The Construction and Use of the general Table.As the Planets move in Elliptick Orbs, so do the Comets in Parabolick ones, having the Sun in their com… - Edmond Halley

Next to Ticho, came the Sagacious Kepler. He having the Advantage of Ticho's Labours and Observations, found out the true Physical System of the World, and vastly improv'd the Astronomical Science.
For he demonstrated that all the Planets perform their Revolutions in Elliptick Orbits, whose 'Plains pass thro' the Center of the Sun, observing this Law, That the Area's (of the Elliptick Sectors, taken at the Center of the Sun, which he proved to be in the common Focus of these Ellipses) are always proportional to the Times, in which the correspendent Elliptical Arches are describ'd. He discover'd also, That the Distances of the Planets from the Sun are in the Ratio [3:2] of the Periodical Times, or (which is all one) That the Cubes of the Distances are as the Squares of the Times. This great Astronomer had the Opportunity of observing Two Comets, one of which was a very remarkable one. And from the Observations of these (which afforded sufficient Indications of an Annual Parallax) he concluded, That the Comets mov'd freely thro' the Planetary Orbs, with a Motion not much different from a Rectilinear one; but of what Kind, he cou'd not then precisely determine.

All the Elements agree, and nothing seems to contradict this my Opinion, besides the Inequality of the Periodick Revolutions: Which Inequality is not so great neither, as that it may not be owing to Physical Causes. For the Motion of Saturn is so disturbed by the rest of the Planets, especially Jupiter, that the Periodick Time of that Planet is uncertain for some whole Days together. How much more therefore will a Comet be subject to such like Errors, which rises almost Four times higher than Saturn, and whose Velocity, tho' encreased but a very little, would be sufficient to change its Orbit, from an Elliptical to a Parabolical one.

Yet almost all the Astronomers differ'd from this Opinion of Seneca; neither did Seneca himself think fit to set down those Phænomena of the Motion, by which he was enabled to maintain his Opinion: Nor the Times of those Appearances, which might be of use to Posterity, in order to the Determining these Things. And indeed, upon the Turning over very many Histories of Comets, I find nothing at all that can be of Service in this Affair, before, A.D. 1337, at which time , a Constantinopolitan Historian and Astronomer, did pretty accurately describe the Path of a Comet amongst the Fix'd Stars, but was too laxe as to the Account of the Time; so that this most doubtful and uncertain Comet, only deserves to be inserted in our Catalogue, for the sake of its appearing near 400 Years ago.