This inquiry accurately provides an analytical solution of the orbital free-falling time for the system of galaxies Andromeda-Milky Way within a non-expanding tired-light-dominated framework. The mathematical and physical background involves a two-body problem based on the orbital dynamics in which, in the first scenario, the gravitational interaction between local galaxies dominates over the expanding space. The latter is the standard astrophysical approach undertaken by public fund-based universities all over the world. However, in the second alternative scenario, Andromeda’s blueshift has to be corrected for the apparent recession velocity provided by the photon energy loss as a result of multiple interactions between photons and crystallized electrons through the intergalactic medium provided by a Tired Light, specifically, a New Tired Light process. This leads towards a substantial temporal deviation between the classic research approach and this unconventional and independent mindset. Hence, the outcome gives out a disagreement consisting in an orbital free-falling time equal to 1.7 rather than 4.5 billion years. Accordingly, the encounter of the two main galaxies of the Local Group will occur much earlier than estimated thus far. Accordingly, this implies an urgent shift in the scientific mindset as well as a course change in the application of the boundary conditions into forthcoming computational methods.
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