May 16, 2016
In this work, we will assume that the recessional velocities of galaxies observed from our location can be explained by a shell expanding away from the center with a centralized mass located at the center of our universe. We will assume that the mass in the shell has a constant linear rest density. At this time we do not know whether there is actually a significant mass at the center. We will allow for a mass at the center to test whether the assumption is true. We will derive the equations for the acceleration inside a shell, we will give the equation for the acceleration caused by a centralized mass and allow the acceleration and make it symmetrical with the acceleration within the shell. In the acceleration equation there are two constants. One of these two constants relates to the linear rest density and the other to the mass at the center. Both of these constants are invariance in the Lorentz’s transformation. After obtaining the rest equation for our model we will boost the equation derived for the shell model to a sub-light velocity. The volume density would change as the universe expand; however, the linear rest density would remain constant. We obtained a reduce velocity equation that is a function of the thickness of the shell and the radius at an arbitrary point within the shell and the two constants defined above. We derived the reduced recessional velocity as a function of the parameters in the reduced velocity equation with an angular dependency.