# I Centre of mass of the observable universe

1. May 12, 2017

### Richmonder

Ok so I have read several of the threads regarding the impossibility of determining the centre of the universe based on observations of expansion of the universe. That one seems to have been beaten to death. So this is a slightly different question. When we look at all the matter that we can currently observe in the universe, where is this system's centre of mass? Should be a pretty simple calculation no?

2. May 12, 2017

### Staff: Mentor

Fair enough, but based on your wording I'm not sure you got the point that was being beaten: the point isn't that we can't find the center, it is that there isn't one.
Don't even need a calculation: it's right here.

3. May 12, 2017

### Staff: Mentor

Why would the center of mass be located directly on us? Is it literally on top of us, or simply nearby (within a few million light-years)?

4. May 12, 2017

### Richmonder

Yes, I accept that there isn't a centre of the universe for good reasons - the main argument that convinces me is that the universe is unbounded. And it would make sense to me that we are at the centre of the observable universe, by definition. But why would we necessarily be at the centre of mass of the observable universe? Is the mass distribution so even in every direction? I thought we had observed large scale structure.

5. May 12, 2017

### phinds

Based on (1) the Cosmological Principle and (2) the size of the OU, I'd estimate that the center of mass is for all practical purposes conincident with the geometric center, which is of course your left eyeball when you close your right eyeball.

6. May 12, 2017

### Richmonder

OK thanks for pointing me in the right direction for further reading. Much appreciated.

7. May 12, 2017

### kimbyd

Because mass is distributed close to evenly throughout the universe, the center of mass of the observable universe is always located close to the observer, no matter where they are. It won't be exactly at the observer's location, because the mass distribution is not perfectly uniform, but it'll be pretty close (close in a cosmological sense, so possibly outside our galaxy).

8. May 12, 2017

### phinds

I disagree. I refer you to post #5

9. May 12, 2017

### kimbyd

That post assumes a perfectly homogeneous universe. Our universe is not perfectly homogeneous.

To do a really, really simple calculation, there are approximately $10^{11}$ galaxies in our universe. If they were distributed with a uniform random distribution (which isn't the case), then you'd expect the center of mass to be off by (very roughly) $\sqrt{10^{11}}/10^{11}$ times the diameter of the universe in each direction, for an expected deviation of (again, very roughly) 300,000 light years off from the center in each direction, or an expected magnitude of the deviation of about 500,000 light years.

So, my instinct of saying that the center might be outside our galaxy was roughly accurate. The real universe, of course, does not have galaxies distributed evenly at all: they're clustered in a very specific manner. That clustering will definitely modify this calculation, though it might go both ways: the overall uniformity of the early universe may make galaxies, on average, more evenly-distributed than the uniform random distribution case, which would make the distance smaller. But the locations of the galaxies themselves are also highly correlated, which would mean that the effective number is not $10^{11}$, but some number much smaller than that, which would increase the expected distance.

10. May 13, 2017

### timmdeeg

The assumption is that the universe is perfectly homogenous on larger scales compared to the observable universe. The FRW-model is based on that. But will we ever know? I don't think so.

11. May 13, 2017

### phinds

I think you're right. I was overestimating the uniformity of the galaxy distribution. I mean, I KNEW it was not uniform, and roughly HOW it is not uniform, but I now think that my assumption that the huge size of the OU would smooth out the large scale distribution was overly optimistic. Thanks for correcting me on this.

12. May 13, 2017

### Staff: Mentor

Even if the OU were uniform, wouldn't the COM be closer to the BH at the center of the Milky Way Galaxy? Our local COM is closer to there than to where Earth is, no?

13. May 15, 2017

### kimbyd

I don't think the local mass distribution has any impact. A galaxy one billion light years away is weighted exactly the same in the center-of-mass calculation as our own is.

14. May 15, 2017

### kimbyd

The question was about the center of mass of the observable universe, so this statement doesn't apply.