Mass: How much there is (atoms) of something.
Density: How tightly packed the mass is. (atoms within a given space)
Weight: How strong the force of gravity is pulling on something. This is directly correlated with Mass of both the planet and the object, but not density.
Example: A rock vs a pebble of the same composition. Rock is bigger, so it has more mass, but they will have the same density. The rock will also weigh more than the pebble.
If we somehow squeeze the rock so it shrinks to the same size as the pebble it’s mass hasn’t changed, but it is now very dense, more dense than the pebble (more atoms in a smaller space).
Its weight, however, has not changed. The earth is still pulling on the rock the same as it had before, because the number of atoms in the rock hasn’t changed. The only way to change the rock weight would be to add or remove mass (atoms) from the rock OR move the rock to another planet with a different mass
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