A toolkit for working with natural units

marcus

The temperature of the CMB and its dipole have been measured with great accuracy, see for example Lineweaver, Tenorio, Smoot et al
http://arxiv.org/PS_cache/astro-ph/pdf/9601/9601151.pdf
"The Dipole Observed in the COBE DMR Four-Year Data"

The CMB has a hotspot in Leo and a coldspot 180 degrees opposite Leo. See this picture:

http://aether.lbl.gov/www/projects/u2/

The dipole is 3.358 millikelvin----that is how much hotter it is in Leo over the average. And how much colder is the coldspot on the opposite side of the sky, in Aquarius.

The overall CMB temperature is 2.726 kelvin.

If you are limited to metric units you probably should know the speed the solar system is moving relative to CMB in meters or kilometers per second. It is our motion relative to the cosmic rest frame so it is sort of a basic thing to know about the universe. Think about how you would calculate it, if you havent already. Its real easy even in metric.

In natural units our speed, in the Leo direction, relative to the Hubble flow or the CMB (however you think about it) is
1.23E-3---------1.23 thousandths of the speed of light

You calculate it merely by dividing 3.358 mK by 2.726 K.
It is simply the ratio of the two temperatures.
And it is clearly 12 times the earth's orbital speed (E-4) around the sun, so the position and size of the dipole are essentially uneffected by the earth's orbital motion (it has only a small percentagewise effect).
It is an absolute velocity. Cosmology is not like Special Relativity where there are no absolute velocities. Cosmologists have a preferred rest frame given by the expansion of space.[:)]

The COBE researchers (Lineweaver et al) gave the direction of the dipole in galactic coordinates (264 degrees, +48 degrees)
and in celestial coordinates (11 h 12 m, -7.22 degrees)
These were given in much higher precision, with confidence intervals but I have rounded off for easy writing. This confirms that the direction of the hot spot and the solar system's motion is in Leo. A figure for our speed relative to CMB that they give is (quoting verbatim)
1.231 +/- 0.008 x 10^-3 This agrees with the 1.23E-3 which I calculated earlier.

marcus

I just went out into the garden and there was a lot of light---and some things flying around pollinating the fruit trees or whatever they do. And I thought of the Income Tax Form called the "Ten-Ninetyone"
Because ten-ninetyone is the occupancy of space by sunlight.

There are 10^-91 photons per unit volume of sunlight at this distance.

It is clear because 10^-119 is the solar constant and the average energy per photon is 10^-28 and one subtracts 28 from 119 and gets 91. Trivial arithmetic.

How many photons are in a cubic meter, if you like working with them?

So if I want to know the photons per cubic mile I just multiply by the cube of E38, which is E114, and get (since 114 - 91 is 23)
that there are E23 photons in a cubic mile of sunlight.

Or if I'm looking at a square pace of ground---E35 by E35---and wonder how many photons would impinge on it in a minute---E45---in vertical sunlight....Then I just add those exponents---E115---and multiply by the occupancy "ten-ninetyone" number E-91. That tells me E24-----a trillion trillion---photons would land on that square patch of ground in a minute.

Oh, E45 is 54 seconds, so only 9/10 of a minute. Had better add it to the dictionary.

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Here's the current dictionary:

E60-----1.7 billion years
E45-----9/10 of a minute
E44-----a million miles
E38-----a mile
E35-----a pace
E6 ------22 grams
E-50----1.2 micronewtons

Here's the list of constants etc, for review:

the proton compton wavelength----2.103E-14 meter---13E18
the CMB temperature-----2.725 kelvin----------1.93E-32
the Hubble time----4.35E17 seconds------------8.06E60
average sunlight photon----2E-19 joules----------E-28
the distance to the sun----150 million km---------93E44
earth orbit speed------30 kilometer/second--------E-4
solar constant----1380 watts/sq.meter------------E-119
2.701k----3.73E-23 joule/kelvin-------------------2.701
sigma-----5.67E-8 watt/sq.meter kelvin⁴--------pi²/60
a (the aT⁴ law)---7.565E-16 joule/cub. meter kelvin⁴---pi²/15