Our favourite guest blogger Chris Graney is back with a question. Busy translating the Disquisitiones mathematicae de controversis et novitatibus astronomicis (1614) of Johann Georg Locher, a student of Christoph Scheiner at the University of Ingolstadt, he came across a fascinating theory of orbital mechanics, which he outlines in this post. Chris’s question is how does this theory fit in with seventeenth-century force dependent orbital theories? Read the post and enlighten Chris with your history of astronomy wisdom!
Did Johann Georg Locher write something very interesting in 1614 about how the Earth could orbit the Sun under the influence of gravity? I am hoping that the RM and his many readers might be able to weigh in on this.
Who is Locher? He is the author of the 1614 Disquisitiones Mathematicae (Mathematical Disquisitions), an anti-Copernican book known primarily because Galileo made sport of it within his Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican. It is the “booklet of theses, which is full of novelties” that Galileo has the anti-Copernican Simplicio drag out in order to defend one or another wrong-headed idea. Galileo describes the booklet’s author as producing arguments full of “falsehoods and fallacies and contradictions,” as “thinking up, one by one, things that would be required to serve his purposes, instead of adjusting his purposes step by step to things as they are,” and as being excessively bold and self-confident, “setting himself up to refute another’s doctrine while remaining ignorant of the basic foundations upon which the greatest and most important parts of the whole structure are supported.” As far as I can tell, little is known about Locher himself other than what he says in his book: he was from Munich; he studied at Ingolstadt under the Jesuit astronomer Christopher Scheiner. This is the same Scheiner who Galileo debated regarding sunspots. Some writers treat the Disquisitions as Scheiner’s work.
I became better acquainted with the Disquisitions through Dennis Danielson’s work on Milton, in which it plays a part. This prompted me to look at Locher’s work directly. Then I discovered that Locher wields Tycho Brahe’s star size argument against Copernicus, that he illustrates the Disquisitions lavishly, and that the Disquisitions is short. So I decided to read and translate it cover-to-cover.
The Disquisitions turns out to be fascinating. It is nothing like what one might expect from reading the Dialogue. And among the gems within it is this thing that Locher thinks up:
Imagine an L-shaped rod, buried in the Earth, with a heavy iron ball attached to it, as shown in the left-hand figure below. The heaviness or gravity of the ball (that is, its action of trying to reach its natural place at the center of the universe—in 1614 Newtonian physics was many decades in the future; Aristotelian physics was the rule) presses down on the rod, but the rigidity of the rod keeps the ball from falling.
Now imagine the rod being hinged at the Earth’s surface (at point A in the right-hand figure below). The heaviness of the ball will now cause the rod to pivot about the hinge. The ball will fall along an arc of a circle whose center is A, striking the Earth at B.
Now imagine the Earth is made smaller relative to the rod. The same thing will still occur—the rod pivots; the iron ball falls in a circular arc (below left). If the Earth is imagined to be smaller still, the rod will be what hits the ground, not the ball (below right), so the ball stops at C, but the ball still falls in a circular arc whose center is A.
If you imagine the Earth to be smaller and smaller, the ball still falls, driven by its gravity, in a circular arc (below). You can see where Locher is going! He is thinking his way toward a limiting case.
At last Locher says to imagine the rod to be pivoting on the center of the universe itself—the Earth vanishing to a point. Surely, he says, in this situation, a complete and perpetual revolution will take place around that same pivot point A (fiet reuolutio integra & perpetua circa idem A).
Now, he says, we have demonstrated that perpetual circular motion of a heavy body is possible. And if we imagine the Earth in the place of the iron ball, suspended over the center of the universe, now we have a thought experiment (cogitatione percipi possit—it may be able to be perceived by thought) that shows how the Earth might be made to revolve about that center (and about the sun, which would be at the center in the Copernican system). But this sort of thing does not exist, he says, and if it did exist, it would not help the Copernicans any, because no phenomena are saved—that is, no observations are explained—by means of it.
Below is Locher’s sketch of this. Curves MN, OP, and QR are the surface of the Earth, being imagined smaller and smaller. S is the iron ball. A is the center of the universe. Circle CHIC is the path of the orbiting ball.
So it seems that in 1614 an anti-Copernican—a student of one of Galileo’s adversaries—proposed a mechanism to explain the orbit of the Earth, and that mechanism involved a fall under a central force. This is not the Newtonian explanation of Earth’s orbit, but it does have significant elements in common with Newton. And, Locher was definitely an anti-Copernican. Indeed, while he illustrates telescopic discoveries such as the phases of Venus, and states that the telescope shows that the world is structured according to the Tychonic system (sun, moon, and stars circle Earth, planets circle sun), he clearly rejects Copernicus—on the grounds of the star size problem (and the Copernican tendency to invoke the Creator’s majesty to get around that problem) and on the grounds that a moving Earth grossly complicates the motions of bodies moving over its surface.
The history of orbital mechanics is not my bailiwick, so I ask RM readers whether they think Locher is a “first”? Is this really as interesting as it seems to me? Or do RM readers know of others who proposed the “an orbit is a fall under a central force” idea prior to Locher? Whether I search in English or in Latin I can find neither primary nor secondary sources that discuss the Disquisitions’ treatment of orbits, nor can I find primary or secondary sources that discuss orbits and central forces in general prior to the late-seventeenth century. In fact, I can find little written on the Disquisitions itself (outside of its role in the Dialogue), and what I have found typically conflicts with what is actually in the Disquisitions (for example, one author describes the Disquisitions as a book “in which the proponents of Earth’s motion were violently attacked,” but actually Locher’s worst words are for Simon Marius, a fellow supporter of the Tychonic system, while his most favorable words are for Galileo). But many of you are much more well-read than I am.
My searches did turn up one interesting item, however. Locher uses the term forced suspension to describe what is going on in an orbit (motus huius continui caussa est violenta suspensio—the cause of this continuing motion is forced suspension) and I have found that term in what appears to be another seventeenth-century Jesuit’s commentary on the work of Thomas Aquinas.
With luck the translation of Disquisitions will be published in a year or so.
16 responses to “The orbital mechanics of Johann Georg Locher a seventeenth-century Tychonic anti-Copernican”
More treasures from Chris and RM. Any chance of a link to the full version of Chris’s paper cited just above the last image?
I find the size-of-the-stars argument a fascinating argument against the Copernican scheme, but I’ve been wondering whether the “invoking the Creator’s majesty” response from some Copernicans (mentioned by Chris in a few places) was truly an argument from religion. Since the basic nature of stars was not known at the time, could it be that the “majesty” argument was really the technical point that there was no known reason why stars had to be limited to a certain size, translated into the language of the day? I gather many supporters of the Copernican scheme were anxious to portray the model as in harmony with the Church (as much as possible), so couching arguments in religion-friendly terms seems a reasonable tactic if one is trying to convince the public as well as one’s peers…
Thanks for the paper Chris, excellent stuff. One is left hungry for more – what, if anything, was the Gal’s counterargument in the Dialogues? Or did he just ignore the issue? (His response is not spelled out in your article, as far as I can make out). If the Gal simply ignored the size argument, can we think of any conceivable scientific reason why he did so? Apologies if you’ve already written on this
Sounds a lot like Newton’s cannon. Maybe he was the first.
I’m going to answer Cormac’s star-size questions via e-mail, just to avoid filling up the comments with stuff on star sizes rather than Locher’s orbital mechanics. And yes, this makes me think of Newton’s cannon, too.
Much appreciated Chris and we’ll all look forward to the Locher book!
There is a problem with going to the limit of zero size and that is that the base of the ‘L’ shaped rod and the line from the centre of mass of the ball to the centre of the universe in the last diagram become coincident, so there is no rotational moment, but I think that you need calculus to prove that rigorously. The model he shows is not valid because in it gravity is not a central force (i.e. acting through a).
One fun thing is that the L shape of the rod is a red herring: it might as well be a straight line from A to the centre of the planet/ball S, or a spiral that coils around S like a watch-spring (assuming that the rod is perfectly rigid and has zero mass/weight, and ignoring the possibility of the rod hitting the surface of the planet on anywhere other than its pivot). Presumably Locher used the L shape because he was worried about S balancing on top of a straight rod pointed at the centre of S, or at least about readers coming up with that objection. But a) that would be an impressively unstable equilibrium when the the length of the rod or the size and weight of S become large enough relative to the friction in the pivot: a pin balanced on its point—with a planet stuck to its head! b) in any case you can avoid the unstable equilibrium while considering a straight rod by starting the example with the rod at a diagonal to the surface of the Earth rather than perpendicular c) just as you can *also* put the planet-on-an-L-shaped-rod into an unstable equilibrium by tilting it back so that the centre of S, A, and the centre of the Earth are aligned, and in fact this is the same arrangement of those three points at which the straight rod or any other possible rod is at unstable equilibrium *and* d) as you point out, as A and the centre of the Universe converge, then those three points converge towards being perfectly aligned no matter where you put S, let alone what the shape of the rod is.
(Of course all this is easier to see with the benefit of hindsight…)
Locher does get to saying that all sorts of shapes will work, so long as the ball is there.
Coming late to this party on my own blog I did have one thought on the topic. It is generally considered that Kepler was the first astronomer to consider orbits in term of forces rather that anima, earning him the dubious title of “the first astrophysicist”. He presents his ideas on orbital mechanics in both the Mysterium Cosmographicum and much more fully in the Astronomia nova complete with complex diagrams. It might be interesting to compare the presentation Kepler/Locher to see if the latter was in anyway influenced by the former. Scheiner, Locher’s teacher and the actual author of the Disquisitiones mathematical, was certainly well aware of Kepler’s work and was in fact the first to develop Kepler’s theories of vision further. It was Scheiner and not Descartes, as is usually claimed, who first proved empirically that the image in formed on the retina as hypothesised by Kepler and not in the lens as had been perviously believed.
Yes, it does seem very likely that “The heaviness or gravity of the ball” was conceived as “its action of trying to reach its natural place at the center of the universe—in 1614 Newtonian physics was many decades in the future; Aristotelian physics was the rule”. One of the things that may imply, is that there may have been no need, from a viewpoint inherited from Aristotelian physics, to invoke any other cause for the falling? The questions may in turn arise, did Locher nevertheless mention a cause of the falling? — and if he did, was that in terms of a force? — and if it was, is there any clue about what he meant by such a force?
In pre-Newton writing, ‘force’ seems to have been a rather unspecific concept, maybe something that produces swirling, something that produces velocity. Bruce Stephenson, for example, has interesting things to say about the nature of Kepler’s use of the idea of force (in ‘Kepler’s Physical Astronomy’).
Locher says things like “the points of the sphere [and rod] … continually press down toward A … their propensity to fall causes a force to be applied … They haul down on [the rod] and urge it to incline….” Or, that’s how I translated it.
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Thony – do you know whether Newton was the first to use velocity and acceleration as it still known today for most calculations?
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