If a distant galaxy were to suddenly disappear due to the expansion of the universe, the time it would take for someone on Earth to notice would depend on the distance between Earth and that galaxy, as well as the rate of expansion of the universe.
The expansion of the universe is typically measured by a parameter called the Hubble constant (Hâ‚€), which represents the rate at which galaxies are receding from us. Currently, the most accepted value for the Hubble constant is around 70 kilometers per second per megaparsec (km/s/Mpc), although there is ongoing scientific debate and refinements in its measurement.
Assuming a constant Hubble constant value, we can estimate the time it would take for the disappearance of a galaxy to be observed. Let's consider an example: if a galaxy is located 1 billion light-years away from Earth (which means the light from that galaxy took 1 billion years to reach us), and the expansion rate is such that the galaxy is moving away from us at a speed of 70 km/s/Mpc, it would take approximately:
1 billion light-years / (70 km/s/Mpc * 3.26 million light-years/Mpc) ≈ 15,267 million years
So, in this example, it would take approximately 15,267 million years for someone on Earth to notice that the galaxy has disappeared.
It's important to note that this calculation assumes a simplified model of the expansion of the universe and a constant Hubble constant, which may not accurately represent the complexities of the universe's dynamics. Additionally, there are other factors that could influence the visibility of a distant galaxy, such as the presence of intervening objects or the effects of gravitational interactions.