more galaxies up to a certain distance because you think they're closer than they are. 
But this can be corrected as you know how much lensing to expect.
tugi
CC BY-SA 3.0
2017-01-19T10:27:31.983Z
2017-01-19T10:27:31.983Z
tugi
<p>The widely known phenomenon termed <em>gravitational lensing</em> is believed to curve space, thereby affecting the path followed by light and other electromagnetic waves.</p>

<p>This effect is associated principally with galaxies and galaxy clusters, as it requires considerable mass. But in theory any star or star cluster, or black hole, can have this effect to some degree.</p>

<p>What can we tell for sure about the position of external galaxies, if we are uncertain that their light is actually coming to us along a straight path: i.e. if light follows the curvature of space, and that curvature is not uniform, how can we be sure we are not observing, for example, the light from a single source appearing to us as more than one object.</p>

<p>Can a galaxy appear to be in more than one place in the sky?</p>

CC BY-SA 3.0
2017-01-17T23:03:45.140Z
Look up gravitational lensing. Also we know how to do the math, thanks to general relativity.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-01-17T23:15:12.710Z
The objects we see are often not where they appear, or may not even exist now. In what way is this a different question to http://astronomy.stackexchange.com/questions/19784/if-dark-matter-bends-light-how-do-we-know-the-stuff-in-the-sky-is-where-we-thin?rq=1 ?
ProfRob
CC BY-SA 3.0
2017-01-18T13:47:33.357Z
@RobJeffries I do think it is sufficiently different. The other question seemed to be more focused on nearby objects vs galaxies. Plus this question also has the additional question about galaxies appearing in more than one place in the sky.
zephyr
CC BY-SA 3.0
2017-01-18T14:24:25.923Z
Agree w/ Rob J. --  pretty much a dupe of http://astronomy.stackexchange.com/questions/19784/if-dark-matter-bends-light-how-do-we-know-the-stuff-in-the-sky-is-where-we-thin , even tho' that is allegedly for "dark matter"
Carl Witthoft
CC BY-SA 3.0
2017-01-18T19:25:19.743Z
I specifically asked this question about the _general_ effect of gravity, rather than restrict it to the gravitational effect of dark matter alone, because ordinary matter has a significant mass, while the local effects of dark matter are negligible in our immediate neighbourhood. So the other question simply invites the reply: dark matter has a negligible effect. Also, the most significant implication of gravitational lensing is that, in theory, it could cause a single source galaxy to appear to be in two locations, yet the other question does not even mention this.
Ed999
<gravitational-lensing>
Given that gravity bends the path of light, how confident can we be that galaxies are where they seem to be?
Ed999
# Given that gravity bends the path of light, how confident can we be that galaxies are where they seem to be?

(Asked by: username_0 on 2017-01-17)

The widely known phenomenon termed *gravitational lensing* is believed to curve space, thereby affecting the path followed by light and other electromagnetic waves.

This effect is associated principally with galaxies and galaxy clusters, as it requires considerable mass. But in theory any star or star cluster, or black hole, can have this effect to some degree.

What can we tell for sure about the position of external galaxies, if we are uncertain that their light is actually coming to us along a straight path: i.e. if light follows the curvature of space, and that curvature is not uniform, how can we be sure we are not observing, for example, the light from a single source appearing to us as more than one object.

Can a galaxy appear to be in more than one place in the sky?

**Tags:** gravitational-lensing

> **Comments:**
> **username_1**: Look up gravitational lensing. Also we know how to do the math, thanks to general relativity.  
> **username_2**: The objects we see are often not where they appear, or may not even exist now. In what way is this a different question to http://astronomy.stackexchange.com/questions/19784/if-dark-matter-bends-light-how-do-we-know-the-stuff-in-the-sky-is-where-we-thin?rq=1 ?  
> **username_3**: @RobJeffries I do think it is sufficiently different. The other question seemed to be more focused on nearby objects vs galaxies. Plus this question also has the additional question about galaxies appearing in more than one place in the sky.  
> **username_4**: Agree w/ Rob J. --  pretty much a dupe of http://astronomy.stackexchange.com/questions/19784/if-dark-matter-bends-light-how-do-we-know-the-stuff-in-the-sky-is-where-we-thin , even tho' that is allegedly for "dark matter"  
> **username_0**: I specifically asked this question about the _general_ effect of gravity, rather than restrict it to the gravitational effect of dark matter alone, because ordinary matter has a significant mass, while the local effects of dark matter are negligible in our immediate neighbourhood. So the other question simply invites the reply: dark matter has a negligible effect. Also, the most significant implication of gravitational lensing is that, in theory, it could cause a single source galaxy to appear to be in two locations, yet the other question does not even mention this.  

---

## 1 answers

### Answer by username_5 on 2017-01-19. Score: 1 | Accepted answer

> The widely known phenomenon termed gravitational lensing is believed
> to curve space, thereby affecting the path followed by light and other
> electromagnetic waves.

and gravitational waves! In fact, the paths followed by light and other massless particles (for the lack of a better word) are called *null geodesics* and they have in common that $$\mathrm ds^2 = 0, $$ i.e. the 4-distance they experience is zero.

> This effect is associated principally with galaxies and galaxy
> clusters, as it requires considerable mass. But in theory any star or
> star cluster, or black hole, can have this effect to some degree.

One could argue that the Shapiro delay is of the same nature, only temporal rather than spatial. You can observe the Shapiro delay from the sun using radar probes!

> What can we tell for sure about the position of external galaxies, if
> we are uncertain that their light is actually coming to us along a
> straight path:

It is by definition! The path that light takes *is* straight, even if it seems bent to us in 3-dimensional space. Therefore, galaxies appear where they are because that's where they are. It's just that we project our idea of Euclidean (i.e. unbent) space onto the sky!

I know what you want to ask though: How can we be sure that the sky isn't curved in some insane way somewhere and we're actually looking somewhere else? We *do* assume that on the whole, space is Euclidean.

Well, on the small scale this might be the case: We might be looking at stuff whilst it is "really" somewhere else (note that it is really there, the "really somewhere else part" is just us imposing our coordinates on the sky!!).

But we know beyond reasonable doubt that the Universe, as a whole, is more or less Euclidean. At least up to redshift z~1000, i.e. about 300,000 years after the Big Bang. We can observe the Cosmic Microwave Background, and it tells us something about the curvature in the sky. We know that there's structures there which have a certain angular size, as we know that they had 300,000 years to form and we know the speed at which they formed. So we can predict their typical size, and it turns out that the angle under which they appear would be bigger if the universe were oblate/hyperbolic and smaller if the universe were closed. They are just right for a flat universe. So we know that on big scales, space is indeed Euclidean. It might not be the case for individual stars, galaxies, etc. but on average, it works. And cosmology / gravitational lensing usually works with averages and statistics.

> Can a galaxy appear to be in more than one place in the sky?

Totally. There's a plethora of cases of [multi image lens-source systems](http://www.roe.ac.uk/~heymans/website_images/148928main_image_feature_575_ys_4.jpg). You can usually sort them out by looking at their spectra and checking their time-variability.

> **Comments:**
> **username_0**: Actually what I wanted to ask is whether the potential for objects to appear in more than one location has any implications for (the tendency of astronomers to "know") how many galaxies exist in the universe - such as the recent analysis of Hubble deep field images at Nottingham, which led to yet another upwards revision of the total. What is the likely margin for error, if a percentage of the objects have accidentally been counted twice? In one of the example images, one object appeared to be five separate objects.  
> **username_5**: Oh for sure, but this isn't due to multiple imaging of galaxies (because it's a super rare occasion for a galaxy to be positioned 'just right'). However, because lensing can magnify your image, you can look farther than you'd expect, and you count more galaxies up to a certain distance because you think they're closer than they are.  But this can be corrected as you know how much lensing to expect.  

---

