Why wasn’t Newton’s Principia the end of the gradual emergence and acceptance of a heliocentric astronomical model for the then known cosmos? There is not one simple answer to this question, but a serious of problems created in different areas all of which had still to be addressed if there was going to be an unquestioned acceptance of heliocentricity. Some of those problems were inherent in the Principia itself, which should best be viewed as a work in progress rather than a finished concept. In fact, as we will see, Newton carried on working on improving the Principia over two further editions, expanding and correcting the first edition. Other problems arose in the philosophical rejection of key aspects of Newton’s work by highly influential and knowledgeable detractors. Finally there were still massive unsolved empirical problems outside of the scope of the Principia itself. These sets of problems run chronologically parallel to each other some of them all the way into the nineteenth century and beyond so in dealing with them I will take each one in turn following it to its conclusion and then return to the starting point for the next problem but first I will sketch in a little bit more detail the problems listed above.
To begin with we need to look at the reception of the Principia when it was first published. On a very general level that reception can be viewed as very positive. Firstly there were only a comparatively small number of experts qualified to judge the Principia, as the work is highly technical and complex. There is a famous anecdote of two men observing Newton walking in the gardens of Trinity College and one says to the other, “there goes a man, who wrote a book that is so complex that even he doesn’t understand it.” However, those, who could and did understand it all, acknowledged that the Principia was a monumental piece of mathematic physics, which had no equal at that time. They also acknowledged that Newton belonged to the very highest levels both as a natural philosopher and mathematician. However, both the Cartesians and Leibnizians rejected the whole of Newton’s work on fundamental philosophical grounds and as we will see it was a long uphill struggle to overcome their objections.
Of course the biggest obstacle to the general acceptance of a heliocentric system was the fact that there was still absolutely no empirical evidence for movement of the Earth, either diurnal rotation or annual rotation around the Sun. This was of course no small issue and could not be dismissed out of hand no matter how convincing and coherent the model that Newton was presenting appeared to be.
The final set of problems were astronomical ones that Newton had failed to solve whilst writing the Principia, open questions that still needed to be answered. There were two major ones the succeeding history of which we will examine, comets and the orbit of the Moon. As we will see showing that the orbit of the Moon obeys the law of gravity proved to be one of the biggest astronomical problems of most of the next century. In the 1680s Newton had only managed to show that the comet of 1680/81 had rounded the Sun on a parabolic orbit and extrapolated from this one result that the orbits of all comets obeyed the law of gravity. This was an unsatisfactory situation for Newton and it was here that he first began his programme to revise the Principia.
For what might be termed project comet flight path, Newton engaged Edmond Halley, who following his efforts as copyeditor, publisher, financier and midwife of the Principia became Newton’s lieutenant and most loyal supporter and one of the few fellow savants, whom Newton apparently never fell out with. Halley willingly took on the task of trying to determine the flight path of comets other than the 1680/81 comet, already included in the 1st edition of Principia.
Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons
Starting around 1695 Halley began searching for and collecting observation data on all of the comets throughout history that he could find. Having acquired enough raw data to make a start he set about analysing it in order to try and determine flight paths. In the 1680s Newton had been the first astronomer to develop a technique for determining the flight path of a comet given three accurate observations at equal or nearly equal time differences. However, the method that he devised was anything but simple or practicable. Using his data he created a geometrical, semi-graphical plot of the flight path that he then iterated time and again, interpolating and extrapolating producing ever more accurate versions of the flight path. This method was both difficult and time consuming. Halley improved on this method, as he wrote to Newton, that having obtained the first three observations he had devised a purely numerical method for the determination of the flight path.
Halley started with the comet of 1683 and found a good fit for a parabolic orbit. This was followed by the comet of 1664, recognising some errors in Hevelius’ observations, and once again found a good fit for a parabolic orbit.
The Great Comet of 1664: Johann Thomas Theyner (Frankfurt 1665) Source: Wikimedia Commons
At this point he first began to suspect that the comet of 1682,
which he had observed, was the same as the comet of 1607, observed by Thomas Harriot, William Lower and Johannes Kepler,
David Berlitz, Von dem Cometen oder geschwentzten newen Stern, welcher sich im September dieses 1607. Source
and the comet of 1531 observed Peter Apian amongst others.
Halley’s Comet 1531 Peter Apian Source
He also in his correspondence with Newton on the topic began to consider the problem of perturbation, that is deviation from the flight path caused by the gravitational attraction of Saturn and Jupiter, as a comet flew passed them. Neither Halley nor Newton succeeded in solving the problem of perturbation. In 1696 Halley held talks at the Royal Society in which he presented the results of his cometary research including his belief that the comets of 1607 and 1682 were one and the same comet on an elliptical orbit, which would return in 1757 or 1758.
Over a period of ten years Halley calculated the orbits of a further twenty comets presenting the results of his researches to the Royal society in 1702. Following his appointment as Savilian Professor for Astronomy at Oxford in 1705 he published the results of his work in the Philosophical Transactions of the Royal Society, Astronomiae cometicae synopsis, and also as a separate broadsheet, with the same title, from the Sheldonian Theatre in Oxford.
An English translation, A synopsis of the astronomy of comets, was published in London in the same year. This work contained a table of results for twenty-four comets in total. Over the years Halley continued to work on comets and a final updated version of Astronomiae cometicae synopsis in 1726.
In his work Halley emphasised the problem inherent in working with inaccurate historical observations. Newton used some of Halley’s results in both the second and third editions of Principia.
Diagram of Halley’s orbit in the Solar System Popular Science Monthly Volume 76 Source: Wikimedia Commons
Halley would have been one hundred and one years old in 1757 meaning he had little chance of seeing whether he had been correct in his assumptions concerning the comet from 1682; in fact he died at the ripe old age of eight-five in 1742. A team of three French mathematicians–Alexis Clairaut (1713–1765), Joseph Lalande (1732–1807) and Nicole-Reine Lepaute (1723–1788)–recalculated the orbit of the comet making adjustments to Halley’s results.
Alexis Claude Clairaut Source: MacTutor
Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons
Taken from Winterburn The Quite Revolution of Caroline Herschel see footnote 1
The comet returned as predicted and was first observed on Christmas Day 1758 by the German farmer and amateur astronomer Johann Georg Palitzsch (1723–1788).This was a spectacular confirmation of Newton’s theory of gravity and Halley’s work. The comet was named after Halley and is officially designated 1P/Halley. It is now know that it is the comet that appeared in 1066 and is depicted on the Bayeux tapestry
Bayeux Tapestry depiction of Comet Halley in 1066
Halley comet in 1066 after emergence from the sun rays artist unknown Source: Wikimedia Commons
and it was also the comet observed by Peuerbach and Regiomontanus in 1456.
Comet Halley 1456 artist unknown Source: Wikimedia Commons
Comet Halley 1456 a prognostication!
It still caused a sensation in 1910
An image of Halley’s Comet taken June 6, 1910. The Yerkes Observatory – Purchased by The New York Times for publication. Source: Wikimedia Commons
The Renaissance Mathematicus 
The comment of the “two men” about the Principia apparently originates from Newton, who related it as something a student said as Newton passed him in the street: “there goes a man that writt a book that neither he nor any body else understands”.
Wasn’t there at least a tiny bit of evidence for a heliocentric system in the retrograde motion of Mars, Jupiter, and Saturn?
Of course I would agree that that was completely swamped by the obvious fact that the Earth is plainly standing still and neither spinning at a thousand miles an hour nor zooming thru space at seventy thousand miles an hour. 🙂
Of course, in fact that heliocentricity offers a very rational explanation for retrograde motion of the planets was one of Copernicus strongest arguments. However, a Tychonic geo-heliocentric model also explains retrograde motion
Thank you for this as I do admit that comets have always fascinated me. I do wish I could have imaged those great comets. They are certainly spectacular.
Here is link some may find of interest to Halley´s Book on Comets which can be either read on line or downloaded.
https://archive.org/details/synopsisofastron00hall