posted
So, I have a bit of a math problem that has me stymied - which is no surprise, since I am terrible at math.

In 2004, a study claimed that the universe has a diameter of about 156 billion light years. I am trying to figure out, if the universe were a sphere, what would the surface area of that sphere be?

I used the equation:

Surface area of a sphere = 4(pi)(rsquared)

and I got the result of 305, 815 billion light years squared. The problem is, I want to know what that is in kilometers. A light year is 9.4605284 × 10 to the 15 light years squared. I multiplied those and got 2.89 e to the 18th power.

Now, what on earth does that mean? Or did I even do it right?
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posted
Your answer to the surface area seems to be wrong.

Google says 4 * pi * (156000000000/2)^2 = 7.64537988 × 10^22

Google also says (4*pi * (156000000000/2)^2) lightyear^2 is 6.84273714 × 10^54 m^2, or 6.84273714 × 10^48 kilometer^2

That means the universe is big.

Of course, it is also wrong. The universe probably isn't spherical (there's almost certainly been research on that). It also might not mean quite what it seems from physical analogues like balloons -- how does the boundary of the universe behave, after all?
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posted
The problem is you assumption that the Universe is Spherical. Modern thoughts range from Ovid to Donut Shaped. My belief is that it is a semi-quadra-hepta parralellagram Rhapiziod with 4 sides 2.756 times the length of the shortest side.

Or its in the shape of Marty Feldman's face.
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posted
i got the same surface area as fugu(in light years). My value in kilometers seems off from that one.
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posted
not necessarily. We may have the same surface area and yet completely out of proportion body types!!!
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posted
Nighthawk: you forgot to divide the diameter by two for the radius (edit: and you multiplied by two for some reason).

Using your kilometers per lightyear measure ( 4*pi*(9,460,730,472,580.8 * 156000000000/2)^2 ), the answer is the same as google's conversion until the third place after the decimal.

Btw, I suspect the initial answer is wrong due to overflow problems, since it is far too small.
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quote:Originally posted by Strider: not necessarily. We may have the same surface area and yet completely out of proportion body types!!!

Yes, I might have the same surface area as Cindy Crawford. Arranged in a more aesthetically pleasing way, of course.
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quote:Originally posted by fugu13: Of course, it is also wrong. The universe probably isn't spherical (there's almost certainly been research on that). It also might not mean quite what it seems from physical analogues like balloons -- how does the boundary of the universe behave, after all?

I'm aware of the debate regarding the size, shape, and consistency of the universe. This was more of a hypothetical "what if the Titanic never sank?" type scenario than an actual assumption that the universe is spherical. I probably should have made that clearer from the outset.

Your question about the boundary of the universe is an interesting one - I don't know. I imagine it is made of chedder, or perhaps something a bit fancier.

Also, fugu, that figure about what a light year meant was provided by Google, which, admittedly, is not the best resource for this kind of thing. Google is great for finding out how many husbands Britney Spears has had, bad for scientific accuracy. (NB: The figure is not squared; that was an oversight on my part.)

Which brings me to what Nighthawk said about Wikipedia not agreeing with Google, and makes me wonder if anyone has an actual scientific number for a light year? Both Google and Wikipedia are dubious.

quote:Originally posted by Dan_raven: Or its in the shape of Marty Feldman's face.

quote:Originally posted by mistaben: What exactly do you mean by diameter of the universe?

Well, I assume that the scientists who did the study were figuring that, given what we know about the big bang and the cosmic background radiation, the distance from either extending edge of the universe is the figure I gave you, which is pretty much the definition of diameter. However, if you want to go by the specific terminology from the site you linked, I think they were talking about "light travel time distance".
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posted
My question as to what you meant was more focused on this part of the sentence :

quote:A light year is . . .light years squared.

It doesn't much matter what value you pick, though, all the ones mentioned are close enough for horseshoes. You'll want to use the results of my computation, though, yours are not correct.

The boundary of the universe question is not quite so silly. What is outside the universe? Is it just 'more space' (if so, is it really outside the universe)? If it isn't, how do you go 'outside' the universe? If you can't, what happens when you try?

You also don't seem to quite grasp mistaben's point. There is no single 'distance from either extending edge of the universe'. When you're talking the sorts of velocities (and distances) we're talking, relativity matters a lot. Relativistic transforms are extremely real, and that the edges are not at rest relative to each other matters a lot.

The comoving distance is the closest to what they're talking about in the study.
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quote: The comoving distance from the Earth to the edge of the visible universe is about 46.5 billion light-years in any direction; this is the comoving radius of the visible universe.

Then they calculate the surface area of the observable universe using V=4/3 * R^3* pi But I think you're correct Satlin, it's R^2.

Also, they find problems with the 156 billion light year figure, although in your link I think that's a direct quote from an astrophysicist. And they say that 78 billion ly is just a lower bound of the size of the universe.

I have to go, NCIS is almost on. edit: of course fugu is correct.

posted
To be very fair, the universe we live in has 3 macroscopic spatial dimensions (and if string theory is correct, we may actually live in n spatial dimensions, where n is large enough to be intuitively absurd ;) ). Thus, if we live in a spherical universe at all, it wouldn't be a two dimensional sphere, but a 3 dimensional sphere.

To be clear, a sphere's dimension is NOT the size of the space it sits it, but rather the number of "coordinates" necessary to characterize a point in the sphere.

In other words, the "usual" (hollow) sphere is 2 dimensional because to name a point on it, I need simply tell you latitude and longitude.

So, again, if our universe is spherical, then it's a 3-dimensional sphere.

For those who care, the surface "area" of such a sphere of radius r (it's really a volume, though it plays the same role as area in this context) is 2*pi^2*r^3 (yes, I did mean to type pi^2).

Good luck trying to picture a 3-sphere - it sits comfortably in 4-dimensional space, but there is no way to crunch in into 3-space (for the math savvy, I'm saying there is no way to embed it into 3 dimensional space).
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posted
I think Satlin is going for the boring how-much-plastic-wrap-to-wrap-all-around-it definition of surface area
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quote:Originally posted by fugu13: I think Satlin is going for the boring how-much-plastic-wrap-to-wrap-all-around-it definition of surface area ;)

Agreed, but....

By that definition of "surface area", it's a kind of boring question to ask how much surface area the universe has (no offense intended to you, Satlin) - the answer in infinite in this case.

To see this, drop everything down a dimension. Consider "how-much-plastic-wire-to wrap- all - around a sphere". Clearly, if my plastic wire has no thickness, I'll need infinitely much.

I guess my point is that 3 dimensional objects don't have (a finite) surface area, as much as 2 dimensional don't have a (finite) length.

Now, you CAN ask about the surface area of the boundary of a 3-dimensional object, or similarly the length of the boundary of a 2 dimensional object. But there isn't a single model of the universe that I'm aware of where space HAS a boundary. So at least in all cases (that I know of) that physicists care about, the "surface area of the universe" isn't a very interesting question.
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posted
He's talking about the universe being three dimensional in the sense that a ball of clay has three dimensions, not that it is a three-sphere. A ball of clay can be wrapped in plastic wrap, and (ignoring the physical limitations, and the question of what the behavior at the boundary is, and a variety of other things), so could the universe.
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posted
A 2-D round thing (the set of all points on a plane equidistant from a point) is a circle. A point going along the circle would never find an end.

A 3-D round thing (all points in 3D space equidistant from a point) is a sphere. A 2D object embedded in the sphere, going around it, would never find an edge.

The universe is thought to be a 4-D round thing: a hypersphere. A 3D object like one of us, going through it, could never find an end to it.
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posted
Qaz: this is being considered in the sense of the extent of the universe in the three most noticeable physical dimensions, which we do have reason to believe there's a 2D-ish boundary for.
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posted
Actually, my question was just a lead-in and a way of thinking about a completely different problem. But you're right, it is misleading (see: boring) to talk about it like a tenis ball - mostly because of the reasons listed above.

I suppose a more interesting question would be, if the universe were a pizza, what toppings would it have?
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