<p>We can calculate the distance we need to be from an object in order for it to be any arbitrary <a href="https://en.wikipedia.org/wiki/Angular_diameter" rel="nofollow noreferrer">angular size</a> using the formula <span class="math-container">$D=\frac{d}{2\tan(\frac12\delta)}$</span>.  In this case, <span class="math-container">$D$</span> is the distance from the object, <span class="math-container">$d$</span> is its diameter, and <span class="math-container">$\delta$</span> is the angular size.  The Milky Way's diameter is 100,000 light years.  If we want the Milky Way to appear as large as the Sun appears from the Earth (0.5<span class="math-container">$^\circ$</span>), we would need to be 5,700,000 light years away.  If we want it to appear much larger, we could be closer.  For the Milky Way to be the size of a 1 meter circle held at arm's length (90<span class="math-container">$^\circ$</span>), we would need to be 50,000 light years away.</p>

CC BY-SA 3.0
2016-07-19T17:03:49.537Z
Hmm....you said the we'd have to be 5.7 million ly away before it'd appear the same size as the sun from Earth, but the Andromeda Galaxy is only 2.5 million lightyears away and is twice the estimated width of the Milky Way, and we can't see it clearly without telescopes!
temporary_user_name
CC BY-SA 3.0
2016-07-19T17:08:23.900Z
Yes, Andromeda is about 2.97 degrees across from the Earth.  So we would be able to see it, but it would be rather dim.
Phiteros
CC BY-SA 3.0
2016-07-19T17:37:58.240Z
Sorry, what do you mean? By my reasoning, according to your math, shouldn't it be even larger than the sun?
temporary_user_name
CC BY-SA 3.0
2016-07-19T17:44:38.657Z
The Andromeda Galaxy's angular size is larger than the Sun.  However, because it is so far away, it has an apparent magnitude (how bright we see it) of 3.44 (lower means brighter).  In comparison, the star Vega has an apparent magnitude of 0, and the Sun has an apparent magnitude of -26.  

In terms of absolute magnitude (how bright it appears from 10 parsecs away), Andromeda is -21.5, Vega is 0.582, and the Sun is 4.83.  So yes, the Andromeda Galaxy takes up more space on the sky than the sun, but it is much, much dimmer.
Phiteros
CC BY-SA 3.0
2016-07-19T18:39:43.650Z
@Aerovistae  [See this article](http://www.slate.com/blogs/bad_astronomy/2014/01/01/moon_and_andromeda_relative_size_in_the_sky.html), which includes a nice image depicting how large a "bright" andromeda would be in our sky.
zibadawa timmy
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2016-07-19T23:47:35.893Z
Math is amazing..
NuWin
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2016-07-20T03:02:02.197Z
The field of view for binocular vision is approximately $114^\circ$. So I think $\frac{100\ 000\text{ ly}}{2\tan(\frac{1}{2} 114^\circ)} = 32\ 370\text{ ly}$ belongs in this answer.
KRyan
CC BY-SA 3.0
2016-07-20T05:28:16.897Z
By binocular vision means "with two eyes" not "with binoculars" (binoculars have a field of view of 5-10 degrees). We only have detailed vision for 20-40 degrees. Also, accuracy: your data is accurate to one or two significant figures, hence your answers should be similarly rounded.
James K
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2016-07-20T15:01:11.697Z
@JamesKilfiger Ah, I see.  I'll just take that bit out.
Phiteros
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2016-07-25T17:51:15.723Z
could give a physical example:
Jack R. Woods
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2016-07-26T05:04:58.543Z
I didn't see mention of the thickness of the galactic bulge nor the direction of travel in the answers or comments. The bulge extends 15-20000 light years above the galactic plane and I would think that "straight up" along the Z axis of galactic coordinates would be the direction to go. That being said, 50000 light years sounds good.
Jack R. Woods
CC BY-SA 3.0
2016-07-26T05:11:52.713Z
@JackR.Woods I was assuming he wanted to see the Galaxy face-on, so there is no need to consider the galactic bulge. The Galaxy is just modeled as a circle.
Phiteros
CC BY-SA 3.0
2017-04-10T23:52:58.270Z
I interpreted the question as "What is the shortest distance a starship can go to see the Milky Way as a galaxy (ie. spiral structure)?".
Jack R. Woods
CC BY-SA 3.0
2017-04-11T00:02:09.223Z
@Aerovistae Rethinking the answer to my interpretation of this question: 95% of disk stars (and nearly all star formation) are in the thin disk which extends only to about 1000 LY above the galactic plane. Thus, I would guess that you might be able to start seeing structure at about 10000 LY due galactic north.
Jack R. Woods
CC BY-SA 3.0
2017-04-11T00:03:46.033Z
Of course, the bulge would still obscure the far side.
Jack R. Woods
CC BY-SA 4.0
2016-07-19T16:49:58.730Z
2019-06-11T07:53:48.787Z
2019-06-11T07:53:48.787Z
Phiteros
<p>If in the distant future a ship were somehow able to move beyond the galaxy and into intergalactic space, how far would it have to go before we could look out a window and see the Milky Way in its entirety, rather than just edge-on as we see it from Earth?</p>

CC BY-SA 3.0
2016-07-19T16:40:45.230Z
This is a better question for astronomy than here, but I'm not going to migrate it there because as this question stands, it isn't very well defined. And I don't think it's the kind of question that can be well defined, unfortunately. The answer is a very long ways away, but it largely depends on which direction you go.
PearsonArtPhoto
CC BY-SA 3.0
2016-07-19T16:43:15.337Z
I don't think it's that unclear.  He's basically asking how far away you would have to be in order to see the Milky Way like we see pictures of other galaxies.  It's an angular size question, and it just depends on how large you want it to appear.  Ultimately, it comes out to ~50,000 light years.
Phiteros
CC BY-SA 3.0
2016-07-19T16:43:46.950Z
@PearsonArtPhoto I was actually writing out an answer to this when you closed it.  I agree, though, it might be better in Astronomy.
Phiteros
<photography>
How far into intergalactic space would you have to go to see the Milky Way?
temporary_user_name
# How far into intergalactic space would you have to go to see the Milky Way?

(Asked by: username_0 on 2016-07-19)

If in the distant future a ship were somehow able to move beyond the galaxy and into intergalactic space, how far would it have to go before we could look out a window and see the Milky Way in its entirety, rather than just edge-on as we see it from Earth?

**Tags:** photography
> **Comments:**
> **username_1**: This is a better question for astronomy than here, but I'm not going to migrate it there because as this question stands, it isn't very well defined. And I don't think it's the kind of question that can be well defined, unfortunately. The answer is a very long ways away, but it largely depends on which direction you go.  
> **username_2**: I don't think it's that unclear.  He's basically asking how far away you would have to be in order to see the Milky Way like we see pictures of other galaxies.  It's an angular size question, and it just depends on how large you want it to appear.  Ultimately, it comes out to ~50,000 light years.  
> **username_2**: @PearsonArtPhoto I was actually writing out an answer to this when you closed it.  I agree, though, it might be better in Astronomy.  

---

## 1 answers

### Answer by username_2 on 2016-07-19. Score: 18 | Accepted answer

We can calculate the distance we need to be from an object in order for it to be any arbitrary [angular size](https://en.wikipedia.org/wiki/Angular_diameter) using the formula $D=\frac{d}{2\tan(\frac12\delta)}$. In this case, $D$ is the distance from the object, $d$ is its diameter, and $\delta$ is the angular size. The Milky Way's diameter is 100,000 light years. If we want the Milky Way to appear as large as the Sun appears from the Earth (0.5$^\circ$), we would need to be 5,700,000 light years away. If we want it to appear much larger, we could be closer. For the Milky Way to be the size of a 1 meter circle held at arm's length (90$^\circ$), we would need to be 50,000 light years away.

> **Comments:**
> **username_0**: Hmm....you said the we'd have to be 5.7 million ly away before it'd appear the same size as the sun from Earth, but the Andromeda Galaxy is only 2.5 million lightyears away and is twice the estimated width of the Milky Way, and we can't see it clearly without telescopes!  
> **username_2**: Yes, Andromeda is about 2.97 degrees across from the Earth.  So we would be able to see it, but it would be rather dim.  
> **username_0**: Sorry, what do you mean? By my reasoning, according to your math, shouldn't it be even larger than the sun?  
> **username_2**: The Andromeda Galaxy's angular size is larger than the Sun.  However, because it is so far away, it has an apparent magnitude (how bright we see it) of 3.44 (lower means brighter).  In comparison, the star Vega has an apparent magnitude of 0, and the Sun has an apparent magnitude of -26.    In terms of absolute magnitude (how bright it appears from 10 parsecs away), Andromeda is -21.5, Vega is 0.582, and the Sun is 4.83.  So yes, the Andromeda Galaxy takes up more space on the sky than the sun, but it is much, much dimmer.  
> **username_3**: @Aerovistae  [See this article](http://www.slate.com/blogs/bad_astronomy/2014/01/01/moon_and_andromeda_relative_size_in_the_sky.html), which includes a nice image depicting how large a "bright" andromeda would be in our sky.  
> **username_4**: Math is amazing..  
> **username_5**: The field of view for binocular vision is approximately $114^\circ$. So I think $\frac{100\ 000\text{ ly}}{2\tan(\frac{1}{2} 114^\circ)} = 32\ 370\text{ ly}$ belongs in this answer.  
> **username_6**: By binocular vision means "with two eyes" not "with binoculars" (binoculars have a field of view of 5-10 degrees). We only have detailed vision for 20-40 degrees. Also, accuracy: your data is accurate to one or two significant figures, hence your answers should be similarly rounded.  
> **username_2**: @JamesKilfiger Ah, I see.  I'll just take that bit out.  
> **username_7**: could give a physical example:  
> **username_7**: I didn't see mention of the thickness of the galactic bulge nor the direction of travel in the answers or comments. The bulge extends 15-20000 light years above the galactic plane and I would think that "straight up" along the Z axis of galactic coordinates would be the direction to go. That being said, 50000 light years sounds good.  
> **username_2**: @JackR.Woods I was assuming he wanted to see the Galaxy face-on, so there is no need to consider the galactic bulge. The Galaxy is just modeled as a circle.  
> **username_7**: I interpreted the question as "What is the shortest distance a starship can go to see the Milky Way as a galaxy (ie. spiral structure)?".  
> **username_7**: @Aerovistae Rethinking the answer to my interpretation of this question: 95% of disk stars (and nearly all star formation) are in the thin disk which extends only to about 1000 LY above the galactic plane. Thus, I would guess that you might be able to start seeing structure at about 10000 LY due galactic north.  
> **username_7**: Of course, the bulge would still obscure the far side.  

---

