Density is the amount of mass that exists in a given 3d volume of space. It means that a small object can be heavier than a larger object, like how a brick is heavier than a microwave-sized block of styrofoam.
The strength of gravity that any object exerts is due to how much mass it has. So when we want to find how much gravity something like a planet exerts, we don’t just consider the physical size of it, we have to consider how *dense* it is, aka how much mass is actually contained within it.
Strange things can happen with gravity if objects have a very very high density. We don’t experience them here on Earth, but they happen far away in outer space. If an object with consistant mass is crushed down to a small enough size, the density can get so high that the force of gravity also gets so high that there is a runaway effect that makes the object shrink down to practically nothing, much smaller than any particles like atoms that make up you or me. It still has the same mass, but the density is so unimaginably high that scientists consider it infinite. This is what exists at the middle of a black hole. Because such a strong force of gravity is contained within such a small space, it has very strange effects on the surrounding region of the universe. The gravity is so high that space and time are warped around the black hole, and even light beams cannot escape its pull.
Density is a measure of how much mass is within a 3-dimensional area. For example, water has about 1g per cubic millimeter.
Gravity is a function of mass, where an object attracts other objects based on the amount of stuff inside it.
But gravity is a fairly weak force, and the further away the second object is, the less gravity pulls it towards the first, larger, object.
So, when you take two objects with the same mass, but one is the size of the Earth and the other is the size of the Moon, then standing on this very dense moon will have more gravity than standing on the relatively less dense earth, because you are closer to the center of gravity.
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