Dynamic-between-3-galaxies for an observer on one of them, in such case, on Milky Way.

     In the animation, we have seen galaxies P and Q, with the same Redshifts, moving away from Milky Way (Earth L) 
at deviation velocities com Vp = Vt . In the age of universe T1 = 5,66 billion years, such galaxies emitted light ray in direction of Earth that arrived at it in the actual age T = 13,7 billion years, in which such galaxies occupy the positions P and Q and the Earth occupies the position L .

     In the age T1 = 2,12 billion years, the galaxy Q on the position Q1? emitted a light ray in direction of galaxy P on position P1. Such ray has always increased in direction of  P at velocity c and it was dragged by the deviation velocity 
V_aq of galaxy Q.

    Both galaxies P and Q are at a constant velocity V_az of deviation between them. The light ray between them moves 
away from Q at velocity c and get closer to P at velocity c1 = c - V_az.

Interesting results in the calculus of spreadsheet of 3 galaxies

     1) When a galaxy is not located in the visible universe of the other one.

           We have chosen galaxies P and Q:

            The galaxy P CDFB: [SAG99] G05

                - Equatorial latitude: 12,134819
                - Equatorial longitude: 12,809164
                - Z = 4,486

      The galaxy Q CFRS 14.1166 G

          - Equatorial Latitude: 52,737567
          - Equatorial Longitude: 213,985087
          - Z = 1,0196

             Both galaxies P and Q are located in our visible universe; however, they are not in the visible universe of each other.

             Let´s use the spreadsheet of 3 galaxies:

            Where we have obtained the deviation velocities:

                  - Between L and P      Vap =  0,935683451
                  - Between L and Q     Vaq =  0,606204962
                  - Between P and Q      Vaz  = 1,295903128

            Let´s use the spreadsheet of visible universe (Va) between:

               - The Earth and galaxy P;

             - The Earth and galaxy Q;

             - Galaxies P and Q;

           Comments:

                We have seen that the spreadsheet of visible universe between galaxies P and Q provides the
        following results:

                     - x = 17,35 billion light years;
                     - R = Ray of visible universe = 13,7 billion light years, being x > R;

                 It means that galaxy P is not in the visible universe of galaxy Q and vice versa.

                    - Z = it was not calculated;

                 Because it is impossible the light of galaxy P arrives at galaxy Q and vice vers

                    - negative numbers;

                 Because the triangle LPQ does not close, since there is no light ray PQ that represents the
             side of triangle LPQ.

                    - Ho = 71,386861314 Km/s/Mpc.

                 Such result above proves that Hubble?s constant is valid for all galaxies in the real universe, 
            even being valid between galaxies that do not belong to the same visible universe.

     2) When the light of a galaxy arrives at another as a deep radiation.

         We already know that:

             - there is a deep radiation that arrive at us in all directions, in microwave frequencies that come from
         the limit  of our visible universe covering distances close to such visible universe´s ray, it means,
         R= 13,7 billion light years, at light´s velocity c;

                  - The universe has a uniform galaxies distribution;
                  - When, through telescope, we look at a galaxy, we are seeing it in the past, in the age <> T1 of 
                    the universe when the photons that arrive at us nowadays were emitted.

         Thus, we can consider a galaxy X located in the limit of our visible universe with:

         Galaxy P (X):

             - equatorial latitude 40 ,
             - equatorial longitude 175 ,
             - Z (<>Redshift) 280;

         and the galaxy (Q) CFRS 14,11666 with:

             - Equatorial latitude 52,737567?,
             - Equatorial longitude 213,985087?,
             - Z (Redshift) 1,0196.

        Using data above, for both galaxies in the Spreadsheet of 3 galaxies, we have:

        Let´s use the spreadsheet of visible universe, between: P and Q;

        - The Earth (L) and Q;

        - Earth (L) and P;

        Comments

              The spreadsheet of visible universe used between Earth and galaxy P(x) provides us the results:

                     - f = 1,3914545 x 1010 Hz;

              It means that light of galaxy P(x) arrives at us in the frequency of microwave.

                     - T1 = 349.478 years;

              It means that it represents the age that universe was when photons of galaxy P(X) were emitted. In
         such age, there was no galaxy P(X) yet, and therefore, the whole universe was composed of atoms,
         which means that photons were emitted by atoms that after would form the galaxy P.

                    - the combination of results above show us that, actually, the photons of galaxy P(X) that arrive
                      at us nowadays are a deep radiation.

Elaboration of spreadsheet of 3 galaxies for an observer located in one of them, in such case, in Milky Way  Earth.

 We already know that:

 - The light´s velocity:  [1]                                                     c = 1                                           - unit of velocity;
 - The age of universe: [2]                                                    T = 13,7                                       - billion light years;
 - The galaxy P: [3]                                                              name of  P = (CDFb : [SAG99] 605:
 - angle of latitude of 9 in equatorial coordinates: [4]               g. (Lat.) = 12,134619                    - degrees;
- We calculated the complement of such angle:?? [5]               g. (comp. Lat.) = 90 - [4]               - degrees;
 - angle of longitude of P in equatorial coordinates:[6]             g. (Long.) = 12,809164                  - degrees;
 - the Redhift of P: [7]                                                         Zp = 4,486;
 - The galaxy Q: [8]                                                            name of Q = (MUNICS S4F - 0230)
 - angle of latitude of Q with equatorial coordinates: [9]           g.(Lat.) = 0,095759                       - degrees;
 - We calculated the complement of such angle: [10]               g. (comp. Lat.) = 90 - [9]              - degrees
- angle of longitude of Q in equatorial coordinates: [11]          g. (Long.) = 48,697208                  - degrees;
 - the Redshift of Q: [12]                                                     Zq = 4,82
 - Let´s turn the equatorial coordinates into a Cartesian system (x, y and z):
 * P
[13] x
 [14] y
[15] z
 * Q
 [16] x
 [17] y
 [18] z
 * auxiliar distance PQ [19]

In such new system, we calculate the angle of directions between coordinates P and Q:

 [20] g. L Radian
 [21] cos L
 [22 ] ?g. L.

 We calculated:

 - [23] Deviation velocity between galaxies:

 between galaxies L and P:
 
[24 ]

 between galaxies L and Q:

 [25 ]

Triangle LPQ of sides xp, xq and xz :

      As the parameter T is the same for all sides in such triangle, knowing Vap, Vaq and also the angle L, we are able to calculate the deviation velocity between galaxies P and Q:
 [26 ]

      Now, as we already know the velocity of Vaq, Vap and Vaz , we can calculate, using the spreadsheet of visible universe, for observers located on galaxy L (Milky way ? Moon), P and Q, all data provided by such spreadsheet; even such data between P and Q that are galaxies that we can not access.

      Example:

     Data between galaxies:
      - L and P
        Vap = 0,935683451

     - L and Q
       Vaq = 0,942648054

      - P and Q
         Vaz = 0,605179942