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Another factor that reduces the impact suffered by any GC going through the plane of the galaxy is that it is so thin. So for the millions of years it may take a cluster to go around the galaxy once, only a very tiny amount of this time will be spent under the potential influence of stars in the parent galaxy. Sort of like the rings of Saturn, they are very thin and consist mostly of nothing. Any effects caused by stars interacting with the galaxy would be fleeting at best, gravitationally or otherwise.
It would be interesting to know if any GCs have been found actually inside the galaxy and just passing by? Statistically I would expect this would be very unlikely for the reasons above.
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