Why did Edmond Halley visit Isaac Newton at Cambridge in 1684?

In 1684, Edmond Halley visited Isaac Newton at Cambridge because he was troubled by the problem of orbital dynamics.1

At the time, Halley, along with Robert Hooke and Sir Christopher Wren, was attempting to find a mechanical explanation for planetary motion—specifically, what forces kept a planet in orbit around the Sun without it flying off into space or falling inward. Although Halley and his colleagues had reasoned that the force must decrease as the inverse square of the distance, they were unable to deduce a theoretical orbit that matched observed planetary motions.2

Upon visiting Newton, Halley learned that Newton had already solved the problem, determining that the orbit would be an ellipse. Newton, however, had mislaid his calculations. Encouraged by Halley, Newton expanded his studies, which eventually led to the publication of his masterpiece, the Principia.21