# How does a parsec relate to the age of the univers?

1. Dec 21, 2008

### TalonD

The age of the universe is 13.7 gyrs. The distance to the CMB is 13.7 giga parsecs, maybe I don't understand what a parsec is. Can someone explain?

2. Dec 21, 2008

### mgb_phys

A parsec is a unit of distance 3 *10^16 m, or about 3,1 light years.
The distance to the CMB isn't really 13.7GPa - there isn't really a distance to the CMB.

At the start of the universe everywhere was at one point, as it expanded it cooled and after about 0.5M years it was cool enough for matter-radiation to separate, the CMB is the remains of that radiation. that was about 13.7Gyr ago and the photons have been travelling since then as the universe expanded, so they have travelled 13.7G lightyears (or around 4.2GPa) but that doesn't mean the CMB is that distance away.

3. Dec 21, 2008

### marcus

Heh... you might get several explanations. Here's wikipedia
http://en.wikipedia.org/wiki/Parsec

A parsec is 3.26 lightyears. Conceptually it goes back to 1838 the first determination of the distance to a star by a guy named Bessel, who used trig with the diameter of the earth's orbit as a baseline for a long skinny triangle. Or maybe it was HALF the diameter---something like that.

You know the surveyors trig technique where you measure out a baseline and then you sight a distant tree or marker from each end of the baseline, and the angle of bearing is just slightly different. The difference angle is called parallax.

You experience a parallax angle when you stretch your arm straight out and look at your thumb from now your left eye and now your right eye. In that case the baseline distance is the distance between your two eyeballs.

So you asked what is a parsec? It is the distance from which the radius* of the earth's orbit would subtend an angle equal to one arcsecond (that is 1/3600 of a degree)

*more precisely not the radius, because it's an oval, but half the major axis of the ellipse. It's also called an AU or astronomical unit.

Wikipedia has a diagram that makes it clear, so I won't belabor it. Parsec is short for PARallax angle equals one arcSECond.

If the distance between your eyes was one AU, and your arm was one parsec long, and you squinted at your thumb with one eye and then the other, your thumb would appear to jump by an angle of 1/3600 of a degree---that is by an angle of one arcsecond.

It is just an accident that a parsec is about 3.26 lightyears, and a meaningless accident that 13.7 times 3.26 equals 44.7 which is nearly equal to the 45 or 46 we give for the current distance to the matter that emitted the light we are now getting as CMB.

If the earth orbit had a different radius, or if the babylonians had divided the circle up into 490 degrees instead of 360 degrees. Or if Bessel in 1838 had used an angle measure different from seconds of arc (1/3600 of a degree), then the parsec would have turned out to be an altogether different distance

4. Dec 21, 2008

### marcus

Not exactly, but close. The CMB redshift is commonly given as 1090.
If you put z=1090 into Wright's calculator, it gives you the today distance to the matter which emitted the light we are now getting as CMB.
It says 45.65 billion LY, but you can round that off to 45 or 46.

OK strictly speaking that is not the "distance to the CMB". The distance to the CMB is zero, it is all around us. It is radiation and some of it is in this room.

46 billion LY is the distance to the MATTER that emitted the CMB radiation that we are currently receiving.

Technically, 46 billion LY is called the distance to the "surface of last scattering".

But as far as I'm concerned calling it "the distance to the CMB" is fine. I know what you are trying to say: the current distance to the source matter.

Now let's take 45.65 and divide by 3.26 to convert to parsecs. I get 14.00 billion parsecs. So I don't get 13.7 like you say, I get 14.0.
Either way it doesnt mean anything, just accidents involving an antique unit still used by astronomers, perhaps out of a sense of tradition.

Last edited: Dec 22, 2008
5. Dec 22, 2008

### TalonD

Here is another good explanation of parsec that I found
http://www.wisegeek.com/what-is-a-parsec.htm

Ok, now I understand what a parsec is. I had kind of an inkling before. so I wondered instead of light years how far away is the CMB in parsecs so I put into the google calculator 45 billion light years in parsecs and it gave the answer 13.7 giga parsecs. and of course I said wow, thats the same as the age of the universe. :P so just a wild coincidence, but I had to ask!

Marcus, I like what you said about the CMB haveing a distance of zero. Very well put. The only perception any of us have of anything is by our 5 senses. All of which require zero distance. It is indeed the matter that produced the CMB radiation that is now 45gly away approximately. But you knew what I meant. ;)

---- Merry Christmas everyone
or for those of you who don't believe... Merry big bang quantum fluctuations...

:)