Why do the planets that are closer to the sun have a higher density?

Answer 1

They don't. In our own solar system this is at best only approximately true. Each of the four inner planets is more dense than any of the four outer planets, but comparing the planets in order from the sun outward, the relationship between them goes:

* Merury is more dense than * Venus, which is less dense than * Earth, which is more dense than * Mars, which is more dense than * Jupiter, which is more dense than * Saturn, which is less dense than * Uranus, which is less dense than * Neptune. So, of the possible ways to choose neighboring planets, the inner one is more dense than the outer one in only 4 of 7 cases. Statistically this is no different from what would be expected had they been chosen entirely at random.

It was believed until fairly recently that the inner/outer planet division happened because planets near a star (relatively speaking) would be too hot to retain much gas, so inner planets would be terrestrial (high density) and outer planets would be gas giants (low density). The discovery that "Hot Jupiters" not only exist but seem to be fairly common has cast doubt on previous notions, and it's possible that it will turn out that the way our own solar system is arranged is simply a coincidence.