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Science can no longer claim planets cannot influence one another
Scientists do not claim this, though. The scientific argument is that the planets do not influence us. I would say any argument that they might is that other planets can influence climate on earth and the Moon has an influence on things like the ocean waves and has been implicated in incidents such as increases in police activity. There used to be a legal defense known as "lunar defense" during full moons.

Personally, I do not believe the planets, beyond maybe the moon, exert influence on us but their patterns seem to show events in our lives and we are somehow connected to one another. I see astrology and the patterns of movement of the planetary bodies sort of like a weather forecast. A weather forecast predicts, but it doesn't cause the weather to do anything.

Also, planetary bodies influence each other all of the time via gravitational force, so it isn't a new concept that they influence each other in some capacity.