The concept of tracing the trajectories of galaxies backward to determine the location of the Big Bang is based on the idea that the universe is expanding uniformly. However, this is not the case. The expansion of the universe is a complex phenomenon, and it is important to clarify a few key points.
First, the expansion of the universe does not involve galaxies moving through space like objects on a cosmic conveyor belt. Instead, it is the space itself that is expanding between galaxies. The galaxies themselves can have their own motions due to other factors, such as gravitational interactions with neighboring galaxies.
Second, the expansion of the universe is not uniformly distributed. It is described by a concept called the "metric expansion of space," where the space between galaxies (or any two points) increases over time. This expansion is often visualized using the analogy of an inflating balloon, where dots on the surface (representing galaxies) move away from each other as the balloon expands.
Given these factors, it is not possible to simply trace the trajectories of galaxies backward to pinpoint the exact location of the Big Bang. The Big Bang is thought to have occurred approximately 13.8 billion years ago, and our current understanding of the universe's evolution is based on various lines of evidence, including the cosmic microwave background radiation, the abundance of light elements, and the observed distribution of galaxies.
While we can use observations of the universe's expansion to estimate the age of the universe and the rate of its expansion, determining the precise location of the Big Bang requires more intricate calculations based on the principles of general relativity and the early universe's conditions. These calculations involve sophisticated models and theoretical frameworks that are still actively researched by cosmologists.
In summary, tracing the trajectories of galaxies backward alone is insufficient to determine the actual location of the Big Bang, given the complexities of the universe's expansion and our current understanding of its evolution.