Copernicus' measurements

Hi Jeff,

Am on holiday at the moment, so can't reply in great detail... but Venus is certainly visible whilst the Sun is still above the horizon.

You need to choose your time carefully... just before sunset, or just after sunrise (depending on the position of Venus in its orbit). It should be possible to measure the angular separation of Venus from the Sun, and from that determine when greatest elongation takes place.

Mike.

Jeff, with a great question like that, you should be in the Flamsteed. (Now where did I put those membership forms???)

Hi again Mike and Andy

Thanks for that! I will now scour the tables for next time this daylight appearance of Venus occurs.  If anyone knows anything about Copernicus' methods to do this that would be great. Enjoy your holiday Mike.

Andy, yes I think you're probably right! I think I have most Monday eves free next term so might well work for me if Tuesday AMs are late starting at work.  I like the look of the programme, it looks very cosmological and I'd be very interested to learn about that stuff. By the way,  I have lots of dumb questions too 🙂 !!

Jeff

Hi again Jeff.

Am back from holiday now, so have had the opportunity to review my copy of Copernicus’ De Revolutionibus Orbium Coelestium!

He only mentions one observation of his own of Venus - "

We ourselves made observations of a second position of Venus in the year of Our Lord 1529 on the 4th day before the Ides of March, 1 hour after sunset and at the beginning of the 8th hour after midday. We saw the moon begin to occult Venus at the midpoint of the dark part between the horns...

"

He used this observation to give a more accurate measurement of the mean motion of Venus.

For calculating the relative distance of Venus to the Sun, he simply used existing accepted observations for the greatest elongation. These observations have been made at least since Ptolemy's time. It is possible to determine the position of the Sun through simple calculation (see https://en.wikipedia.org/wiki/Position_of_the_Sun#Calculations ).

The position of Venus can be found by comparing its position to that of background ("fixed") stars in the sky.

There are lots of mentions of observations documented by Ptolemy in De Revolutionibus:

-

(Ptolemy) took as his observation one made by the mathematician Theo of Alexandria in the 16th year of Hadrian, he tells us, on the 21st day of the month of Pharmuthi, at the first hour of the following night; and that was in the year of Our Lord 132 on the evening of the 8th day before the Ides of March. And Venus was seen at its greatest elongation evening distance of 47¼° from the mean position of the sun while the mean position of the sun was by calculation 337°41' in the sphere of the fixed stars.

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Once more for the further confirmation of the thing, he (Ptolemy) assumed another observation made by Theo in the 4th year of Hadrian at morning twilight on the 20th day of the month of Athyr, which was in the year of Our Lord 119 on the morning of the fourth day before the Ides of October, at which time Venus was again found at a great distance of 47°32' from the mean position of the sun at 181°13'.

Anyway... you get the idea!... these observations have been going on for a very long time, and don't require the Sun and Venus to be in the sky at the same time.

Hi MIke

Wow!!!!! That's amazing - I'm VERY impressed! Thank you for writing all that out, it's very enlightening. I have heard of de revolutionibus though never of anyone actually having a copy!  Just looked on Amazon and there's something in the 'great minds series' that looks like it's a translation.  It may be I have to get that! So there were some observations, but largely he used existing tabulated data.  I find that incredible that it would have been possible for people to have worked out the planetary distances before Copernicus, but nobody bothered doing so.

While you were away I also browsed the discussion on the 'magnetic crusades' here... I spent the best part of a day pursuing that, including reading the entries on it in the book that someone recommended on the forum here - that entire section in the Reidy book on the magnetic crusades Humboldt and Gauss etc. is on Google books.  I knew nothing about this, and it looks like an incredible story.

So thanks for that Mike - there's alot to enjoy here!

I have heard of de revolutionibus though never of anyone actually having a copy!

It's not an original 😉 First of all, I don't think my Latin would be up to the challenge, and secondly I haven't got $2,000,000 spare!!

I use this translation, but there are many others.

I find that incredible that it would have been possible for people to have worked out the planetary distances before Copernicus, but nobody bothered doing so.

Yes, but remember it was Copernicus who challenged the convention that the Earth was the centre of the Universe. Without this postulation, it wouldn't have been possible to make the calculations. You have to first assume that the Earth is a planet and that all of the planets orbit the Sun. Then it's just simple geometry.

This model was nothing new, of course. Aristarchus of Samos had proposed such a model in 200 BC, and Copernicus refers to Aristarchus in the text (though he doesn't refer to Aristarchan cosmology - merely that "some even say that Aristarchus of Samos was of that opinion"). The idea never really caught on, and lay dormant for several centuries.

The Copernican model itself wasn't really accepted by astronomers - only after the work of Galileo and Kepler did the heliocentric model become more accepted.

I'd highly recommend The Sleepwalkers: A History of Man's Changing Vision of the Universe by Arthur Koestler (published in 1959) for a great account of this story. Koestler has a very different view of Copernicus to most authors that I've read - he portrays him as a coward, reluctant to publish his work for fear of ridicule. There is certainly some truth in this - De revolutionibus orbium coelestium was published during the year of his death, though he had arrived at his theory several decades earlier!

    Jeffocks wrote:

I find that incredible that it would have been possible for people to have worked out the planetary distances before Copernicus, but nobody bothered doing so.

Yes, but remember it was Copernicus who challenged the convention that the Earth was the centre of the Universe. Without this postulation, it wouldn’t have been possible to make the calculations. You have to first assume that the Earth is a planet and that all of the planets orbit the Sun. Then it’s just simple geometry. 

Hmmmmm..yes indeed I think I see what you mean Mike.  I may be misunderstanding,  or I'm not being clear (probably both!) - but my surprise is due to the fact that, even when assuming Earth to be at the centre with the moon in the next 'circle' etc. and using the tables available from Ptolemy etc. it would have been possible (??) to construct a geometry and compute relative distances (albeit wrong ones!) e.g. someone could have reasoned that taking the AU = 1 as, say, the Earth-Moon distance and then working out, by angular measurements, a series of (wrong) geocentric distances from that?   It just seems to me that it must have struck someone to do this, especially as the geocentric geometry would have been a bit simpler as well (ie Copernicus had to adjust his geometric method for the heliocentric outer planets).  However, I sense I'm missing a crucial concept here somewhere! 🙂

You see what trouble I will be to any astronomy club!! 😉

...it would have been possible (??) to construct a geometry and compute relative distances...

Absolutely... and it was done. Ptolemy was probably the first to achieve a coherent model, but he built on work by Aristarchus, Eratosthenes and Hipparchus. This was all published in the Almagest (2nd century AD).

Ptolemy determined the distances to the Sun and the Moon, which allowed him to predict solar eclipses. He also determined the distances to various other heavenly bodies - including the "fixed stars". His estimates were a mixture of geometry and philosophy - in particular, the measurement to the "fixed stars" has no scientific merit whatsoever! However, it's worth reproducing here, just for fun...

Measured in multiples of the Earth's radius - Ptolemy assumed the value of the Earth's radius at 28,667 stades (about 2,867 miles - or 1,100 miles less than it actually is).

Moon: 48 Earth radii (137,616 miles)
Mercury: 115 e.r.
Venus: 623 e.r.
Sun: 1,210 e.r.
Mars: 5,040 e.r.
Jupiter: 11,503 e.r.
Saturn: 17,026 e.r.
Fixed stars: 20,000 e.r. (57,340,000 miles)

The Islamic astronomer al-Farghani also computed the distances, based on the theory in Ptolemy's Almagest, in around 850 AD - dimensions that seem to be accepted all the way up to Clavius in 1612.

Ah, Mike.  Many thanks indeed! - the almagest yes I should have looked there - I had been reading an american textbook which said that Copernicus was the first to compute distances, and it gives the impression that no previous attempt was made, though other books give this impression too.  Now that you say it...I feel I should have known, or at least looked further and checked this more carefully!  I don't know what book you are using.  I am kind of using Hawking's Brief History of Time to set me off looking for the background reading to the story from Aristotle to Newton.

The trouble is I find a lot of the Astronomy books I've looked at seem to 'compress' the history so you get a diagram from Galileo (e.g. Venus' phases and inner orbit) illustrating Copernicus' method (not Galileo's) for verifying heliocentrism (e.g. Wenham's book on Planetary Astronomy).  I suppose these books convey the essential science of the situation... But one of the things I am now more alert to in reading the Hawking are the fundamental breaks that occur in understanding physics pre and post Galileo/Newton.  I think the history actually helps to bring out the shock in the ideas - e.g. at school one learns that 2 different weights fall with the same acceleration etc. just a bland fact about mass and velocity etc. But put into historical context (as Hawking describes it) it actually becomes shocking when you put yourself in the position of someone who assumes that heavier weights fall faster 🙂

Anyway, all fun stuff for cloudy evenings!  Thanks again for taking the trouble to look that material out. Most appreciated