 Complete the following phrase:  Halley spent most of his time on lunar observations, but was also interested in the problems of gravity. One problem that attracted his attention was the proof of Keplers laws of planetary motion. In August 1684, he went to Cambridge to discuss this with Isaac Newton, much as John Flamsteed had done four years earlier, only to find that Newton had solved the problem, at the instigation of Flamsteed with regard to the orbit of comet Kirch, without publishing the solution. Halley asked to see the calculations and was told by Newton that he could not find them, but promised to redo them and send them on later, which he eventually did, in a short treatise titled On the motion of bodies in an orbit. Halley recognised the importance of the work and returned to Cambridge to arrange its publication with Newton, who instead went on to expand it into his Philosophiæ Naturalis Principia Mathematica published at Halleys expense in 1687. Halleys first calculations with comets were thereby for the orbit of comet Kirch, based on Flamsteeds observations in 16801681. Although he was to accurately calculate the orbit of the comet of 1682, he was inaccurate in his calculations of the orbit of comet Kirch. They indicated a periodicity of 575 years, thus appearing in the years 531 and 1106, and presumably heralding 