I have no idea where you got the idea that "Modern Materialistic Science" is even a thing, but regardless, a single disproof is not how scientific theories are overturned. When a theory is challenged because it fails to explain an observed phenomenon for which it should have an explanation, a crisis occurs. As a direct result of this crisis, new hypotheses are proposed, and experimentation results in a new theory, which must explain everything that the old one did, in addition to the phenomenon that caused the crisis. Science is not a uniform gradual process, but rather a series of somewhat abrupt paradigm shifts, for example when perturbations in Mercury's orbit created a crisis for Newtonian mechanics. Thomas Kuhn explained this broader process in his book titled The Structure of Scientific Revolutions, which is one of many books that I recommend everyone read.
I'm not touching the issue of dark matter or dark energy for the simple reason that neither are actually part of General or Special Relativity, despite being connected. For all we know, what astrophysicists call "dark matter" today may very well be the same elusive substance called "aether" in the 19th century. Mathematically speaking, something must be out there, we simply don't know what it is. String Theory is also a hypothesis, not an actual theory, and it is not widely accepted.
Astrology cannot be "disproven," for the simple reason that the claims it makes are unfalsifiable. An unfalsifiable claim is a logical fallacy, and therefore cannot be the basis of any scientific theory. For this specific reason, Critical Race "Theory" is also unscientific bunk.
The Earth may not be a perfect sphere (its diameter varies by several times the height of Mt. Everest), but it's definitely not a disc. I'm a pilot, though I haven't flown in a few years, so I could prove that the Earth is vaguely ball-shaped quite easily. I'm also a shooter, and in long-range shooting (>1000 metres), the Coriolis Effect noticeably changes a bullet's trajectory, so it must be compensated for. @galenkp could probably explain precisely how this works better than I can. Then again, I wouldn't even need to go through all that trouble to prove that the Earth is round. Simply go down to the shore and watch the ships for a while.