Our universe is rapidly expanding due to the constant emergence of a new space at every point in the universe. Thus, the farther the objects are from each other, the more space is formed between them every second, and the faster they move away from each other as a result.
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However, objects located at relatively short distances are attracted to each other strongly enough not to fly apart: the acceleration imparted to them by gravity is greater than the acceleration from the expansion of the universe, so most objects can quite come together, although the expansion of the universe affects the speed of this rapprochement.
Such objects include galaxies and their clusters, as well as increasingly smaller structures in the universe. So, for example, despite the expansion of the universe, our galaxy is approaching the Andromeda galaxy. This is because our galaxy and Andromeda are attracted to each o ther faster than the space between them has time to expand.
On the scale of planetary systems, the expansion of the universe in our time is almost imperceptible, as well as the distance between the planets, because it changes by a value that many orders of magnitude smaller than any equipment can detect.
Now, our universe is expanding with acceleration, and according to many cosmological forecasts, this will not change, which means that over time, the expansion will become significant both on the scale of stellar systems and even on the scale of atomic nuclei, at some point all these structures will simply be torn apart by the expansion of the universe.
This cosmological scenario is called the Big Rip. At the same time, according to scientists, the Big Rip will happen in about 22 billion years. Clusters of galaxies will decay about a billion years before the BR, galaxies – 60 million years before the BR, and planetary systems – just 3 months before the BR.
As for distance measures in modern physics, they are determined through physical processes and constants, independent of the expansion of the universe, so they do not change.