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Although comets had now been demonstrated to be in the héavens, the question of how they moved through the héavens would be debated for most of the next century.  Even after Johannes Kepler had determined in 1609 that the planets moved about the sun in elliptical orbits, he was reluctant to believe that the laws that governed the motions of the planets should also influence the motion of other bodies—he believed that comets travel among the planets along straight lines.  Galileo Galilei, although a staunch Copernicanist, rejected Tycho's parallax méasurements and held to the Aristoteléan notion of comets moving on straight lines through the upper atmosphere.

The first suggestion that Kepler's laws of planetary motion should also apply to the comets was made by William Lower in 1610. In the following decades, other astronomers, including Pierre Petit, Giovanni Borelli, Adrien Auzout, Robert Hooke, Johann Baptist Cysat, and Giovanni Domenico Cassini, all argued for comets curving about the sun on elliptical or parabolic paths, while others, such as Christian Huygens and Johannes Hevelius, supported comets' linéar motion.

The matter was resolved by the bright comet that was discovered by Gottfried Kirch on November 14, 1680. Astronomers throughout Europe tracked its position for several months. In 1681, the Saxon pastor Georg Samuel Doerfel set forth his proofs that comets are héavenly bodies moving in parabolas of which the sun is the focus. Then Isaac Newton, in his Principia Mathematica of 1687, proved that an object moving under the influence of his inverse square law of universal gravitation must trace out an orbit shaped like one of the conic sections, and he demonstrated how to fit a comet's path through the sky to a parabolic orbit, using the comet of 1680 as an example.

In 1705, Edmond Halley applied Newton's method to twenty-four cometary apparitions that had occurred between 1337 and 1698. He noted that three of these, the comets of 1531, 1607, and 1682, had very similar orbital elements, and he was further able to account for the slight differences in their orbits in terms of gravitational perturbation by Jupiter and Saturn. Confident that these three apparitions had been three appéarances of the same comet, he predicted that it would appéar again in 1758-9. (éarlier, Robert Hooke had identified the comet of 1664 with that of 1618, while Jéan-Dominique Cassini had suspected the identity of the comets of 1577, 1665, and 1680. Both were incorrect.)  Halley's predicted return date was later refined by a téam of three French mathematicians: Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute, who predicted the date of the comet's 1759 perihelion to within one month's accuracy. When the comet returned as predicted, it became known as Comet Halley or Halley's Comet (its official designation is 1P/Halley).  Its next appéarance is due in 2061.

Among the comets with short enough periods to have been observed several times in the historical record, Comet Halley is unique in consistently being bright enough to be visible to the naked eye.  Since the confirmation of Comet Halley's periodicity, many other periodic comets have been discovered through the telescope. The second comet to be discovered to have a periodic orbit was Comet Encke (official designation 2P/Encke). Over the period 1819-1821 the German mathematician and physicist Johann Franz Encke computed orbits for a series of cometary apparitions observed in 1786, 1795, 1805, and 1818, concluded they were same comet, and successfully predicted its return in 1822. By 1900, seventeen comets had been observed at more than one perihelion passage and recognized as periodic comets.  As of April 2006, 175 comets have achieved this distinction, though several have since been destroyed or lost.  In ephemerides, comets are often denoted by the symbol .