Would Copernicus have been more convincing if he’d been more accurate?

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As a follow-up to yesterday’s post, I was won­der­ing if Copernicus would have been more con­vin­cing if he’d used ellipses in his model instead of circles. By using circles Copernicus had to use epi­cycles like Ptolemy, though not so many. Still, it gave the impres­sion that epi­cycles were neces­sary. If that’s the case then why not have a sta­tion­ary Earth as well? The dis­cov­ery that plan­et­ary motion would be bet­ter described by ellipses didn’t come about till Kepler’s work almost a cen­tury later. As far as the post title goes, I think Dr* T’s Theory #1 applies here: Any tabloid head­ing that starts ‘Is this.…’, ‘Could this be…’ etc. can be safely answered ‘No’

So my post title is a bit of a cliché, but the reason I’ve used it is that if the answer is no, then some­thing strange is hap­pen­ing. More accur­ate is less convincing?

The reason I think that is that Copernicus’ model wasn’t isol­ated from the rest of thought for that period. It used and built on a num­ber of assump­tions of the time. One of those ideas was the cre­ation of the uni­verse by a per­fect being. Another was the idea that a circle was a per­fect shape, derived from clas­sical geo­metry. By telling people the Sun was at the centre of the uni­verse and not the Earth, Copernicus was ask­ing people to make a big shift in their think­ing. A lot of people thought it non­sense. If he’d made the orbits ellipt­ical as well then many people who would have been will­ing to listen to Copernicus’ ideas would have balked at that, redu­cing his poten­tial audi­ence fur­ther. In terms of num­bers, the pop­u­la­tion of math­em­at­ic­ally minded people who could exam­ine his work was small enough already.

If he’d reduced the num­ber of ini­tial read­ers fur­ther, would his ideas have spread enough for oth­ers to pick them 50 years later? It’s impossible to say, but if Copernicus hadn’t given Kepler the idea of a put­ting the Sun at the centre of uni­verse, could Kepler have dis­covered it inde­pend­ently? It’s hard to say but, given how Kepler struggled with let­ting go of circles and using ellipses, I think it’s unlikely.

This is why I’m wary of his­tor­ies of sci­ence that are purely about who got it right and who got it wrong. Copernicus’ use of circles isn’t ‘right’, but it was neces­sary at the time.

I’ve «cough» bor­rowed the por­trait of Copernicus from Prof Reike’s page on Copernicus. It’s well worth vis­it­ing if you want to find out more about the astronomer.

You can read more about Kepler’s dis­cov­ery of the ellipt­ical path of plan­ets at:
Boccaletti 2001. From the epi­cycles of the Greeks to Keplerʼs ellipse — The break­down of the circle paradigm

10 thoughts on “Would Copernicus have been more convincing if he’d been more accurate?

  1. Rebekah Higgitt

    Thanks for these last couple of posts. I wanted to add though that, rather than, as you seem to sug­gest, Copernicus keep­ing circles to make his helio­centric ideas more pal­at­able to his audi­ence, it was his desire to bol­ster the clas­sical ideal of uni­form cir­cu­lar motion that led him to helio­centrism. His use of circles was not just “neces­sary at the time” but a fun­da­mental driver to the devel­op­ment of his the­ory — as, in fact, was his rev­er­ence for Ptolemy, on whose Almagest Copernicus mod­elled the struc­ture of De Revolutionibus.

    • Alun

      Thanks for adding that. I think that shows even more that set­ting up Ptolemy and Copernicus in oppos­i­tion to each other doesn’t work his­tor­ic­ally. I know that’s well-known to Renaissance his­tor­i­ans, but it’s sur­pris­ing how much of the pop­u­lar belief about this period is wrong. It reminds me I really need to get a copy of Gingerich’s “The Book Nobody Read”.

  2. Peter R.

    Just another point to make here. We know that ellipses are cor­rect, because Kepler even­tu­ally con­vinced every­one about it. But Kepler had avail­able a much lar­ger, and much more accur­ate set of data on plan­et­ary motions, com­piled by Tycho. It was only when cir­cu­lar orbits no longer matched the data, that Kepler aban­doned circles. Copernicus had only the data cur­rently avail­able at the time (and he made almost no obser­va­tions him­self). He simply reworked the cos­mo­lo­gical sys­tem to helio­centrism with the same data. The res­ult was pre­dict­ive mod­els just as accur­ate as geocentrism–very import­ant to make helio­centrism even plaus­ible from the stand­point of tech­nical astronomy.

    But the major objec­tions to helio­centrism since antiquity always had come from physics–how can we jus­tify a mov­ing earth, when it so vis­ibly appears sta­tion­ary to us? Accuracy or inac­cur­acy of the math­em­at­ical sys­tem played little role.

  3. Peter L. Griffiths

    The main motive for Kepler’s dis­cov­er­ies was to adjust the recor­ded obser­va­tions to take account of Copernicus’s dis­cov­ery that the Earth as the obser­va­tion point was not sta­tion­ary but orbited round the Sun.

  4. Peter L. Griffiths

    Further to my com­ment of 5 April 2011, how does Galileo fit into this? Galileo and Kepler were con­tem­poror­ies and were both in agree­ment with Copernicus, but Galileo did not agree with Kepler’s ellipt­ical orbits. However Galileo did dis­cover the law of fall­ing bod­ies v^2=d which can be incor­por­ated into Kepler’s sys­tem. The works of both Galileo and Kepler suffered from reli­gious pro­hib­i­tion, which explains even to-day why these works are not as well known as they should be.

  5. Peter L. Griffiths

    Further to my com­ment of 15 April 2011, the con­nec­tion between Galileo’s v^2=d at the empty focus end of the ellipt­ical orbit and Kepler’s v^2=(1/r) at the Sun focus end is math­em­at­ic­ally incred­ibly inter­est­ing and not at all straight for­ward. Kepler’s ver­sion can be adap­ted for fur­ther research pur­poses by includ­ing a con­stant V being the max­imum velo­city, then the vari­able velo­cit­ies can be expressed as V/#r where # is my nota­tion for square root. In this way the same velo­city arises on both the accel­er­at­ing side as well as the decel­er­at­ing side, but in oppos­ite dir­ec­tions. As one of the prop­er­ties of all per­fect ellipses d is the dis­tance from the curve to the empty focus, and r is the dis­tance from the curve to the Sun focus, d+r equals the major axis of the ellipt­ical orbit.

  6. Peter L. Griffiths

    Further to my pre­vi­ous com­ments, in about 1600 to 1603, Kepler wrote a paper which does not seem to be men­tioned among his lis­ted works. This paper con­tains the title Conic Section and is writ­ten in both Latin and German. What this paper con­tains is men­tion of pins and thread. This would indic­ate that Kepler knew about the way a per­fect ellipse should be drawn, even though the paper’s descrip­tion is not com­plete. Kepler does men­tion else­where that one of his biggest prob­lems was try­ing to recon­cile Apollonius’s conic sec­tion with the per­fect ellipse which is a cyl­indric sec­tion con­tain­ing foci.

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