Appendix
Equations and assumptions:
The latest estimate of the Age to of the Universe is 13.7 billion years (Gyr) +/- 10%. For convenience we calculate with an age of 14 Gyr.
Hubble's Law says that the redshift of remote galaxies is proportional to their distance from the Earth or from each other.
The Redshift z is defined as the increase in wavelength of the observed spectral line of the light from remote galaxies or quasars divided by the wavelength of the same line as observed on Earth.
Z
= Vr/C, where Vr
is the Radial Velocity
for a receding light emitter at the time when we observed its light. Vr
= 2 * ((to/t)
^ (1/3) - 1), and
C
is the
Speed of light. For simplicity I posit C
= 1 and Vr
in % of C,
thus canceling C out
in the calculations.
The
Distance r
is the time in billion years (Gyr) the light has traveled since it was emitted
till today. In my table it is simply (to
- t)
Gyr.
The
(Distance
Then) DT
= 3
* t *
((to/t)
^ (1/3) - 1)
Gly.
The
(Distance Now)
DN = DT *
Cpr
Gly. They are both explained
in the text.
The
Compression factor
Cpr = (z + 1).
Light emitted with a redshift z
= 1 thus had a Cpr of
2, meaning that the Universe was compressed to half its present size (see table
1).
The
Scale factor Rt
is the inverse of the Compression factor and shows the expansion of the Universe
as a function of time. Rt
= 1/(z + 1) = 1/Cpr,
and this leads to the Scale always being two-thirds power of time. This may be
written as Cpr
= (to/t)
^ (2/3)
where to
= 14 Gyr.
The Density parameter Ωo (Omega) is the ratio of the average density of the Universe to the critical density. I have posited the Ωo = 1, corresponding to a Universe which contains just enough matter to barely manage to expand forever, but is gradually brought to a standstill without ever recollapsing. This Universe is flat, it has no curvature. Today, the Density parameter Omega has become a very complex factor, but for our purposes we will keep it at Ωo = 1.
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