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Mass can be determined either by weight or by inertia. Weight is how much force gravity exerts on it. Inertia is how much force is needed to accelerate it a given amount. Neither of these are affected by vacuum. In fact, it is easier to determine weight in a vacuum, because you don't have to worry about taking buoyancy in air (how much it "floats") into account. If you meant a zero gravity or freefall situation instead of a vacuum, then the inertia is still exactly the same and you can determine mass that way.

Posted
How do we determine mass in a vacuum?

 

That is easy! m=0. A vacuum is a space with nothing in it and nothingness has no mass. :P

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