Final answer:
Halley's Comet is the first comet whose return was predicted by Edmund Halley using the mechanics developed by Isaac Newton. Halley's prediction came true after his death, resulting in the comet being named after him.
Step-by-step explanation:
The first comet whose return was correctly predicted is Halley's Comet. The prediction was made by Edmund Halley, who built on the work of his contemporary, Isaac Newton. Halley noticed that the comets observed in 1531, 1607, and 1682 had very similar orbits.
Using Newton's mechanics, he suggested that these comets were actually the same entity returning periodically and predicted its return around the year 1758. Despite Halley's death before the comet's return, its appearance validated his predictions, and as a result, it was named after him.
The comet's orbit is highly eccentric, with an eccentricity of 0.967, stretching to the edge of the solar system beyond Neptune's orbit. Through Halley's work and subsequent observations, the role of gravity in the motions of comets became better understood.