The existence of Neptune, the eighth and farthest known planet from the Sun in our solar system, was not initially known by direct observation. Instead, its existence was inferred through mathematical calculations based on the observations of Uranus, a planet closer to the Sun.
In the early 19th century, astronomers noticed irregularities in the orbit of Uranus. It seemed that the gravitational influence of another celestial body was causing perturbations in Uranus' path. Several astronomers independently began to calculate the position and mass of an undiscovered planet that could explain these perturbations.
One such astronomer was Urbain Le Verrier, a French mathematician. Using Newton's laws of motion and celestial mechanics, Le Verrier predicted the existence and approximate location of an unknown planet that could account for the observed deviations in Uranus' orbit. He communicated his predictions to Johann Galle, a German astronomer, who successfully observed and confirmed the presence of Neptune on September 23, 1846.
The discovery of Neptune through mathematical predictions and subsequent observation provided strong evidence for its existence. Since then, further observations and exploration, including space missions like Voyager 2, have provided detailed information about Neptune's composition, atmosphere, and moons.
Today, the existence of Neptune is widely accepted and confirmed through numerous observations, including direct imaging, spectroscopic analysis, and spacecraft flybys. Our understanding of the planet's characteristics, such as its size, mass, orbit, and composition, has been greatly enhanced through these observations, making Neptune a well-studied and recognized member of our solar system.