How did Isaac Newton apply gravity to the paths of comets?

Isaac Newton applied his law of universal gravitation to comets by demonstrating that they, like planets, move in orbits governed by the gravitational attraction of the Sun.1

Specifically, Newton used his laws of motion and gravity to calculate the path of the comet of 1680. He showed that a body moving under a central force that varies inversely with the square of the distance follows a conic section—an elliptical, parabolic, or hyperbolic path—depending on its initial velocity. Because the observations of the time were not precise enough to distinguish between these shapes, Newton modeled the orbits of comets as parabolic.23

This application was a significant extension of his work on planetary dynamics, confirming that the same gravitational force operating on Earth and between planets also dictates the motion of comets as they travel through the solar system. His methods later allowed astronomers like Edmond Halley to predict the return of periodic comets by accounting for the gravitational perturbations exerted by massive planets.124