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A toolkit for working with natural units

by marcus
Tags: natural, toolkit, units, working
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May22-03, 06:58 PM
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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.

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

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