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One piece of evidence that is supposed to show that dark matter exists is the rotation curve diagram. Apparently Fritz Zwicky used the Viral Theorem to make a prediction which does not fit with the measured data.

How do we actually measure the masses of far away stuff (Galaxies, suns etc.) in order to compare it to the theory?

Also, why did Fritz Zwicky use Newton (and his notion of gravity as a force) instead of Einstein (and his notation of gravity as curvature)?

Edit: In case any answer uses Newton or Kepler: Why can you apply it instead of General Relativity?

Edit: This questions seems to be dublicate where the main answer seems to be Gravitational lensing. So is this the only legit method that is used at all times?

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