Which from scratch? (group survey)

[marcus]

I'd like to take a poll to see how inclined to hands-on calculation we are, collectively, at cosmo forum.

Generally speaking what I mean from scratch is from basic numbers most of us know like 71 and 0.73
(estimated current Hubble rate H = 71 km/s per megaparsec and
current dark energy density = 0.73 of the critical energy density need for flatness)

If you want, try some of the calculations and respond to the poll later.
The poll is multiple answer, so you can recall several things you've calculated and check them all off.
The abbreviations in the poll are informal and intended to be self-explanatory.
That's basically it, but here's some more detailed explanation if desired:
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My idea is we probably all remember at least some quantitative facts about the universe such as
The current Hubble rate is 71 km/s per megaparsec
The current dark energy density is about 0.73 of crit (or 73% of estimated total)
Space is nearly flat. (That's usually enough to remember but in rare cases when you need a numerical handle you could express it by saying the current total density is less than 1.018 crit at 95% confidence.)
CMB temp is 2.728 kelvin and its redshift is 1090.

What features of the universe do you know how calculate from scratch? From scratch here means mostly from the numbers 71 and 0.73. Plus any other basic stuff you happen to remember, but in the poll concerns mostly what you can get just from those two numbers. And which features have you in fact actually calculated from scratch recently? I'd like to get a reading on how hands-on our group is, calculation wise. If you haven't done much of this recently you might be rusty and you might want to take a few minutes to get fluent again. In other words see what you can do, before you answer the poll. It's a multiple answer poll, so if you calculated several things you can check them all off.

The Google calculator is a great help with this kind of cosmo calculation because it takes care of units like "megaparsec" and you can specify what units you want the answer in. It also knows some fundamental constants like G, which can save a lot of bother.
Here some explantion of some of the shorthand abbreviation.
HUBBLE TIME---the Hubble time is 1/H--so you type "1/(71 km/s per megaparsec) in years" into Google and it gives the time in years

HUBBLE RADIUS----the Hubble radius c/H is the current distance of objects receding at speed c----"c/(71 km/s per megaparsec) in light years"

RADIUS OF CURVATURE (minimum, 95% conf)---This is the minimum radius of curvature according to the latest WMAP report, at 95% confidence level. It is the radius of the 3-sphere which space would be if it did turn out to have a slight positive curvature and was therefore finite volume. Calculating is easy, just HUB RAD/sqrt(.018). The number 0.018 represents the curvature and the smaller the curvature the bigger the radius of curvature. Zero curvature means flat-out infinite.

VOLUME OF SPACE (minimum, 95% conf)---This is the minimum estimated spatial volume corresponding to the minimum estimated radius of curvature---it is the volume of a 3-sphere of the given radius: 2 pi² (RAD CURVE)³

CRITICAL DENSITY---the usual formula for the total energy density needed for spatial flatness: 3c²H²/(8 pi G)

DARK ENERGY DENSITY----The dark energy density is 73% of the critical density: 0.73 CRIT

deSITTER RADIUS----This gives a good estimate of the cosmological event horizon: c²/sqrt(G DARKE)

COSMIC MICROWAVE BACKGROUND STUFF---self explanatory, anything you calculated from 2.728 kelvin and 1090

OTHER----let us know about other basic cosmo calculations you've done that only need a few basic numbers as input.

 

[marcus]

For people who enjoy calculating basic quantities for themselves rather than getting them out of a handbook or Wikipedia, calculating can be good context for learning why some particular formula.

In each case, you are invited to figure out why the formula offered here is the right one (if there's an error please tell me ). If it's clear to you, fine. Otherwise you are cordially invited to ask, and get it explained.

To take a rudimentary example (in case you're not already familiar with calculating Hubble radius), take a look at the formula c/H

Hubble law essentially says that for any distance D, the recession rate v of a stationary object at that distance is given by v = HD. That's the definition of H. The Hubble radius is defined as the distance at which objects are receding at rate c. So we find it by setting c = HD, and solving for D. In other words, D = c/H

The Hubble law is a regular pattern of increasing distances. Another way to define Hubble radius is as that distance which is increasing at rate c. I know, it's a dumb example. But some of the other formulas have more interesting explanations. So if you use them make sure you understand them. I expect I'll explain a few more over the next couple of days, and anyone else is welcome to jump in and explicate.

Anyway, you can calculate c/H in a minute by typing "c/(71 km/s per megaparsec)" into Google. The only catch is that it might give you the answer in meters, and it is a lot of meters. We aren't used to seeing it expressed in meters. So you can tell Google to present you with the answer in lightyears. You just type in
"c/(71 km/s per megaparsec) in lightyears"