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We may not be able to measure their weight because of the lack of significant gravitational pull, but they still have mass.

This means that they will have momentum, since p (momentum) = mass x velocity. Going at the same speed, the elephant, having more mass, will have much more momentum. Because momentum must always be conserved, when the elephant bumps into you, it will have more effect than the mouse, as more momentum will transfer to you. The elephant bumping into you will send you careening away with more velocity than if the mouse bumped into you in space.