The planet that takes the longest time to move around the sun is Neptune.

Here's why:

* Kepler's Laws: Kepler's Third Law of Planetary Motion states that the square of a planet's orbital period (the time it takes to orbit the sun) is proportional to the cube of its average distance from the sun.

* Distance: Neptune is the furthest planet from the sun in our solar system.

* Orbital Period: It takes Neptune approximately 165 Earth years to complete one orbit around the sun.