Neptune

Now that Pluto is considered to be a Dwarf Planet instead of a planet, Neptune is classified as the most distant planet from the sun.
Oddly, even while Pluto was considered to be a planet, there were times that Pluto (which has an extremely eccentric orbit) actually crossed the line of Neptune's orbit, making Neptune the outermost planet.
Though Neptune, like the other gas giants, is quite large compared to earth, Neptune's rocky core is probably about the same size as Earth.
Like the other gas giants, Neptune also has rings.
When scientists concluded that something was "messing up" the orbit of Uranus, they predicted that another (unknown) planet's gravity was disturbing the orbit. Calculations were done, and predictions were made. The result was that Neptune was discovered mathematically.