The issue that does come into play where density is concerned is surface gravity.
The closer an object gets to the centre of gravity of a body, the greater the gravitational force exerted upon the object. If the earth was only one quarter its diameter (say about 2,000 miles � roughly the size of the moon) but retained its current mass (and so was much denser) then objects upon its surface would appear to �weigh� sixteen times as much. The gravitational effect increases inversely with the square of the distance from the centre of gravity. Objects on the �new� Earth would be four times as close to the centre than those on the �old� Earth, so the gravitational effect would be 4 x 4 = 16 times greater.
One of the effects of this is that the �escape velocity� from the earth would be much greater than at present. Escape velocity is that needed to escape the gravitational pull of the body and for the Earth it is about 25,000mph. From the �new� Earth it would rise to about 52,000mph.
This is the principle that leads to the conclusion that �Black Holes� exist. It is thought that their densities are so great (and so objects on their surface � if they could exist � would be so close to the centre of gravity) that the escape velocity would be greater than the speed of light. So not even light can escape the clutches of their gravity.