The expansion of the universe is so tiny that it is insignificant compared with local gravity. It would be like trying to factor in the gravitational pull of Pluto on an object as it falls from your desk to the floor; technically there would be a contribution, but it would have no meaningful effect.
And this doesn’t just apply to other stars within our galaxy; it applies to galactic clusters as well.
Universal expansion is only a meaningful thing on the scales between galaxy clusters. It happens on scales smaller than that but not to any degree that is worth caring about or is measurable, even over non-trivial timescales (at least for now).
No. Imagine space like a big piece of stretchable fabric. Our galaxy is a load of marbles in the center of this fabric. The weight of them all means they stretch the fabric and create a dent that keeps them all clustered together. Now very very far away from our load of marbles is another load of marbles creating its own dent and clustering together.
Now stretch that fabric from all sides. The clusters themselves don’t separate into individual marbles. However each cluster gets farther from each other.
That’s an analogue to what’s happening with space. The dent aka gravity in space that out planets and stars make keep us all together in one cluster aka galaxy. The same with every other galaxy. However the space between galaxies is being stretched farther and farther apart because there’s no gravity to hold them together.
No. Gravity keeps them from drifting off. Even nearby Galaxies are moving towards us because the rate of space expansion is so tiny on the small scale, It’s a bit like those travelators in airports. We have all done that thing where you walk backwards and appear to remain still, except in this case you are full on sprinting down the travelator. It slows you down a bit but won’t stop you reaching the other end.
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