Who discovered each planet in the solar system, and when did they discover it?
Some of the planets have been known to people for as long as they have been watching the stars. Mercury, Venus, Mars, Jupiter and Saturn can all be seen with the naked eye, so it's impossible to say who was the first human to discover them, and when that was!
Uranus was discovered by William Hershel on March 13, 1781. He was searching the sky with his telescope, and realized that Uranus was moving with respect to the stars. Other people had seen Uranus before--even marked it on their star charts--but they didn't realize that it wasn't a star.
Based on small perturbtions in the orbit of Uranus, John Adams and Urbain Le Verrier predicted the position of another, more distant planet. Though John Adam's prediction was first, by about a month, the observers Johann Galle and Heinrich Louis d'Arrest used LaVerrier's position, and were the first people to observe the planet Neptune--and know what they were looking at--on September 18, 1846. Again, many people had seen Neptune before, including, surprisingly, Galileo Galilei, who noted a "star" in the field during his observations of Jupiter, which we now believe was actually Neptune.
Pluto (now a dwarf planet), was discovered by Clyde Tombaugh on February 18, 1930. He found it in a location predicted by apparent perturbations in the orbit of Neptune. However, we now know that Pluto is too small to cause a measureable change in Neptune's orbit, and that the "perturbations" were actually just errors in the measurement of the positions of the planets, so Tombaugh was just lucky.
Here is an excellent article about how mathematics and the laws of physics were used in the discovery of the outer planets.
This page updated on July 18, 2015.