How did scientists from before 1900’s measure the Earth’s weight and other planets/stars
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They didn’t really measure them. They calculated them using assumptions about density and mass. For example, if you know the diameter of the earth, and you make an estimate of its average density, you can calculate its mass. Of course, in the 1800s, they didn’t know what we do now. But even today, that’s how we calculate the mass of celestial objects.
Also, we can observe how other objects behave around the earth and other objects which allow us to deduce their mass.
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