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Original greek text.
AUGUST 2003
IMPORT
In this article I will try to present certain
calculations and simulations in PC of evolutionary course of universe.
It will be supposed from beginning I clarify in order to do not exist
misapprehensions, that the thoughts and the calculations constitute simple a approximate script As the is not scientifically
ascertained the rhythm of dilation of universe Ho in present but much more and
in the past. In the calculations I consider that for each time moment the
(billion years) is in effect To=1/Ho that as we will
see in the next unit for the astrophysics today it is a clue but is not precise.
RHYTHM OF DILATION
The rhythm of dilation you relate with
"regularly" the
Hubble (Ho). The inverted
commas enter As the even if is named regularly the Ho
it is sure that it is altered with the time.
It expresses the rhythm of dilation of space and it is the number of Km that grows in a
sec distance of Mpc (»30820824 * 10^15 Km).
In the classic kosmologjka' models, without kosmologjki' regularly, the time Hubble is a top limit of age universe, while
in the models with accelerating dilation it can be also smaller than the age
universe.
The price of Ho has been measured with enough ways last decades http:// www. geocities. COM / Area51 / Nebula /
3735/dates. html
http://
www. astro. uni - bonn. de / ~ dfischer / mirror / 249. html
http://
bicomnet. COM / ritchieobs
/ bpnlr55. pdf
Last measurements of NASA have
calculated that the Ho = 71 ± 4 Km / s
Mpc = 67-75 Km / s
Mpc. Changing the measurements of Ho in billions years of light (bly)
with the press To=1/Ho we calculate To=14,59-13,04 bly.
Reversely the age universe
(To) was measured in February
2003 in 13,7 ±1% of billion years of light (bly) =
13,563-13,837 bly that correspond in
Ho=72,108-70,68 respectively..
We observe therefore that the press To=1/Ho is in
effect today with a biggest percentage divergence 5%. This is the biggest
divergence and it is owed in our weakness to measure with bigger precision the
Ho. They are also important that the medium prices of measurements verify
almost the press.
Personally I believe that the divergence - if it exists - will be particularly
small something that will show that the script that we make does not abstain
from the reality. Also the script considers that the himself
was also in effect in the past. The likely deceleration past or the likely
acceleration present and the kampy'lwsi universe from
his mass-energy (that it changes age) do not influence in particularly
important degree the precision of press To=1/Ho.
As the universe is
homogeneous and isotropic in each point they practise
equal and opposite forces in the 3d space to all the directions. Consequently
does not have meaning the point to change his kinetic situation. In the 4d
space (with addition of dimension of time) things differ but do not know exist
proofs that we can use the dimension of time in applications of forces.
In every case I receive axiomatic the force of press To=1/Ho,
and continue with the calculations.
MAINER ATTRIBUTES OF DILATION WHERE TO=1/HO
1. I consider that what it should we are careful particularly they are that in
the dilation where To=1/Ho exists a particularly important attribute that we
will need below:
As we will see then the speed of removal 2 objects (B = S * Ho) remains constant
with the byway of time, As the in the press
that profit we have from the increase of distance (S), him we lose from the reduction of Ho .
Mathematics this is proved as
follows:
Be it initially distance of bodies A,V SAB the moment .
After time dt the
distance will have become SA'B' = SAB + Ho *
SAB * dt.
Initial speed was VAB = Ho
* SAB = (1/)
* SAB ==> SAB = VAB *
The final speed is VA'B' = Ho' * SA'B' = (1/(+ dt)) * ( SAB + Ho *
SAB * dt) =
= (1/(+ dt)) * ( VAB *
+ VAB * dt) = VAB * (+ dt)/(+ dt)) = VAB
2. it is obvious that in order to it is doubled the
size universe you require time that also
the running age (ph it will become double in 13,7 billions years).
As we see therefore the calculations
in the 3 units that follow receiving that
Age universe=To=13,7 billion years
Ho=1/To=71,38686 Km / s Mpc
Universe he is homogeneous and isotropic
Topical velocity of the bodies as for the space they are not taken into
consideration.
The speed of light you consider constant in all the
development universe.
The calculations become with simulation in computer with step of calculations
capable it ensures the precision of computers.
A. HORIZON of INCIDENTS No 2 (OS2)
I was lented
the title from the black holes. The subject is if exists the utmost limit, a
conceivable circular surface that a body or wave might not never reach in the
ground even if it is moved with the speed of light.
The law of Hubble
is B = S * Ho where:
B is the speed of removal of body that abstains distance S. (I point out here that for speeds of
dilation of space does not exist limit neither naturally the speed of light.
The theory does not limit the speed with which is only expanded the space, the
speed of bodies has superHor limit of - light -).
http://www.physicsû.gr/faq/quasardistant.html
In order to becomes B = c = 299,792 Km / sec should be removed distance:
S1 = c / Ho = 299.792 Km / sec / 71,38686
Km / s Mpc = 4199,54
Mpc.
In this distance all speed covers the light in time Dt,
so much is added because the dilation and consequently the distance that
remains it is covered she is same. Consequently the luminous beam appears that
it will not accomplish us approaches never. This is
specious but no true. With the byway of time Ho you become smaller and consequently
for constant distance S1 then S1 * Ho
become smaller speed c, so that
the luminous beam begins to approach also in particular accelerating as well
as S it will be decreased with
continuously increasing rhythms.
Of course because with the
S you decrease also the
Ho, the light can cover any distance, despite that nead
a huge but finite time..
In the beginning if the distance is bigger than S the light is removed.
Then however because the
Ho minimizes always also the interval that remains it slows down his dilation
it accomplishes the light it covers the distance.
They follow diagrams on distance 2S and 5S where appear the enormous years of
where nead
SPEED AND DIAMETER OF
UNIVERSE
Afterwards the season of inflation where it
existed very big rhythm of dilation began the season of dilation that we know
today. This became 15*10 -32 sec and the size universe was 10 cm.
http://www.bHols.susx.ac.uk/home/John_Gribbin/cosmo.htm
After universe it needs time those who also his age in order to it doubles tome'geco's toy(ph will become
double in 13,7 billions years) his speed that the moment was V=10 cm/15*10 -32
sec=(1/15)*1028 Km/sec. This is
also the biggest speed who of his removed points.
His rhythm of dilation was then Ho=1/t=1/15*10 -32 sec=2.05614*10 50 Km/sec *
Mpc.
Today the each Mpc increases at 71Km/sec the distance who of his removed points
is (1/15)*1028/71,38686 = 933,87868112796*1022Mpc =
3044444500,477*1022 years of light that are also the size universe.
DISTANCE of
EMISSION -Actual BODY THAT WE OBSERVE
In a body
that we observe today, exist 3 distances that him characterize.
1.I distance that it had from the ground when it emitted the
electromagnetic' radiation that we receive So
2.I distance that travel the light in order to reaches in the
ground P. Because the dilation of distance So at the
duration of travel S = c * t>So
3.I distance that you find the body today Snow. Obviously
Snow > S>So because the distance of that body is
always bigger than the distance of light and consequently the himself is in
effect for the dilation.
The 3 sizes
are calculated as follows:
1. So. Receiving that we go behind to the time Dt
(years) the distance So it increases at scetos*Dt isl the distance that covers the light in the Dt and is decreased with the dilation of distance, in the
time this (So*Dt/2)*Ho*Dt.
increase is Ds = scetos * dt-(So*Dt/2)*Ho*Dt
where scetos it is the distance in Km that cover the light in one year
Dt in years
Ho se Km/(Km*year).
The total
time is the total of Dt, dil t=S (Dt)
2. S After time t the light taxj'deyse S = scetos * t
3. Snow the Snow counterbalances with the initial distance of emission So plus the distance because the dilation in time t. Since
the speed of removal V(Km/year) as I showed is
constant and equal with Ho of emission (the moment of emission) * So
Snow = So + Ho of emission * So * t.
The
calculations became with step of 10 years going reversely to the time and
receiving price for the diagram each 100.000. 000 years. I want to stress here
that the step of calculations has been received with base possibilities of current
PCS so that they remove result in legitimate time. In any
case because the enormous time interval that you calculate the step of calculatHon it has very small effect. In the diagram
that follows we sea the same calculation for step 1,10,100
and 1000 years. We see that the difference is optically non-existent
In the next diagram you can see the result of
calculations
I have made 2 diagrams. In first appear also the 3 sizes So, S, Snow in order
to becomes perceptible the difference. In second
appear only the So, S in order to they appear better.
In order to we imagine
better the measurements as we imagine that we can freeze the time and measure
distances of emission and receptions in various moments.
That the So
curve is absolutely physiologic, and does not constitute any change of phase
universe. Do not forget that universe they were in the first stages
very small in size and consequently the beam of light that began ph 10.000.000
years afterwards the big explosion would be obligatory in small distance from
the matter of our solar system (then did not exist
neither ground neither solar system shaped).
We observe therefore that
the body that was more far when it emitted and reached his light in the ground
were roughly 4,76 10^22 Km (5,03*10^9 years of light)
far and emitted before 8,66 billons years. Naturally it is not who removed body
from what we see now, simply the light of other bodies that was older shorter
in the ground began initially to remove in order to they reverse then the
direction of their relative speed and they reach now the ground.
As second observation the older radiation that we receive (emission 380.000
afterwards the big explosion they were from matter that abstained then only
3,769 10^19 Km (3.986.570 years of light) and needed 12.999.620.000 years in
order to it reaches in the ground
The up diagram in order to it has usefulness it should we know the years that
the Snow or the years that travel the light. We you use the shift to red
(redshift) the radiation that you symbolize with z
It is in effect that 1 + z = Snow/So èz = snow/so-.
After I calculated the diagram that will give from z the years where travel the
light, and thus we can use this diagram in order to find the Snow, So.
The diagram is drawn and partially.
validakis Constantine
(konstantinos) 045518761
validakis@gmail.com