Although it is not really accurate to say that Uranus, Neptune, and Pluto were discovered by accident, fortuitous circumstances contributed to the discovery of each of the outer planets.
Uranus and Neptune are so similar in mass, diameter, and rotation rate that they are often called "twin planets." Their axial tilts, however, are very different. Neptune's is similar to the Earth's, but Uranus's is so great that its pole lies almost in its orbital plane.
Uranus is a nearly featureless blue sphere, whereas Neptune shows banded structure, bright clouds, and storm systems. The difference between the appearances of the two planets is caused by the lack of convection in the atmosphere of Uranus and the presence of convection in Neptune's atmosphere.
The interiors of Uranus and Neptune probably consist of rocky cores surrounded by thick shells of a fluid mixture of rock and ice. On top of that are relatively thin envelopes rich in hydrogen and helium. The two planets apparently were less effective than Jupiter and Saturn in gathering thick envelopes of hydrogen and helium while they formed.
Neptune is significantly self-luminous, whereas Uranus is not. It seems likely that Uranus, like Neptune, has a hot interior but that heat is unable to escape easily.
The magnetic fields of Uranus and Neptune are about one hundred times stronger than the Earth's magnetic field but about one hundred times weaker than Jupiter's. Moreover, Uranus's and Neptune's magnetic fields are tilted with respect to their rotation axes, and offset from the centers of the planets. The current theory is that the magnetic fields are generated by currents in the icy shells of Uranus and Neptune rather than in their cores.
The ring system of Uranus consists of thin rings of large particles separated by regions filled with fine dust. Neptune has two thin rings and a broad inner ring, all made of very small particles. The arcs in Neptune's outer ring are probably caused by the gravitational influence of Neptune's satellite, Galatea.
Pluto and its satellite, Charon, are locked in synchronous orbits with periods of 6.4 Earth days. The orbital period and distance of Charon made it possible to show that Pluto is smaller and less massive than our Moon. The density of Pluto suggests that it is made of a combination of ice and rock.
It was once thought that Pluto was an escaped satellite of Neptune. Now, however, it seems unlikely that Pluto could have been ejected from Neptune's satellite system without separating it from Charon and giving Pluto escape velocity from the solar system.
Despite a number of searches and attempts to find gravitational perturbations, no solar system planets beyond Pluto have been found. There may be additional planets, but if they are as dim and as small as Pluto, they may escape detection for a long time.
