Astroblog

V Puppis, an Algol-style variable star that can help show that the Earth orbits the Sun.

How can we demonstrate that the Earth orbits the Sun, using simple amateur astronomy kit? I've discussed this before, but I have been inspired to visit the idea again by two things; firstly, the new astronomy stack exchange (as mentioned by the Bad Astronomer), particularly the stack on determining how to determine if the Earth orbits the Sun, secondly the report that a group misrepresented themselves to astronomers to make a film promoting geocentrisim.

So,what is the simplest way to show the Earth orbits the Sun. This is a slightly different question from showing that the other planets orbit the Sun. Remember, there are two models that have the Sun orbiting the Earth, the Ptolemaic system and the Tychonian System. In the Ptolemaic system the Sun, all the planets and the fixed stars revolve around the Earth. In the Tychonian system the planets orbit the Sun and the Sun orbits the Earth.

This has implications for the kind of tests you can do. To disprove the Ptolemaic system is relatively easy. Observing the phases of Venus will disprove the Ptolemaic systemand you can observe them with decent binoculars or a small telescope (see here), but you will get phases of Venus in the Tychonian system.

To disprove the Tychonian system you need a bit more. Things like the aberration of starlight and parallax shift are a bit beyond the average amateur with an average telescope. But there are two ways you can show that Earth orbits the sun with just binoculars.

Location of the Algol-style variable RZ Cassiopeia.

The first way is the annual variation in the paths sunspots take across the sun (explained here, and with a diagram at the end of the post here).

But I've just found another one. Using the time lags in the timing of maxima of of Algol -type variable stars over the period of a year, you can show that the Earth revolves around the Sun.

The basic idea is that the finite time it takes for light to cross the Earths orbit will cause the time of the Maxima of variables to differ by +/- 5.3 minutes. The details can be found here. The author used RZ Cassiopea, an Algol-style variable which has decent magnitude fluctuation that can be picked up in decent binoculars. The maxima and minima can be adequately timed with a good quality watch.

Of course, it takes some time to meausre the maxima and minima, and you need a couple of years of data to do it accurately, but it can be done by amateurs armed with nothing more than binoculars and a decent watch. For Southern Hemisphere observers, RZ Cas is not visible, but V Puppis, an Algol-style variable with a period of 1.4545 days may be an acceptible subsitute, although it may be below the horizon at some points.

Not that this will convince die-hard geocentricists, every observable motion, from Sunspot movement to the abberation of stratlight to changes in maxima timing to parralax motion is due to a magical aether (the one that was shown to be non-existent by the Michelson-Morley experiment) or magical properties of high altitude winds.

But you can do it yourself to your own satisfaction.

Labels: binocular, Copernhttp://www.blogger.com/img/blahttp://www.blogger.com/img/blank.gifnk.gificus, Galileo

Einstein rings, a spectacular prediction of relativity, taken from Hubble (Image credit Hubble/NASA)

You may remember a little while back I wrote about a conference of modern Geocentrism (Galileo was Wrong). Geocentrism is the belief that Earth is the centre of the Solar system, nay the entire Universe and everything revolves around it.

Todd Wood attended the conference, and you can read the about his growing sense of incredulity in his posts (part 1, part 2, part 3, part 4, part 5).

It turns out that these folks are relativity deniers.

Image of the crescent Earth and Moon on October 3, 2007, taken by the HiRISE instrument of the NASA’s Mars Reconnaissance Orbiter.

Which is pretty strange, the usual tack is to argue for Geocentrism based of relativistic frame equivalence. Arguing against relativity is pretty hard, as it is one of the best confirmed theories of physics we have. From gravitational lensing (see images above) to frame dragging, relativity has passed increasingly stringent tests with flying colours.

These geocentricists apparently need relativity disconfirmed so the the Michelson-Morely experiment proves the Earth at rest.

Now there is a lot of problems with this (not the least because they need a non-moving ether to explain the M-M experiment, then a moving ether to explain Foucault's Pendulum) and other geocentrist positions. Some of the problems can be demonstrated with intensive mathematics, some with not so much maths (like the claim that GPS doesn't use relativistic corrections, which is untrue.)

Earth as seen from Mars taken by the Spirit rovers' panoramic camera in 2004.

However, in the spirit of my first post on this conference, where I tried to get people to do observations themselves that disproved first the Ptolemaic then the Tychonian systems, I want to get people to do something much simpler, related to observational astronomy.

Also in the spirit of Einstein, who tried to imagine what the word would look like if you were travelling on a photon, I want you to imagine your are standing on Mars.


The evening sky on Mars on April 29, 2005 as simulated by Stellarium (the location isn't at the same latitude and longitude as opportunity, so the view is slightly different from the rover).

What would you see from the surface of Mars that would be different in a Tychonian system (the system favoured by our modern geocentricists) versus a heliocentric system system?

As the Tychonican system is an inverted Copernican system, things like the phases of the Earth would be identical (see this JAVAscript model, advance the time to October 3, 2007 to match the image of crescent Earth and Moon above, and flip between the Tychonian and Heliocentric models to see what I mean).

Earth imaged by the panoramic camera of Opportunity an hour after Sunset on April 29, 2005 (Image Credit NASA/JPL).

There is a big difference that would be immediately apparent. Whether in the Tychonian or Heliocentric systems, from the point of view from Mars, Earth would appear to be a morning or evening star that appeared to revolve around the Sun.

However, the geocentricists are using a geostationary model, where the 24 hour day is produced by the Sun rotating about the Earth. So in a period of 24 hours, an observer on Mars (armed with an occultation disk) would see Earth rise from the sun, then fall back, then reappear on the other side of the sun and repeat the process again.

During the period that the Mars rovers took images of the Earth, at maximum elongation Earth was 42-47 degrees from the Sun as seen from Mars. For the Earth to move from maximum elongation to inferior or superior conjunction (at least, as it would appear from Mars, because in the Tychonian system Earth can't have conjunctions) takes 6 hours (in a 24 hour day there will be four 6 hour segments as the Earth goes out, comes back, goes out and comes back again from the solar disk).

So the Earth will appear to move 42 degrees (taking the lowest figure) in 6 hours, or 7 degrees per hour against the background stars (approximately, it's slightly more complicated than this, but rough figures are all we need). That's 14 Lunar diameters per hour! Earth is fairly hooting along compared to the background stars. In one minute Earth would move 1/4 of a Lunar diameter which is quite noticeable.

Now look at the image above. It is a composite of 3 x 15 second images taken with the panoramic camera, you can see the image of Earth is slightly elongated. However, remember that Mars rotates, and any 15 second exposure will cause slight star trailing due to its rotation. The trail we see of Earth is nothing like what we would expect if it was moving to a 24 hour rhythm, as it hares along the sky (roughly 1/5th of a Lunar diameter). Still, for confirmation we have to check Earth's movement against that of the background stars.

Fortunately, in the original image there is a background star just above Earth (it's best seen in the TIF file). It has the same degree of elongation that the Earth does. This falsifies the Tychonian system, thus the solar system is heliocentric.

So "Eppur si muove" because it um, doesn't move (with respect to the background stars as seen from Mars).

Labels: Galileo, science, Science Blogging, science matters

There’s been a lot of blank disbelief on the blogosphere of late, due to the announcement of a conference on Geocentrism (Galileo was Wrong). Geocentrism is the belief that Earth is the centre of the Universe and everything revolves around it. You would think that, 400+ years after Galileo, people would have cottoned on the the idea that the Earth orbits the sun, the sun orbits the galactic centre and the Milky Way galaxy does … well …complicated stuff with other galaxies, but basically we worked out long ago that the Earth is not the centre of the solar system, let alone the Universe.

Other people, especially Ethan at Starts with a Bang and the Bad Astronomer, have dealt with the technical details (and I have an earlier discussion here and here). My goal is to get you, the ordinary person on the Clapham omnibus (or in my case, the Outer Harbour train, where I am writing this), to try and demonstrate the Earth is heliocentric for yourself and to do so with common household materials. After all, science is at heart a practical endeavour, and non-professionals should be able to find the evidence for themselves.

So for this journey into the starry spheres, we will need a pair of binoculars, a camera tripod, some cardboard and alfoil, and lots of gaffer tape. We also have some luck, as the sky is currently cooperating in the Geocentrism debunking stakes.

First we have to ask ourselves, which “geocentric” theory are we disproving. The classic geocentric theory is that of Ptolemy, in which the planets, Moon and the Sun all orbit the Earth. The most famous variant of this is Tycho Brahe’s helio-geocentric system, where the Sun and Moon orbits the earth and everything else orbits the Sun. There are important differences in the systems which we will explore later.

First off, let’s look at the phases of Venus. For this you will need binoculars and the camera tripod. You will also need a way of attaching the binoculars to the tripod. These days I use a special attachment (but this requires modern binoculars that have a screw thread on the body), but in the past I have used gaffer tape to good effect. Why attach the binoculars to the tripod? Because otherwise there will be too much shaking for you to see the image properly.

The image to the left is the setup I use for observing Sunspots (we come to that later), showing the binoculars gaffer taped to the tripod.

At the moment, Venus is prominent above the western horizon. Point your binocular lash-up at Venus, in my 10x50 binoculars Venus is very small but is a disk which has a distinct “half –Moon” shape. If your binoculars don’t have decent anti-glare coatings, you may have to observe in the early twilight in order to see Venus’s shape without internal reflections from the binocular lenses getting in the way.

As you watch over the coming weeks, you will see Venus expand in size and become more crescent- shaped. Sketch the shape so you can follow its progress. This is so fast you should see a visible change in just one week. By mid-October Venus will be a thin crescent almost 2/3rds bigger than when you started observing. By late October Venus has nearly doubled in size and is a thin, glistening wire. Then Venus vanishes into the Suns glare and reappears in the morning. Over the next few months you can watch Venus shrink and become a tiny disk.

And now you have demolished the Ptolemaic geocentric system. Venus does have phases in this system, but quite unlike what you see here (I leave it too the reader to work out what a Ptolemaic systems Venus phases would look like, you can see a model of Ptolemaic Mercury here, which will give you a good idea). And you have only taken almost 6 months to do it (what, you thought it would be easy). As a reward, here's an animation of the Phases of Venus.

But wait! You say What if it is just an illusion, a trick of the optics? Well, you have a control. Having observed Venus, swing your binocular lash-up to the east, to the brightest object there (and second brightest non-lunar object in the night sky after Venus), Jupiter. Jupiter is a distinct oval in my binoculars, and the four bright Medicean Stars glitter around it. Over the nights you watch Venus swell and thin, keep an eye on Jupiter as it does…well…nothing.

Jupiter and three of its moons imaged with a mobile phone.

But Ah! The Medicean Stars, now known as the Galilean Moons, they will shuttle backwards and forwards during the nights as you watch. The realisation that these “stars” were Moons of Jupiter were not a blow to any form of geocentrism per se, although they were the second of a series of powerful blows against the Aristotelian physics that underpinned Ptolemy’s system, which aided its demise. Determining that these specks actually orbited Jupiter, and were not just accidentally there, took a lot of effort.

Try keeping track of these sparks, and without reference to an almanac, try and determine their orbits (heck, try and keep track of which near identical points of light are which). It may take a while, you will need to keep careful sketches, and track the Moons and Jupiter with respect to the stars as Jupiter moves through the heavens, but a) You are sketching Venus anyway and b) it will be well worth it (hey, you proving things for yourself!).

The next bit is more demanding. The Phases of Venus demolished the Ptolemaic Geocentric system, but the Tychonian- Geo-heliocentric system had Venus phases just like a pure heliocentric system (which is not surprising, as Tycho’s system is an inverted Copernican system). To eliminate the Tychonian system, we need to observe sunspots.

Luckily the Sun is coming out of its quiet phase, so you will have some to record. For this you will need to set up a safe binocular projection system (as shown above), where the image of the Sun is projected onto a surface so you can record the Sunspots. NEVER LOOK DIRECTLY AT THE SUN WITH BINOCULARS AS SEVERE EYE DAMAGE WILL RESULT.

Anyway, while you are recording the Phases of Venus and the orbits of Jupiters’ Moons, record the passage of Sunspots over the Suns face, over the 5-6 months you are recording the susposts, you will notice the path taken by the sunspots moves up and down. This is due to the Earths orbit not being exactly in the plane of the Suns rotation. In a geocentric system, with the Sun orbiting the earth once a day, this variation would show up on a daily basis, but what you observe can only be seen in a heliocentric system.

So, congratulations, you have just demonstrated that geocentric models don’t describe the solar system we see using very simple tools. It took a while, and was hard work, but you have demonstrated it yourself, and all the blovation of geocentricists won’t take that away (yes, Stellar parallax gets all the glory, but annual Sunspot variation was a powerful blow to Tychonian geocentric models). If you want to, you can take this further by making your own Foucault's Pendulum.

Labels: Copernicus, Galileo, Science Blogging, science matters

Galileo's 1610 drawing of Saturn

I’m writing this post especially for the 100th Carnival of Space, because it involves the 400th anniversary of Galileo looking through his telescope, so the post is a double 00 double whammy. It also combines my love of astronomy and science history with my love of biology.
Galileo's 1616 drawing of Saturn

The article it is based on is old news though. Italian Scientists are trying to recover DNA from Galileo’s remains. Amongst other things they wanted to understand was the source of Galileo’s blindness and why he saw Saturn as an object with “ears”. The first is a reasonable question, although probably not answerable. The second question is not, as a bit of thought (and a bit of history) would reveal.

What about Galileo’s blindness? Surely he went blind from observing the Sun through his telescope. Well, that’s a very common perception, but no he didn’t. Galileo observed sunspots from around 1611 to 1614. However, Galileo didn’t become blind until he was 68, nearly 30 years later. Furthermore, he became blind in both eyes. Even if you take the line that subclinical photodamage to his eyes developed progressively into blindness, this should have only occurred in the dominant eye he used for observation not both.

Now, for a dramatic example of what happens when you look at the sun directly through a telescope; look at this video...nasty isn’t it. Why didn’t Galileo’s eye boil? Firstly, he observed only very close to sunset, when the Sun was dimmed by atmospheric haze. That, and the optics of his telescope dimmed the image of the Sun as well. Secondly, while he did some direct telescopic observations (again, around sunset when the suns image was dim), during 1612 he started using a projection technique, so the period when he was directly observing the Sun was short.

So, if we want to find out why Galileo went blind what sort of diseases should we be looking for? Well, they have to be diseases that occur relatively late in life, and cause blindness in both eyes. This leaves out the majority of mitochondrial gene diseases, which tend to occur in early life. This is a bad thing for our researchers. Galileo’s body wasn’t preserved with future DNA specialists in mind, so his body has undergone substantial decomposition. Which means the DNA in the nuclei of his body’s cells have decayed too, and been chopped up into little fragments. This is not such a big problem for mitochondrial DNA, that gets chopped up too, but there are lots of copies of mitochondrial DNA (as there are lots of mitochondria, the powerhouses of the cell) so it's more likley you will recover enough fragments to make sense of the genes. The first DNA recovered from Neanderthal remains was mitochondrial DNA for example.

So, with Galileo’s nuclear DNA in little fragments, finding disease genes is going to be hard. What sorts of blindness that occur in both eyes in old age are known to be associated with genetic defects? Macular Degeneration is the commonest form of blindness in old age in western countries, and is associated with genetic defects. However, there are a wide range of defects associated with this disease, they don’t all occur in the same individual (or even in all diseased individuals), and require environmental interaction. So, if Galileo had Macular Degeneration, your have to scrummage through huge numbers of gene fragments looking for disease genes which may not even be there.

Worse still, Macular Degeneration is probably not the condition Galileo had; it doesn’t really fit the description given of Galileo’s disease. There have been a couple of proposals, one is a combination of glaucoma and cataracts which is still quite common, another is he had bilateral iridocyclitis due to his rheumatoid disease. Neither of these diseases has strong genetic linkage, so any attempt to diagnose these causes of Galileo’s blindness from his DNA would be marginal at best, even if Galileo’s DNA wasn’t in lots of itty bitty hard to assemble fragments.

So diagnosing Galileo’s blindness is a pretty marginal ask, even if we had his intact DNA. What about Galileo’s views of Saturn? Galileo wrote to Kepler in code, after his observations of Saturn, "I have observed the highest planet tri-form." Galileo saw Saturn as a triple planet, or sometimes as a planet with “ears”. Why didn’t he see the rings as rings, was his observations in 1610 (before he did any solar observing) and indication of incipient eye disease, which we could pick up browsing through his genes?

Huygens diagrams of Saturn.

We don’t need genetics to explain this. Galileo’s strongest telescope was only 30x magnification, and it’s optics, although finer than almost anyone else’s, were no where near modern standards. Furthermore, no one had experience of ringed worlds. Galileo had to struggle to interpret what he saw through his telescope with no analogues to guide him. If you were to look through a 30x scope today, the rings of Saturn are not particularly obvious, but because we know they are rings, it is easy for us to understand what we see. Another reason to suppose we don’t need a genetic explanation is that no one else could make out Saturn’s rings either; people saw a multitude of bizarre shapes (see Christian Huygens drawings left). So either there was an epidemic of genetic-induced eye diseases making astronomers incapable of seeing Saturn’s rings, or a more mundane explanation is responsible; imperfect telescopes and the sheer unanticipated nature of the observations. It took a combination of better telescopes and systematic observation to discover Saturn was a ringed world.

Galileo revolutionized the world of astronomy, and his blindness was a tragic denouement to a career based around observation. Our curiosity drives us to understand what disease it was that caused it, and I wish the researchers well, but I suspect they will find nothing concrete. But to try an explain Galileo’s visions of Saturn by genetic disease is a fools errand, and one that ironically flies in the face of Galileo’s own commitment to observation. This, the need to find explanations in genes, is a different sort of blindness.

Labels: Galileo, Saturn, telescope

Back in March I wrote a post “Occam's Razor and the Two World Systems”, where I discussed the idea propounded by William Wallace that Occam’s razor failed when applied to the transition from the Ptolemaic geocentric solar system to the Copernican heliocentric solar system. Mr Wallace replied on that post and I promised to respond, but life (and various asteroids and comets) got in the way. Rather than add new comments there. I’ll take this up as a new post.

The starting point of the old post was Mr Wallace’s contention:

I have a counter example, from science, fully described here, where Occam's razor fails. The idea that the "simplest explanation is probably right" was falsified when Tycho Bryhe [sic] rejected heliocentricism for geocentricism, based on his analysis of the best available data.

Once again, I must emphasise that Occam’s razor is not the simplest explanation is probably right, but let’s pick up on Mr. Wallace’s comments. I’m going to do this slightly out of order, so as to address particular issues that arise from the quotes more logically

There were three systems, Copernicus, classical Ptolemaic, and neo-Ptolemaic (or Tycho's). Both Ptolemy's and Tycho's could be accurately described as geocentricism. I just want to clarify that I don't think I ever claimed--and I certainly never intended to claim--that Tycho held a purely Ptolemaic view of the solar system. He held a geocentric view, more consistent with Ptolemy's than Copernicus's (though Kepler's was arguably more akin to Copernicus's than Tycho's was to Ptolemy's.)

This is so very, very wrong. Tycho’s system was not a neo-Ptolemaic system, as I describe below, Tycho explicitly rejected the Ptolemaic system based on observational evidence. Tycho accepted most of Copernicus’s system, but balked at a moveable Earth and produced a Heliocentric-geocentric system (not a geocentric system, for another animation of the respective systems see here). Indeed it is an “inverted Copernican” system, basically a remapping of the Copernican system into a reference frame centred on Earth. Tycho’s system contains nothing of Ptolemy; there are no equants, no great epicycles and so on[1]. I’ll emphasise that again, Tycho’s system was not a re-jigging of Ptolemy, it was an inversion of Copernicus’s system.

The only point of similarity between Ptolemy’s system and Tycho’s system was the Earth was immobile in both systems, but in Tycho’s, everything but the Moon rotated around the Sun. Again, the key features of Ptolemy’s system, the equant and the great epicycles were absent from Tycho’s formulation. This may seem like mere pettifoggery, after all, both Ptolemy and Tycho had the Earth as the centre of the solar system, but Ptolemy’s system was not just “everything goes around the Earth”. Tycho had explicitly rejected the Ptolemaic system, all the key features of the Ptolemaic system, taken all the planets and placed them around the Sun and grounded his system on a reformulation of the Copernican system.

Tycho's system required fewer calculations and was consistent with all known measurements. Copernicus's was not consistent with observations.

Tycho's system required roughly the same number of calculations as Copernicus’s, as it was basically Copernicus’s translated into Earths reference frame [2]. Tycho fully accepted Copernican geometry, used Copernican planetary models, and where he did not explicitly do his own calculations, he used planetary tables based on Copernican models. Where Tycho was more accurate than Copernicus, it was through his greater observational accuracy, not any superiority of his model. Indeed, when he talks of his system, he notes that he has kept all the superior features of the Copernican system. Ironically, it was Tycho’s own measurements of the opposition of Mars in 1582 that showed that the Copernican model was in better agreement with the observed retrograde motion of Mars than the Ptolemaic model.

And yet Copernicus' model defied experimental verification, using the best astronomical apparatus of the time (Tycho's).

Actually, that’s not true. There was a key test of the Ptolemic vs Copernican system and the Copernican system came through with flying colours. It was one of the key results that forced Tycho to reject the Ptolemaic system. However, that test tends to be ignored these days because of modern commentators focusing on the issue of stellar parallax.

We now know that stellar parallax could not be measured with instruments available then. It wasn’t obvious back then, and there were several attempts to measure the stellar parallax. Tycho established that the stellar parallax had to be less than 0.1 degree. However, this did not falsify the Copernican model as negligible parallax was an a priori feature of the Copernican system.

Tycho was well aware of this, and his argument was not that the lack of parallax showed that the Earth did not move, but that if the parallax was so small the distance between Saturn and the stellar sphere would have to be 700 times the distance between the Sun and Saturn. A provident creator would not be so wasteful of space and produce such asymmetry in his creation.
So we can see that the stellar parallax argument as used by Tycho is in the end not a scientific argument.

So what was the measurement that convinced Tycho to reject the Ptolemic system? Ironically, it was a parallax measurement. One of the predictions of the Copernican system was that Mars would be closer to Earth than the Sun at opposition; while in the Ptolemaic system Mars would always be more distant from the Sun. Tycho’s careful measurements of the parallax of Mars showed that Mars was closer to Earth than the Sun. Similar measurement of Venus’s parallax by Tycho also confirmed Copernican predictions. Copernicus was right, Ptolemy was wrong, and Tycho unhesitatingly rejects Ptolemy. But in the end Tycho rejects both Ptolemy and Copernicus.

My ultimate point about Tycho's rejection of Copernican theory was that applying principles of modern science sometimes leads one astray.

Erm. Mr. Wallace. This is what you said:

I have a counter example, from science, fully described here, where Occam's razor fails...

In this case, it was Tycho’s system failed the Occam’s razor test. It requires more assumptions than the Copernican system, introduces two centres of motion, introduces more problems with motions and whilst reproduces the retrograde motions of the planets, it no longer provides these motions as a natural consequence of the orbits of the planets. Altogether it is far less economical than the Copernican system and no longer explains the precession of the equinoxes and is affected by solar eccentricity (and this was pointed out at the time). Occam’s razor doesn’t fail, because Occam’s razor was not used to make the choice between the Copernican and Tychonian systems. What was the basis of Tycho’s rejection of the Copernican system? Let Tycho tell us in his own (translated) words.

Since all these results [parallax measurements of Mars and Venus] did not all agree with the Ptolemaic hypotheses I was urged afterward to put more and more confidence in the Copernican invention. The exceedingly absurd opinion that the Earth revolves uniformly and perpetually nevertheless made up a very great obstacle, and in addition the irrefutable authority of the Holy Scripture maintained the opposite view. [emphasis added]

It wasn’t the principles of modern science that lead Tycho astray.

[1] The equant was seen as a particular drawback to Ptolemy’s system, if one wanted to explain planetary motion in terms of uniform circular motion, and Copernicus reformulation of planetary motion so that the equant was dispensed with. This was seen by contemporary astronomers and mathermaticians and a great benefit of the system. Tycho too saw the equant as something undesirable, and the great epicycles of Ptolemy as unparsimonius.
[2] Tycho got rid of Librations, but generally his scheme was Copernicus’s recast from Earth’s frame of reference.
[3] Ironically, Tycho’s system made the acceptance of the Copernican system easier. It made people familiar with the Copernican system, and smashed key sections of Aristotelian physics which have proved a barrier to acceptance of he Copernican system.

Sources:
The Reception of Copernicus’s Heliocentric Theory 1973 ed Jerzy Dobryzcki, Reidle esp Chapter 3.
Copernicus, On the Revolution of the Heavenly Spheres (translation AM Duncan 1976) Barnes & Nobel
The Copernican Revolution 1957, TS Kuhn Harvard University Press
The Book Nobody Read 2004, O Gingerich, Walker & Company

Labels: Copernicus, creationism, Galileo

Comparing Galileo's drawing of Jupiters Moon's (top) with a modern prediction for the Moon's appearance at that time (Below). For a drawing using a fairly ordinary telescope , drawn by hand and then made into a woodcut, it's pretty accurate (scaling between the images is different, sorry).

The small stars in Galileo's diagram represent Jupiter's Moons.


Continuing my reading of Galileo's Sidereus Nuncius (The Starry Messenger).

Galileo's audience have been shocked by the revelation that the Moon was not a perfect object. They were stunned when the Milky was was revealed to be not an etheric glow in the celestial spheres, but myriads of stars to small to be resolved to the unaided eye. But the next revelation was the most amazing.

Galileo was the first to discover completely new worlds.

On the seventh day of January in this present years 1610, at the first hour of night, when I was viewing the heavenly bodies with a telescope, Jupiter presented itself to me. And because I had prepared a very excellent instrument for myself, I perceived (as I had not done before on account of the weakness of my previous instrument) that there were three bright starlets beside the planet, small indeed, but very bright.

The " very excellent instrument" was probably no more than 20x in magnification (you can get a replica yourself). Now, Galileo was not expecting new planets, indeed nothing would have lead anyone to expect there could be more than the 7 classical planets. But he did note that the three starlets to the east of Jupiter were aligned with the ecliptic. Unusual and interesting, but not the harbinger of new worlds. Imagine yourself looking at three tiny stars near Jupiter, how would your realise that these dots were Moons, not stars?

The next night though the three stars were on the western side of Jupiter.

Now, as Jupiter was travelling westward at the time, there was no way that fixed stars could turn up on the western side of Jupiter. The penny still hadn't dropped, but Galileo now sets watch on Jupiter and the starlets. After two further observations, it was clear that the starlets never moved far from Jupiter, and were travelling in the ecliptic line. Galileo writes:

I now decided beyond all doubt that there existed in the heavens three stars wandering about Jupiter as do Venus and Mercury around the Sun, ... [at this time Galileo had not seen all four Moons]

Note how cheekily Galileo inserts a heliocentric idea in the text, true it could be referring to Tycho Brahes system, but throughout the Starry Messenger there is more than a hint of heliocentrism. However, his discoveries were so astonishing that most people ignored the heliocentrism and attacked the existence of mountains on the Moon, and Moons around Jupiter.

Most of the rest of the book is list after list of Jovian Moon positions. Given that the man had just discovered new worlds, the dry list may come as some surprise. However, it had an important point, and people scoured this section very attentively. Galileo had to establish beyond doubt that the starlets really did circle Jupiter. One way was to establish orbital periods for the starlets, which require two things, accurate measurement of the starlet positions, and some way to identify individual Moons. The furthest starlet was easy, no other Moon went so far from Jupiter, but distinguish three near identical points of light as they merged and separated was an enormous task. Galileo did not achieve it in the Starry Messenger, but did later on. He did get an approximate orbital period for the outermost starlet (IV, which we now call Callisto), and this approximate period got him in trouble later. Also, he was able to show by comparing the motion of Jupiter and the starlets to the fixed stars, that the starlets moved in latitude and longitude exactly with Jupiter. The Moons orbited Jupiter.

But now we have not one planet revolving around another while both run through a great orbit around the sun; our own eyes show us four stars that wander around Jupiter as does the Moon around the earth, while all together trace out a grand revolution about the sun in the space of twelve years.

Naughty Galileo again! More heliocentrisim snuck in. He also resorted to atmospheres to explain the apparent dimming of the Moons as they approached Jupiter (this is really an optical effect due to the brightness of Jupiter).

The existence of the Moons was attacked as soon the the Starry Messenger was published. There was some reason to be sceptical. Galileo's telescopes were far from perfect instruments, and there were know artefacts in them. But Galileo's careful observations put paid to those sorts of arguments. The orbital features of the starlets could not be explained by mere artefact.

Many attacks were supremely foolish, even by the standard of the times. Francesco Sizzi argued that for metaphysical reasons, there could be no more than seven planets, therefore the Medician stars could not be real. Sizzi had even seen the Medician stars himself. But Sizzi also had a more subtle argument up his sleve. If the Mediciean stars were Moons, he said, then they should show a consistent periodic orbit like our Moon. But the orbits he derived from Galileo's observations did not agree with Galileo's stated orbital period. Which was because Sizzi had based his orbits on an incorrect figure. There were several observational errors in the printed work, not surprising given the difficulties of making measurements with the primitive telescope, and Sizzi started his calculations from an erroneous position for Callisto, and them compounded his problem by taking Galileo's approximate orbital period as an exact one.

At this remove, it is hard to understand these attacks, but in those days mere measurement was not match for metaphysics. People were supposed to start from metaphysical reasoning and argue to a conclusion. Observations and measurements came a poor second. However, eventually people like Sizzi were won around by just these measurements. After extended conversations with Galileo, Sizzi derived reasonable orbits and became his supporter.

Gallileo's Starry Messenger is a slim book, most of it is taken up with dry recitations of the positions of the Medician stars; Jupiter's Moons. But it held twin revolutions. It began the shattering of the Ptolemaic astronomy, and heralded the heliocentric solar system. And in shattering the Aristotelian version of the cosmos, and emphasising precise and careful measurement, it ushered in the modern era of science, where metaphysics was discarded and observation and careful testing of hypotheses became the standard.

Twin revolutions, started by a tube that today we would consider a toy.

Blogging the Starry Messenger - Introduction
Blogging the Starry Messenger - The Telescope
Blogging the Starry Messenger - The Moon
Blogging the Starry Messenger - The Stars

Labels: blogs, Galileo, Science Blogging

Comparing Galileo's chart of the Pleiades with a modern chart. For a chart drawn using a fairly ordinary (by modern standards) telescope with chromatic and other aberrations, drawn by hand and the made into a woodcut, it's pretty accurate (scaling between the images is different, sorry). The small stars in Galileo's diagram represent stars never before seen by humans.

Continuing my reading of Galileo's Sidereus Nuncius (The Starry Messenger).

Galileo's audience would be reeling after the revelation that the Moon was not a perfect object. His next shock would not be as great, but would still have an impact. There were far more stars in the heaven than could be seen with the unaided eye.

The issue was not merely that these things were new discoveries, but that they struck at the very heart of Aristotelian cosmology, which was in turn a major prop to the Ptolemaic solar system. These observations laid the foundation for the fall of the Ptolemaic system.

Galileo spends a lot of time describing the appearance of the stars through the telescope. Again, the words sound strange to us today, as he tries to describe effects we know as largely due to atmospheric turbulence, but he was showing that, unlike the planets, the stars showed no, or very small, visible disks.

When stars are viewed by unaided natural vision, they present themselves to us not as of their simple (and so to speak their physical) size, but irradiated with a certain fulgor and fringed with sparkling rays, especially when the [darkness of night is] far advanced.

Once he has established that stars appear brighter in the telescope, but not bigger, he goes on to describe the multitude of stars he can see. He then maps out the previously observed stars along with the new stars in the belt of Orion and the Pleiades, showing that there are over 10 times more faint stars than ones seen with the eye. He then scrutinises the Milky Way, and shows that this is made of large numbers of faint stars. Finally he turns his telescope to certain features called Nebula (not the same as our moden nebula), and shows that these too (the Nebula of Orion and the Nebula in Paraesepe) are composed of multitudes of faint stars. Actually, Orion's Nebula does have a proper nebula in it, but it is unlikely Galileo could have seen it with his instrument. Again, given the primitive nature of his instrument, and the circumstances of making his observations, the star maps he makes are surprisingly accurate.

Unlike showing the Moon to be another world, showing that there were many unobserved stars was not quite so much of a shock. It didn't change the alleged celestial nature of the stars, but it meant that large chunks of the Universe were unobservable to us (just like dark matter today). In the mindset of the times, to have large chunks of the Universe unobservable was nearly unthinkable, the Universe was created for man, but what use were unobservable stars?

Still Galileo had an even bigger surprise waiting in the wings. Planets no one had ever seen before. Next week, we look at his section on the Moons of Jupiter.

Blogging the Starry Messenger - Introduction
Blogging the Starry Messenger - The Telescope
Blogging the Starry Messenger - The Moon

Labels: blogs, Galileo, Science Blogging

Over at my blogging buddy ERV's place, there's a lot of arguing going on [1], which at one stage segued into a silly argument about Occam's Razor and the Heliocentric vs Geocentric theories (See William Wallace's post and subsequent posts, and William Wallace's own webpost on this topic).

First off, Occam's razor is not "Choose the simplest explanation". Occam said entia non sunt multiplicanda praeter necessitatem, which can be translated as "entities must not be multiplied beyond necessity"[2]. These days, in science we understand Occam's razor as (quoting Wikipedia)

When multiple competing hypotheses are equal in other respects, the principle recommends selecting the hypothesis that introduces the fewest assumptions and postulates the fewest entities.

As well, you need to understand that in describing cosmological systems, the preference from antiquity to Galileo was to explain heavenly motions in terms of uniform, circular motions. We may see this as weird or foolish now, but it wasn't back then. Now, on to William Wallace.

I have a counter example, from science, fully described here, where Occam's razor fails. The idea that the "simplest explanation is probably right" was falsified when Tycho Bryhe [sic] rejected heliocentricism for geocentricism, based on his analysis of the best available data.

Okay, there are several things wrong with this. One: Occam's razor isn't "simplest explanation is probably right" (see above). Secondly, Tycho Brahe didn't reject heliocentrism for geocentricism.

A little explanation. If the Earth is the centre of the universe, with the planets and fixed stars revolving around it with uniform circular motions, you should see the all the planets move smoothly across the sky at the same pace and the same brightness. But they don't. The inner planets, Mercury and Venus, never move far from the Sun and change radically in brightness. The outer planets move across the sky, then stop, reverse their motion, stop again, then move back the way they were going in the first place. Any geocentric explanation has to explain this retrograde motion.

Ptolemy solved these problems. First, he had the planets not orbit the earth directly, but orbit a point that itself orbited the Earth. This is the epicycle (for an animation see here). Mercury and Venus required somewhat more complicated solutions (see here for an animation of Mercruy in a geocentric system) than for the outer planets. Even so, this system still didn't quite work. Ptolemy also introduced the equant, the planets did not in fact orbit the Earth, but orbited a point some distance away from the Earth. It worked, and the Ptolemaic geocentric system was the standard description of the Solar system until the time of Copernicus. Copernicus, of course, moved the centre of the universe to the Sun, and had all the planets, including Earth, revolve around that.

Now, in terms of Occam's razor, Copernicus's heliocentric system should have been an outright winner. Both the Ptolemaic system and the Copernican system explained retrograde orbits and the reason Venus and Mercury never travelled far from the Sun, but the Copernican system got rid of the ad hoc large epicycles, the retrograde motions of the planets were natural results of the planets orbiting the Sun, as was the explanation of Venus and Mercury not moving far from the Sun, as they orbited inward of the Earth. Most importantly, the ad hoc equant was removed. In the time of Copernicus, getting rid of the equant was more important than many other innovations, as the equant represented a departure from the ideal of explaining the solar system using uniform, circular motion.

The Copernican system also explained things the the Ptolemaic system didn't. It gave a natural explanation for the ordering of the orbits of the planets, it also explained the precession of the equinoxes and the seasons. So, not only did the Copernican system explain the same facts as the Ptolemaic system with fewer ad hoc assumptions, it had greater explanatory power. It did require the assumption that the Fixed stars were very far away, but that was no more ad hoc than the Ptolemaic assumption that they were relatively near. So, in the Occam's razor stakes, it should have won hands down, and indeed the Copernican system was popular with northern European astronomers. Southern European, not so much.

So, along comes Tycho Brahe, he makes the most accurate observations of the stars and planets ever and he ....

Rejects the Ptolemaic system. He makes a system where all the planets bar Earth orbit the Sun (animation here) and the Sun with its panalopy of planets orbits the Earth. It's a kludge, an obvious kludge. The orbits of Mars and the Sun intersected for criminies sake! In terms of Occam's razor, Tycho's helio-geocentric system fails, introducing unwarranted assumptions. The parallax issues was a problem, but again, if the fixed stars were far away (as they were), then parallax would not be observable.

The observations of the phases of Venus by Galileo, and of the Moons of Jupiter meant that the Ptolemaic system (which Tycho rejected) was wrong. Interestingly, Galileo observed changes in the timing of the eclipses of the Moons of Jupiter that could be accounted for only by the parallax changes due to an orbiting Earth, but didn't realise it. In 1613 the annually periodic seasonal variations of sunspot trajectories across the sun's disc was discovered. This fitted with the hypothesis of a rotating earth, and not one of an orbiting Sun. Then in 1729 James Bradley discovered stellar aberration, which can be only explained by a rotating, orbiting Earth. Finally in 1838 , Friedrich Bessel made the first successful measurements of stellar parallax.

Tycho did not accept the Copernican system, but neither did he accept the geocentric Ptolemaic system. His rejection of the Copernican system in favour of a more complicated system of his own devising was a failure of Tycho, not of Occam's razor. Indeed, the Earth does rotate around the Sun, and choosing Occam's razor would have given us the right result (As Tycho's system made more unwarranted assumptions than the Copernican system - Stars close to earth, two centres of rotation and crossing orbits).


[1] Well, it's basically over now, that's what I get by being distracted by the sky. But I have a point I want to make.
[2] He also said Pluralitas non est ponenda sine necessitate which translates as "plurality should not be posited without necessity."

Labels: Copernicus, creationism, Galileo

Continuing my reading of Galileo's Sidereus Nuncius (The Starry Messenger).

Having described the telescope, Galileo then turns to describing the Moon as seen through his new instrument. This section shows the puzzlement, if not the initial incomprehension, Galileo had when he first viewed the Moon at magnification.

We are used to the idea of craters and mountains on the Moon, but when Galileo first looked, the accepted idea was that all celestial bodies were perfect. The dark splotches so prominent to our unaided eye view were explained in various ways that left the Moon a perfect, unblemished sphere.

Now, Galileo more than most was in a position to realise that if the Earth was a planet, as Copernicus thought, then all planets, such as the Moon, might have features similar to those on Earth. But also recall this was the first time a world had been viewed from such a perspective, with a telescope of roughly 15x magnification, with lenses that had spherical and chromatic aberration, and without our fancy telescope mounts.

Given all this, it is a wonder that Galileo was able to describe and sketch the Moon as he did. Reading his account, you can almost hear the gears in his head grinding as he tries to make sense of the patches of light and dark revealed by his telescope.

First he briefly describes the light and dark patches that people knew for millennia from their nightly views of the sky. Then he goes on to describe things no one has seen before:

On the fourth or fifth day after new moon, when the moon is seen with brilliant horns, the boundary that divides the shaded part form the lighted part does not uniformly run along an oval line, as would happen on a perfectly spherical solid, but traces out an uneven, rough and very wavy line as shown in the figure below. Indeed, many luminous projections extend beyond the border into the darker part, while on the other hand some dark patches invade the illuminated part. Moreover, a great multitude of small scattered dark spots, entirely separated from the dark region, are scattered almost all over the area illuminated by the sun, excepting only that part occupied by the large and ancient spots [the large dark patches that can be seen with the unaided eye IFM]

Let us note particularly that the said small spots agree always in having their darker parts directed towards the sun, while on the other side, opposite the sun they are crowned with bright contours, like shining summits.

Slowly, painstakingly, Galileo describes the effects of sunrise, the appearance of the Moon during different phases. You can see him trying to build a picture of a world that has never been glimpsed before. He also had to convince his audience that what he saw was not mere illusion, an artefact of the telescope. This was not so absurd as it seems to us today. Telescopes were new, and did suffer from chromatic and other aberrations (and even today internal reflections can generate phantom objects). Still, as you can see from one of Galileo's illustrations compared to a modern photograph, for a hand held 15x instrument, he did quite well in accurately depicting the Moon's features (the big crater is today known as Albategnius, it's size is exaggerated due to issues in producing the woodcuts that made the illustrations for the Staryy Messenger).

Galileo did more than just describe. He used geomtery to show that these objects must have sustantial size, and indeed were towering mountains. Some of his explanation seem a bit strange to us today, such as positing an atmosphere to the Moon to explain why you can't see peaks and ridges on the limb of the Moon (rather than it being mostly an effect of our eyes being unable to resolve these small features). Still by the end he has convince at least me that the Moon is not a prefect cellestial sphere, by a world that can be compared to our own.

The notion that the Moon was not perfect was quite shocking, and some peopel refused to accept this, even some who accepted the existance of the Galilean satellites of Jupiter still refused to accept that the Moon had mountains and craters.

That the Moon was a world was quite a subversive notion, and part of the process of demolishing Aristotilean physics neccescary fro acceptig a heliocentric system. If the Moon is a body like Earth, and not a special cellstial object, then Earth can be a planet just like the others, and not be placed in a priveleged postion.

If a non-perfect Moon was a shock, Galileo had more shocks waiting. Next week, we look at his section on the stars.

Blogging the Starry Messenger - Introduction
Blogging the Starry Messenger - The Telescope

Labels: blogs, Galileo, Moon

A I mentioned before, Galileo's Sidereus Nuncius (The Starry Messenger) doesn't actually have chapters. After the dedication it is all one solid block of text, but it has logical subsections, so I'm blogging those.

After the introduction, Galileo goes on to describe how he built his telescope. First he describes briefly how he hear of telescopes that had been built elsewhere. Many people are under the impression that Galileo invented the telescope. He didn't, and he says so, but he produced far better telescopes than the ones that were circulating at the time.

Galileo's description of his telescope is frustratingly short. He takes a tube of lead and grinds two two lenses, sticks them in and "presto!", a telescope. Details of how long the tube was, how big the lenses were, what depth they were ground to etc. are all missing. Later on, when he says that to follow up his observations, you have to make an excellent telescope without flaws one wonders how you are supposed to do that. 17th century savants were a bit more "hands on" than modern day philosophers, but lens grinding was not a widespread skill amongst them (there were spectacle makers around, they could have asked them though). Even Kepler had to borrow a telescope to confirm Gailileo's observations, rather than make his own.

The lenses he describes will also be unfamiliar to those of us schooled in cartoon versions of the telescope. Most of ys think of telescopes as having an adjustable tube, and two convex lenses, like in this illustration. Galileo's lenses were flat on one side. One was spherically convex and one was concave, as shown in this illustration.

Also, by modern standards his telescope was way underpowered, his first scope was only 9x, about as effective as a pair of 10x50 binoculars, his best telescope was only 30x, around the power of many modern finderscopes. For most of his observations of the Moon he use a scope of around 15x magnification. The higest power magnification was impractical because of the small field of view.

Consier that not only did Galileo have a telescope that was low powered by todays standards, but there was no fancy andt-glare coatings, correction for abberation, a decent mounting or anything thing else. The quality and consistency of the glass available at the time was not as high as today. Yet Galileo made a telescope that could uncover the heavens.

What he does sepend a lot of time on (in his wondrfully convoluted fashion) is his mechanism for determining distances between stars in the telescope (a series of thin metal plates with different sized holes in them that could be placed in front of the lens). This is where Galileo stands out. He wasn't the first to make a telescope, he wasn't the first to turn the telescope to the sky. But he was the first to make a seroius instrument capable of aming reasobably accurate measurements of objects. This will turn out to be important in the discussion of Medicaian staleelites later on, and the very conduct of science.

Next week - The Moon!

Blogging the Starry Messenger - Introduction

Labels: blogs, Galileo

Daniel Fischer notes that Florian Freistetter is blogging Kepler's Astronomia Nova. Unfortunately for monoglots it's in German. Chris Mooney is blogging Copernicus's De Revolutionibus, (see also here), and will also start on the Starry Messenger soon.

Labels: Galileo, history

As part of the 200th anniversary of Darwin's birth, and the 150th anniversary of the publication of the Origin of Species, people have been re-reading the Origin and blogging it (and here). There is even an entire blog site devoted to the Origin.

So I thought to myself, it's the 400th anniversary of Gaielo looking through a telescope, why not blog Sidereus Nuncius (The Sidereal or Starry Messenger)? True, it was not published until 1610, but it was the first evidence that the Aristotelian world was finished, and the first step leading to the 'Two World Systems" and the collision with the Church. It also represented a revolution in how astronomy was done, and a large chunk of it relied on observations made in 1609.

Also, it's short. Slogging through page after page of archaic italian translated into twee Victorian English is mentally draining. You have to restrain the urge to shout "Come to the point already" after a page of waffle.

So I'll do a chapter of the Starry Messenger every week. Strictly speaking, it doesn't have chapters, but there are logical shifts in the content I can pretend are chapters. I'm using a 1960's translation by Edward Carlos, so how well the Italian is translated is unknown.

But I do love how the title page has each line in a different font and typeface, and then there is the language itself


UNFOLDING GREAT AND MARVELLOUS SIGHTS,
AND PROPOSING THEM TO THE ATTENTION OF EVERY ONE,
BUT ESPECIALLY PHILOSOPHERS AND ASTRONOMERS,

And it goes on and on...

Respecting the Moon's Surface, an innumerable number of Fixed Stars,
the Milky Way, and Nebulous Stars, but especially respecting
Four Planets ...

... and on and on, you expect it to end "..and that's not all! Every reader gets a set of steak knives!" Still, that was the style in those times, but it does read oddly to the modern mind.

Even odder is the dedication to Cosmo de' Medici, 6 pages of dedication! Galileo praises Cosmo in terms of such fawning fastidiousness that you half expect him to go "gollum, gollum". But again, in those times, overblown praise of the rich and powerful was de riguer, especially if they were your patron (or you wanted them to be your patron).

But in the middle of all this fulsom praise is this ticking timebomb:

"..while with one accord they [Jupiter and its Moons] complete all together mighty revolutions every ten years round the centre of the universe, that is, round the SUN."

Cheeky Galileo. Next week, the Telescope.

Labels: Galileo