Problem with RHO(m) {now}
Chalky
I am currently attempting to tabulate the correlations (and/or lack
thereof)
between the predictions of my own derived system of field equations
(which includes "Chalky's Law"), with the latest WMAP data at
http://lambda.gsfc.nasa.gov/product/map/dr3/pub_papers/fiveyear/cosmology/wmap_5yr_cosmo.pdf
(Table 1)
However, I currently have a problem with converting their given values
for the allegedly physically meaningful values for Omega_baryon*
hsquared, and Omega_cold* hsquared,
given my current understanding that Omega_baryon* hsquared +
Omega_cold* hsquared = Omega_m* hsquared,
where h = H_0/100 (expressed in units of Km/s/Mpc
AFAICT conversion to a genuinely physically meaningful value for RHO
(m) {now} in gm/cc involves somewhat convoluted reasoning along the
the lines described in the below copied comment field for the
unsuccessful translation.
Unfortunately, however, thatconversion function results in a value
for RHO(m) {now} which is 2 orders of magnitude lower than the
generally accepted value of ~ 2.5 x 10^-30 gm/cc, (but excellent in
all other respects).
Obviously I have made an order of magnitude blunder somewhere, but,
for the life of me, I cannot tell where.
(Either because I am exceptionally thick, or because my nose is
currently so close to the grindsone, that I can no longer tell the
wood from the trees [or the sparks from the fire])
Can anyone help?
The explanatory notes for the (2 Order Of Magnitude) failed function
follow
Notes on table compilation
1)
Converting Ho in Km/s/Mpc to H in SI (and MKS) units is
X 1000 / (Mpc to Metre conversion factor of 3.08568025E+22 metres)
So, converting h = Ho/100 will be
X 10 / (Mpc to Metre conversion factor)
Therefore, converting Omega*h*h will be
X 100 / Mpc to Metre conversion factor / Mpc to Metre conversion
factor
But we still have the problem that we then still have to multiply by
critical density/H/H = 3/(8piG) to get a physically meaningful actual
matter density in kg / cubic metre
Consequently, we have to multiply the given values of Omegahsquared by
300/(Mpc to Metre conversion factor)/(Mpc to Metre conversion factor)/
8/pi/G
to obtain the physically meaningful result in SI units of Kg / cubic
metre
However, this is still not the end of the conversion difficulty,
if we wish to express that matter density in the more conventionally
expressed units of gm/cc
Since 1 gm=1Kg/1000
and 1 cubic metre = 100*100*100 cc ,
The resultant answer in Kg / cubic metre must be multiplied by 1000
to get the answer in gm/cc
Thus, the given figure of Omegahsquared for "physical" matter density,
must be multiplied by
300,000/(Mpc to Metre conversion factor)/(Mpc to Metre conversion
factor)/8/pi/G
to get the correct determination of matter density (in gm/cc) from the
published data of the quoted reference
Obviously, the logic of that conversion function is wrong, but why?
Chalky
> Since 1 gm=1Kg/1000
> and 1 cubic metre = 100*100*100 cc ,
>
> The resultant answer in Kg / cubic metre must be multiplied by 1000
>
> to get the answer in gm/cc
Actually, this is wrong. It should be DIVIDED by 1000 to get the
answer in gm/cc
However, this just makes matters even worse, because I then end up
with an EIGHT order of magnitude error
Consequently, the error MUST be that
to convert from Omega*h*h to Omega*H*H you have to MULTIPLY by 10,000,
not divide.
God, I hate this unconventional units shorthand of astrophysicists,
but at least I have now finally got to the correct answer.
Oh No
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)