Olbers's Paradox

Questions:

• Why is the night sky black ?
  
• Was the night sky always black ?
  
• What is the maximum distance that light from Our Sun will reach ?

Purpose

What is Olbers's paradox.

• Consider that the Universe is infinite.
  
• Consider that each Volume of space is filled with the same number of stars.
  

If both are the case then in whatever direction we will look, we will always see a star, implying that we will see (receive) light from all directions. This is Olbers's Paradox.

To solve Olbers's paradox, lies in the fact that the Universe is roughly 20 billion years old, implying that we will only receive light from a finite section of space, and that our sky can de dark.

Answer question 3

Answer question 1

A different type of answer is the following

1. Start from the following constants:
   

   Rgal = Radius of the disc of our galaxy = 60000 ly
   Dgal = Thickness of the disc = 2000 ly
   Rsun = Radius of the sun = 70000 km
   Mgal = Mass of our galaxy in M0 = 2*10^11
   Lightyear = 9460000000000 km

2. calculate the volume of our galaxy in ly.
   Volgal = pi * rgal * rgal * dgal

   Calculate the density of our galaxy in M0

   densgal = Mgal / Volgal

   Calculate the volume of R1 = 10 ly

   Vol1 = 4/3 * pi * R1^3

   Calculate the number of stars in this volume

   nsun1 = vol1 * densgal

   The above calculation is correct because densgal is in units M0

   Calculate the flat surface area of our sun

   areasun = pi * rsun * rsun

   Calculate the flat surface area of nsun1 within R1

   arean1 = nsun1 * pi * rsun * rsun

   This flat surface area indicates the size of the surface if you place all the stars (suns) side by side (together)

   Calculate the surface area of the sphere with radius R1 in km

   arear1 = 4 * pi * r1^2 * lightyear^2

   calculate the fraction in % of space covered by the nsun1

   fraction = arean1 / arear1 * 100 The following table shows the results in line 1

    Radius in ly             Mass in M0                 Fraction in %
1   10                       37.03703640980107          5.069791E-14 
2   100                      37037.03640980107          5.069791E-13 
3   1000                     37037036.40980107          5.069791E-12 
4   10000                    37037036409.80107          5.069791E-11 
5   60000                    7999999864517.031          3.041875E-10 
6   60000                    200000000000               7.604687E-12 
7   100000                   37037036409801.07          5.069791E-10 
8   2250000                  4.218749928553903D+17      1.140703E-08 
9   1.972467937253125D+16    2.842274938609421D+47      100 
10  2250000                  1000000000000              2.703889E-14 
11  10                       8.779149168944421D-05      1.201728E-19 
12  8.321349302006797D+21    5.058638978815996D+58      100 

The above table shows the following

1. Line 1 shows the results for R = 10.
   Column three shows that there are in that volume roughly 37 stars.
   Column four shows the fraction of space ocupied. This is very little

   Line 2 shows the results for R = 100.

   Line 3 shows the results for R = 1000.

   Line 4 shows the results for R = 10000.

   All those lines use the same density

   Line 5 shows the results for R = 60000 with that same density.

   R = 6000 is the radius of the disc of the galaxy.

   Line 6 shows the results for R = 60000 with a corrected density such that the mass is equal to the total mass of the galaxy.

   Line 7 shows the results for R = 100000.

   Line 8 shows the results for R = 2250000.

   R = 2250000 is the distance between Milky Way and Andromeda Galaxy.

   Line 9 shows the results when the whole sky is filled with stars.

   Column 2 shows that the radius is enorm

   Column 3 shows that the mass included is enorm, much more than all the two galaxies and the rougly 10 drawf galaxies in that space.

   Line 10 shows the values for the same radius as line 8, but now for a corrected density such that the total mass is 5 times more than the mass of the Milky Way.

   Line 11 uses that same density to show you how many suns there are within a radius of 10 light years.

   Line 12 uses that same density and shows the results when the whole sky is filled with stars.

   Both radius and mass included are enorm.

What line 12 shows that in order to have a night sky full of light you have to receive light from stars at enormous distances. It does not matter how long it takes.
The question now becomes will light from those enormous distances ever reach the earth (continuous)?
That is why I have included question 3.
IMO the answer is no.
IMO even if our Universe is infinite our night sky will be dark.

Reflection

Links about Olbers Paradox

1. Olbers' Paradox by Scott I Chase.
2. Olbers' Paradox by Scott I Chase. Select Item 8
3. Olbers' Paradox

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