How do we measure the mass of galaxies?

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One of the most common explanations for dark matter I’ve heard goes something like this: we can measure the mass of galaxies by either how fast stars orbit their galactic center, or by how much matter we can “see” in each galaxy. But measuring mass by orbital velocity gives a much higher estimate for a galaxy’s mass than the second method, therefore there must be a bunch of mass we can’t see (i.e. dark matter) to account for this difference. I understand how orbital velocity can be measured by blue/red shift, but how do we measure mass just by “seeing” it? How do we know there isn’t just some ordinary matter in galaxies that we can’t see (like a diffuse gas or something)?

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