<p>The gravitational redshift factor and also the factor by which time dilation occurs in a gravitational field is approximately $GM/Rc^2$. Here, $R$ would be the radius from which light was emitted and $M$ is the amount of mass <em>within</em> radius $R$ (making the crude assumption of spherical symmetry).</p>

<p>Thus, for an external observer,  light emitted from a radius of 10 kpc, might have $M \sim 10^{11} M_{\odot}$ in the galaxy shown. The redshift/time dilation factor is only $5\times 10^{-7}$ and is basically negligible.</p>

<p>This could perhaps gets an order of magnitude bigger as one approaches the denser central bulge, but is still very small.</p>

<p>The only appreciable redshift and time dilation effects will come in the immediate surroundings of any supermassive black hole. By immediate, I mean within about a hundred Schwarzschild radii, where $R_s = 2GM/c^2$. In our Galaxy that would mean within a billion <em>kilometres</em>.</p>

CC BY-SA 3.0
2018-02-19T18:09:19.817Z
So unless your world exist in orbit exclusively around the black whole( in the center of the galaxy: Sagittarius A) there would be no significant time dilation? That distance would be likely inside the acceleration disk orbit and completely inhabitable on any level?
Muze
CC BY-SA 3.0
2018-02-23T19:01:36.673Z
@Muze - that's totally correct.  (I think you meant to spell "accretion" disk, by the way.)
Fattie
CC BY-SA 3.0
2018-02-23T19:04:33.040Z
Just BTW, there seems to be many black holes in our galaxy - as well as the big one in the middle.  If you are very close to any of those BHs, you'd experience such effects.
Fattie
CC BY-SA 3.0
2018-02-19T07:36:37.817Z
2018-02-19T07:36:37.817Z
ProfRob
<p>Quite simply,</p>

<p>in both cases the effect is absolutely tiny.</p>

<p>Here is your basic confusion, on both this and the other similar question:</p>

<ol>
<li>very heavy objects cause time dilation</li>
<li>a galaxy is just <em>totally badass heavy</em></li>
<li>you naturally assumed then that galaxies cause time dilation</li>
<li>Very surprisingly, this is simply <em>not correct</em>.</li>
</ol>

<p>The reason? Galaxies are very big. That is to say very thin.  They have incredibly low density.  Because of this there is simply no dilation at all.</p>

<p>(Well, only a minuscule amount - but that is true of simply, say, standing on Earth.)</p>

<p>That's the story!</p>

CC BY-SA 3.0
2018-02-24T15:39:07.413Z
2018-02-24T15:39:07.413Z
Fattie
<p>Not the same question but is similar to other marked duplicate. 
How much time dilation  does the center of a galaxy can exist and sustain human life from our point of view? What would a day equal to each others point of view looking at each other?</p>

<p>I'm not asking about moving celestial bodies moving from each other but the difference in the gravity wells from the center of our galaxy being generally denser then the edge of a galaxy.</p>

<p><a href="https://i.sstatic.net/JMO2E.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JMO2E.jpg" alt="enter image description here"></a></p>

<hr>

<p>This is another way of asking if I wasn't clear above the line. Not to invalidate any answers.</p>

<p>Point 1 being near the center of the galaxy and point 2 at the the most edge the galaxy. How much would the differences in the galaxies gravity well point 1 being deeper in the center compared to the point 2 the edge effect time?</p>

<p><a href="https://i.sstatic.net/zNUYN.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/zNUYN.jpg" alt="enter image description here"></a></p>

CC BY-SA 3.0
2018-02-19T04:16:25.407Z
Your question does not make much sense. What does the doppler shift due to a galaxy's rotation have to do with time dilation? Why would that affect the evolution of life? How would that affect the length of a day?
Phiteros
CC BY-SA 3.0
2018-02-23T19:00:34.883Z
@Muze - you're not incorrect but the difference is **absolutely tiny** - so small it could never be measured.
Fattie
CC BY-SA 3.0
2018-02-23T19:02:42.283Z
@Phiteros - it makes absolutely perfect sense, what do you mean?  When you're near some gravity (say, on the surface of the Earth), there is a tiny time dilation.  OP is just asking how big it is. The galaxy is ***astoundingly heavy*** so you can really see where it's a good popular science question.  Great question.
Fattie
CC BY-SA 3.0
2018-02-23T22:06:28.230Z
@Fattie That's because he edited the question. The first question was asking about red and blue shifts, then talked about time dilation.
Phiteros
CC BY-SA 3.0
2018-02-24T15:36:29.200Z
@Phiteros - fair enough; sorry about that.  Is question-editing annoying or what?!
Fattie
<galaxy><space-time><redshift><life>
How does space time differ within a galaxy?
Muze
# How does space time differ within a galaxy?

(Asked by: username_0 on 2018-02-19)

Not the same question but is similar to other marked duplicate.
How much time dilation does the center of a galaxy can exist and sustain human life from our point of view? What would a day equal to each others point of view looking at each other?

I'm not asking about moving celestial bodies moving from each other but the difference in the gravity wells from the center of our galaxy being generally denser then the edge of a galaxy.

[![enter image description here](https://i.sstatic.net/JMO2E.jpg)](https://i.sstatic.net/JMO2E.jpg)

---

This is another way of asking if I wasn't clear above the line. Not to invalidate any answers.

Point 1 being near the center of the galaxy and point 2 at the the most edge the galaxy. How much would the differences in the galaxies gravity well point 1 being deeper in the center compared to the point 2 the edge effect time?

[![enter image description here](https://i.sstatic.net/zNUYN.jpg)](https://i.sstatic.net/zNUYN.jpg)

**Tags:** galaxy, space-time, redshift, life
> **Comments:**
> **username_1**: Your question does not make much sense. What does the doppler shift due to a galaxy's rotation have to do with time dilation? Why would that affect the evolution of life? How would that affect the length of a day?  
> **username_2**: @Muze - you're not incorrect but the difference is **absolutely tiny** - so small it could never be measured.  
> **username_2**: @Phiteros - it makes absolutely perfect sense, what do you mean?  When you're near some gravity (say, on the surface of the Earth), there is a tiny time dilation.  OP is just asking how big it is. The galaxy is ***astoundingly heavy*** so you can really see where it's a good popular science question.  Great question.  
> **username_1**: @Fattie That's because he edited the question. The first question was asking about red and blue shifts, then talked about time dilation.  
> **username_2**: @Phiteros - fair enough; sorry about that.  Is question-editing annoying or what?!  

---

## 2 answers

### Answer by username_3 on 2018-02-19. Score: 3 | Accepted answer

The gravitational redshift factor and also the factor by which time dilation occurs in a gravitational field is approximately $GM/Rc^2$. Here, $R$ would be the radius from which light was emitted and $M$ is the amount of mass *within* radius $R$ (making the crude assumption of spherical symmetry).

Thus, for an external observer, light emitted from a radius of 10 kpc, might have $M \sim 10^{11} M\_{\odot}$ in the galaxy shown. The redshift/time dilation factor is only $5\times 10^{-7}$ and is basically negligible.

This could perhaps gets an order of magnitude bigger as one approaches the denser central bulge, but is still very small.

The only appreciable redshift and time dilation effects will come in the immediate surroundings of any supermassive black hole. By immediate, I mean within about a hundred Schwarzschild radii, where $R\_s = 2GM/c^2$. In our Galaxy that would mean within a billion *kilometres*.

> **Comments:**
> **username_0**: So unless your world exist in orbit exclusively around the black whole( in the center of the galaxy: Sagittarius A) there would be no significant time dilation? That distance would be likely inside the acceleration disk orbit and completely inhabitable on any level?  
> **username_2**: @Muze - that's totally correct.  (I think you meant to spell "accretion" disk, by the way.)  
> **username_2**: Just BTW, there seems to be many black holes in our galaxy - as well as the big one in the middle.  If you are very close to any of those BHs, you'd experience such effects.  

---

### Answer by username_2 on 2018-02-24. Score: 0

Quite simply,

in both cases the effect is absolutely tiny.

Here is your basic confusion, on both this and the other similar question:

1. very heavy objects cause time dilation
2. a galaxy is just *totally badass heavy*
3. you naturally assumed then that galaxies cause time dilation
4. Very surprisingly, this is simply *not correct*.

The reason? Galaxies are very big. That is to say very thin. They have incredibly low density. Because of this there is simply no dilation at all.

(Well, only a minuscule amount - but that is true of simply, say, standing on Earth.)

That's the story!


---

