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Reading a question on the Worldbuilding SE site a minute ago about a trip to the other side of the galaxy flying by the supermassive black hole in the center of our galaxy, my immediate first thought was: "How silly, how do you plan flying by close and ever again escaping, that's not just some black hole, it's a black hole strong enough to hold together an entire galaxy".
Which led me to say: "Oh, wait a moment...", and here comes the question:
Is it (and if it is, how?), from everyday observation, plausible that there is indeed any such thing as Sgr A* at the center of our galaxy at all?
Earth rotates around itself and around the sun, and the sun orbits the center of the galaxy, in some kinda-elliptical but not alltogether trivial way. This means that I (and every object on Earth) rotate in some kind of semi-chaotic way, facing in every possible direction now and then. Inevitably, while standing on Earth's surface I will face "towards" the center of the galaxy at some point, and "away from" it at other times.
Now, that means one day the black hole's gravitation (which is strong enough to hold together a galaxy, so it is not as trivial as e.g. the Moon's or Mars' gravitation) would add to Earth's gravitation, and on another day it would pull the opposite way.
In other words, the weight of a constant-mass object should be very observably different on different days. That's apparently not the case, or someone would have wondered during the last couple of hundred years. What now?