# What Kepler and Newton really did.

This has been a good week[1] for people getting the history of astronomy in the seventeenth century wrong. Darin Hayton drew my attention to what is basically a rather good article by John O’Neil in the New York Times on the equation of time and the difference between local time measured by the sun and standard time measured by the clock. The article is just fine except for one sentence that instantly awoke the Histsci Hulk in me.  The author wrote:

The changes in the solar time follow a different cycle. In the early 1600s Kepler discovered that planets move faster at the part of their orbit that is closest to the sun, the perihelion. For Earth, perihelion comes a little after the winter solstice, so from November on, Earth is accelerating. [my emphasis]

Kepler didn’t discover that planets (actually in the case under discussion the sun) move faster in some part of their orbits he suggested a new, and as it turned out correct, solution to explain the differences in speed in the various segments of planetary orbits; a phenomenon that had been know about for at least two thousand years.

In what follows I will mostly talk about the sun. In ancient Greek astronomy explanations of the suns apparent progression throughout the year were governed by the so-called Platonic axioms. All celestial motion including planetary motion, and the sun was considered to be one of the seven planets, was circular and uniform. These axioms as the name suggest go back at least to Plato in the fourth century BCE and probably to Empedocles in the fifth century BCE. The only problem was that planetary motion was obviously neither circular nor uniform. The major problem of Greek astronomical thinking was therefore to fit the observed facts to the a priori theory rather than to develop a theory to fit the facts. This has become know as saving the phenomena. Already in the second century BCE Hipparchus knew, and he probably wasn’t the first to do so, that the seasons measured from equinox to solstice and from solstice to equinox differed in length, whereas if the sun’s orbit were truly circular they should be equally long thus demonstrating that if the segments were equally long as the circular orbit demanded the speed of the sun during its orbit must vary i.e. it was not uniform. Over the centuries various Greek astronomers came up with various geometric models to explain away this anomaly peaking in the epicycle deferent model of Ptolemaeus in the second century CE. This model being further modified, that is improved, by various Islamic astronomers in the Middle Ages. Then along came Johannes!

Using the new more accurate data of Tycho Brahe Kepler, after much calculation and even more soul searching, abandoned the Platonic Axioms and determined the planetary orbits to be ellipses and not circles and the speed of the heavenly bodies to be non-uniform but to follow his second law of planetary motion. As stated above didn’t make the discovery that the speed of planets vary during their orbits he just found the correct explanation for it.

What exactly Kepler did or didn’t do cropped up in another post this time on Chad Orzel’s Uncertain Principles blog. Chad wrote a nice post about the relative merits of theoretical and experimental physics, basically complaining correctly that people tend to underrate experimental physics. The misconceptions about seventeenth century astronomy turned up in the comments column. Commentator Peter Morgan wrote:

I suppose there is a difference between Ptolemy, Copernicus and Kepler that is not much connected to experiment, which are largely different models for more-or-less the same experimental data (that is, all models depend on there being data *to* model, but sometimes there are different models for more-or-less the same data). Even Newton didn’t have that much more experimental data to work with; new data mostly came after him, when it was partly his theories that gave physicists the tools to imagine and construct new apparatus.

This is of course fundamentally wrong as was pointed out to him by Steinn Sigurdsson:

Kepler had Brahe’s data, which was a qualtitative improvement on previous quantifications. Newton most certainly had access to new experimental data, notably that of Kepler and Galileo, but Halley! Newton also did his own experiments, eg in optics.

To add to the fun Eric Lund decide to have his tuppence worth:

@Peter: Your argument about Ptolemy vs. Copernicus might be granted, but by the time Kepler started looking at things, Galileo had disproven Ptolemy’s model–Galileo, using the recently invented telescope, observed phases of Venus that Ptolemy’s model predicted would never occur. And as Steinn points out, Kepler had new data that were not available to Ptolemy or Copernicus–data which in fact disproved the notion (adhered to based on philosophical arguments) that the orbits of celestial bodies were necessarily circular. Without Kepler’s data analysis, Newton probably would not have come up with the inverse square law.

Taken together the three statements contain quite a few errors, which I will now attempt to correct.

Firstly seventeenth century astronomical theory isn’t based on experimental data but on observational data, which isn’t really the same thing. Steinn is perfectly correct to point out that Kepler had a completely new set of observational data, supplied by Tycho Brahe, on which to base his theories; a fact that separates him from Ptolemaeus and Copernicus. The data however does not, as Eric claims, disprove the notion of circular orbits. If Kepler had kept to the Platonic Axioms he could have, using Tycho’s data, provided circular models to save the phenomena. His obsession with accuracy led him to abandon the Platonic Axioms when he realised he could get a better fit with ellipses, a move that cost him an immense amount of soul searching. If he had had a more advanced set of mathematical tools (Fourier Analysis!) he could have obtained exactly the same level of accuracy with an epicycle deferent model.

Turning to Newton we have from all three commentators a lot of confusion concerning the data and theories available to him when he wrote his Principia.

Peter is of course wrong as Newton did have substantially new data, which I will explain in a minute. Steinn is wrong as he did not have any experimental data from Kepler but he did have Galileo’s theory of parabolic motion, his laws of fall and the law of inertia, which he falsely believed came from Galileo. These are theories and laws derived from experimental data but not in themselves experimental data. The data that Newton had and which were central to his theories was that on the orbits of the moons of Jupiter and Saturn. Although Galileo and Marius had supplied the original data on the moons of Jupiter, Newton’s source on both sets of moons was the much more up to date and accurate data of Cassini. Newton of course also had access to the new and considerably more accurate observational data of John Flamsteed.

The data on the orbits of the moons of Jupiter and Saturn provided empirical proof of Kepler’s third law of planetary motion, something that Newton explicitly states in the Principia, this law playing a central role in Newton’s argumentation for his theory of universal gravity, of which more in a minute.

Eric Lund muddies the water with his claim that Galileo’s observations of the phases of Venus (Ptolemaeus’ theory also predicts phases for Venus but they are different to the ones observed) were carried out before “Kepler started looking at things”. Kepler did the work on his Astronomia Nova containing his first two laws of planetary motion between 1600 and 1606 although the book itself was first published in 1609. Galileo, Harriot and Marius first started astronomical telescopic observations in 1609 and the first publication of such observations was Galileo’s Sidereus Nuncius in 1610. It’s difficult to date exactly but the first observations of the phases of Venus are later than the publication of the Sidereus Nuncius.

Also as should be well known to diligent readers of this blog Newton didn’t “come up with the inverse square law”, as claimed by Eric Lund. That honour goes to Ismael Boulliau. I think I’ve probably said this before but its worth repeating Newton’s great achievement was in showing that under the assumption of his three laws of motion the inverse square law of gravity implies Kepler’s third law and under the same assumption Kepler’s third law implies the inverse square law of gravity, i.e. the inverse square law of gravity and Kepler’s third law are, under this assumption, equivalent. As Kepler’s third law had been proved to be empirically valid, remember those Jupiter and Saturn moons, it follows that the law of gravity is also (empirically) valid.

Given that the story of the so-called astronomical revolution is probably the most often told and repeated piece of the history of science I find it sad that even educated people mostly have a very vague and largely inaccurate idea of what actually took place.

[1] I actually wrote this post a couple of weeks ago and have only now got round to posting it. There are a couple of others in the pipeline, too.