It is supposed that dark matter is the source of extra gravity which cannot be traced to detectable sources. Fact is however that **there is no extra gravity at all**. Scientists applied irrelevant Newton’s Theorem XXXI to the galactic rotations and observed that actual effect of gravity was greater than what could be calculated using Theorem XXXI.

But
Theorem XXXI was applicable to systems like solar system or planet moon
systems. **For the galactic settings,
Newton had another Theorem XXXIII and scientists terribly missed to apply the
actually relevant Theorem**. In case Theorem XXXIII is applied, then calculated gravity
would reasonably tally with observed gravity and there will be no need of dark
matter. And it is to be noted that Theorems XXXI and XXXIII are different
variations of Shell Theorem. [i]

[i] https://zenodo.org/record/3530781#.XdalQ9UzbIU

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