Strange Tales of Galileo and Proving: Telescopic Evidence for Earth’s Immobility through Double Stars
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Benedetto Castelli

Benedetto Castelli

This is the fourth in a series of posts on the subject of Galileo and proving the Earth’s motion.  This is the year 2017, and 2017 marks the 400th anniversary of the first observation of a double star, made in 1617 by none other than Galileo and his friend the Benedictine Fr. Benedetto Castelli.  Up until our current century, the first observation of a double star had been attributed to the Jesuit Fr. Giovanni Battista Riccioli, but in 2004 Sky & Telescope magazine published an article by Leos Ondra on how Galileo and Castelli were the first to do it (“A New View of Mizar,” July 2004).  Ondra discovered this by going through Galileo’s observing notes.  An extended version of the Sky & Telescope article is available on Ondra’s web page.

The double star that Castelli and Galileo observed was Mizar, the star in the bend of the handle of the Big Dipper.  Seen with the naked eye, it appears to be a single star, but a telescope reveals it to be double.  Apparently Castelli observed Mizar first; then he informed Galileo about it.

Galileo observed Mizar and measured it with precision.  He did not draw the appearance of Mizar as seen through his telescope, but he recorded both the separation of its two components (15 arc seconds, or 15/3600 of a degree, in complete agreement with modern measurements—Galileo was good* with the telescope), and the apparent diameters of those components (6 seconds and 4 seconds).  Based on this record, we can reconstruct what he saw through his telescope, as seen in the figures below.

How Mizar appeared through Galileo’s telescope, according to Galileo’s measurements.

How Mizar appeared through Galileo’s telescope, according to Galileo’s measurements.

This illustration perhaps gives a better idea of the view through Galileo’s telescope.

This illustration perhaps gives a better idea of the view through Galileo’s telescope.

Galileo also calculated the distance to the brighter of the two Mizar component stars, the one we now call Mizar A.  He assumed that Mizar A was the same true physical size as the sun.  The sun has an apparent diameter in the sky of one-half of one degree, or 1800 arc seconds.  That is 300 times greater than the 6 second apparent diameter that Galileo measured for Mizar A.  If Mizar A was the same true physical size as the sun, then it must be 300 times more distant than the sun (30 times more distant than Saturn, the most distant planet known in Galileo’s time).  That’s pretty far away.

All this is in Galileo’s notes.  If you have read the other posts in this series, especially the second and third, you will be unsurprised to learn that there is something strange about Galileo’s Mizar data!

Recall (from the first, second, and third posts in this series) that, despite the title of Galileo’s 1632 book, Dialogue Concerning the Two Chief World Systems—Ptolemaic and Copernican, the real competition for the sun-centered Copernican system was not the Ptolemaic system but the Earth-centered system of Tycho Brahe.  No observation of the sun, moon, or planets could distinguish between the Copernican and Tychonic systems.  The only astronomical observations that could tell which system was correct were observations of the stars.  As mentioned in the third post, Galileo discussed in the Dialogue using a distant Earth-bound reference point (a wooden beam on a roof of a chapel on a far hill) to use the stars to prove that Earth moves around the sun.  But he also wrote about a way to use the stars alone to prove Earth’s motion.

The Tychonic geocentric (left) and Copernican heliocentric

The Tychonic geocentric (left) and Copernican heliocentric (right) theories.

In the Dialogue Galileo wrote,

I do not believe that the stars are spread over a spherical surface at equal distances from one center; I suppose their distances from us vary so much that some are two or three times as remote as others.  Thus if some tiny star were found by the telescope quite close to some of the larger ones, and if that one were therefore very very remote, it might happen that some sensible alterations would take place among them.

Were this to happen, he wrote, then the stars themselves “would appear in court to give witness” to Earth’s motion.  What does he mean?

What he means is that, instead of using an Earth-bound reference point to detect whether the stars reflect Earth’s motion, one star could be used as a reference point against another.  Suppose two stars are arranged as Galileo says in the quotation above—a small-looking star next to a larger-looking one.  Suppose also that, like Galileo says, this arrangement is the result of the smaller-looking star being farther away than the other.  It follows that, if Earth orbits the sun, the alignment of these two stars must change over the course of a year, as shown in the figures below.  This phenomenon is known as differential parallax.

The Earth orbits the sun (s), moving clockwise from A to B.  Stars q and p are both similar in size to the sun.  They are located at differing distances from Earth.  When the Earth is at A, the line of sight from Earth to q and p is such that the two stars appear very close together, as shown at below left.  When Earth is at B, the line of sight is such that the two stars will appear more separated, as shown at below right.  When Earth returns to A, the two stars will again appear very close together.  This is differential parallax.  The differential parallax for a star at a distance of 300 times the distance to the sun (as Galileo calculated for Mizar A) is quite large, and should reveal Earth’s motion in a very short period of time, especially given Galileo’s great skill with the telescope.

The Earth orbits the sun (s), moving clockwise from A to B.  Stars q and p are both similar in size to the sun.  They are located at differing distances from Earth.  When the Earth is at A, the line of sight from Earth to q and p is such that the two stars appear very close together, as shown at below left.  When Earth is at B, the line of sight is such that the two stars will appear more separated, as shown at below right.  When Earth returns to A, the two stars will again appear very close together.  This is differential parallax.  The differential parallax for a star at a distance of 300 times the distance to the sun (as Galileo calculated for Mizar A) is quite large, and should reveal Earth’s motion in a very short period of time, especially given Galileo’s great skill with the telescope.

But wait a minute!  Granted all this, why does Galileo write “if some tiny star were found by the telescope quite close to some of the larger ones”?  Why the “if”?  After all, he wrote the Dialogue in 1632, but he had observed Mizar—and other double or multiple star systems, including the Trapezium in Orion, which he sketched*—more than a decade earlier, in 1617.

Perhaps the reason why is that Mizar shows no differential parallax!  Neither does the Trapezium.  In fact, no double star that Galileo might have observed shows differential parallax.  And no differential parallax means that the ideas Galileo promotes in the Dialogue, regarding how the Earth is circling the sun and how the stars are suns at differing distances from Earth, cannot be correct.  In fact, for a variety of reasons, Galileo’s Mizar observations really suggest that Earth is not moving at all.*~  Had he published the Mizar observations, no doubt plenty of people would have considered double stars to be an argument against Copernicus.

But, in fact Galileo did not publish his double star observations.  They remained buried in his notes for centuries, waiting for Leos Ondra to discover them.  Meanwhile, Riccioli became known as the first person to observe a double star.

Should Galileo have published his double star observations?  Certainly.  From a scientific standpoint, if he is going to promote the ideas that Earth circles the sun, and that the stars are sun-sized bodies at varying distances from Earth—and that for these reasons a double star might reveal differential parallax and thus appear in court to give witness that Earth does in fact move—then, yes, he should also mention that he has already observed exactly the sort of double star system that he describes, and that those observations contradict the ideas he is promoting.  When Galileo wrote in the Dialogue about how “if some tiny star were found by the telescope” close to a large star, he was sitting on exactly that sort of observation, right in his notebooks.  Scientifically speaking, that’s definitely not cool.

But as we have seen, Galileo could be scientifically uncool in the DialogueHe omitted information he had that ran counter to his theory that the tides showed that earth moved.  He made impossible claims about how supposedly splitting the disks of stars could show that Earth moved.  And, he sat on his own data that challenged his claim that double stars could show that Earth moved.  Galileo was great scientist.  He should be honored as one of the greats.  But, in trying to prove that the Earth moved, he did stuff that scientists are not supposed to do.  Galileo was not punished for proving that Earth moved.  But some of the things he did while trying to prove Earth’s motion would get him in trouble in the scientific world today.

Deirdre Kelleghan, artist and fellow blogger for The Catholic Astronomer, was kind enough to take a crack at observing Mizar with a stopped-down telescope, in order to give an idea of what Galileo might have seen. The magnification in these is 34x, similar to what Galileo might have used. The drawing at right is with a 45 mm aperture—it clearly shows the two stars of Mizar. The drawing at left is with a 15 mm aperture—which is much less clear. Galileo’s view was probably somewhere between these two. I gave Deirdre no hint of what to expect, so that her impression would not be biased by expectations.

Deirdre Kelleghan, artist and fellow blogger for The Catholic Astronomer, was kind enough to take a crack at observing Mizar with a stopped-down telescope, in order to give an idea of what Galileo might have seen.  Deirdre warns that "At this time of year at this latitude, it could hardly be called nighttime. The sky to the southwest was almost in daylight at the time of drawing, the seeing wasn't the best either."  The magnification in these is 34x, similar to what Galileo might have used. The drawing at left is with a 45 mm aperture—it clearly shows the two stars of Mizar. The drawing at right is with a 15 mm aperture—which is much less clear. Galileo’s view was probably somewhere between these two. I gave Deirdre no hint of what to expect, so that her impression would not be biased.


*An illustration of Galileo’s skill is shown in the figure below. 

The white inset figure is Galileo’s sketch of the Trapezium in Orion (a close star grouping, similar in size to the Mizar double).  The larger surrounding figure is that sketch superimposed on a modern photograph of the Trapezium.  Note that Galileo’s sketch lines up almost perfectly with the modern photograph.

The white inset figure is Galileo’s sketch of the Trapezium in Orion (a close star grouping, similar in size to the Mizar double).  The larger surrounding figure is that sketch superimposed on a modern photograph of the Trapezium.  Note that Galileo’s sketch lines up almost perfectly with the modern photograph.

Illustration from John Herschel’s nineteenth-century Treatise on Light, illustrating the appearance of a star as seen in a very small telescope such as Galileo used.  The diameter of this apparent globe is what Galileo measured, but the globe is entirely spurious, a thing formed inside the telescope itself by the diffraction of light waves.

Illustration from John Herschel’s nineteenth-century Treatise on Light, illustrating the appearance of a star as seen in a very small telescope such as Galileo used.  The diameter of this apparent globe is what Galileo measured, but the globe is entirely spurious, a thing formed inside the telescope itself by the diffraction of light waves.

*~The lack of differential parallax in Mizar does not completely rule out a moving Earth.  For example, it could mean that Galileo was wrong about the stars being at differing distances from Earth.  Were they all on a sphere centered on Earth, and not at the differing distances that Galileo said, then they would show no differential parallax.  In this case Mizar A and Mizar B would just be of differing size, and at the same distance from Earth, and their alignment would not change as Earth moved.  The problem with this is that the stars kind of look like they are at differing distances, something Albertus Magnus noted centuries earlier.  Or, Galileo could be right about Mizar A and B being at differing distances, but wrong about how far away they were.  The problem in this case is that they have to be very far away to have no differential parallax, something like 100 times farther than Galileo calculated.  To be 100 times farther away and still measure 6 and 4 arc seconds in apparent size, they would have to be 100 times larger than Galileo supposed, too.  That would make them gigantic, and not like the sun, in contrast to Galileo’s ideas.  Gigantic stars were an idea many people at the time found absurd.  Of course, as mentioned in the third post of this series, the 6 and 4 arc second sizes Galileo measured for Mizar A and B are spurious (as were all such measured star sizes), an artefact of the wave nature of light.  The true sizes of stars were much smaller, so that they could be at the vast distances required to have no differential parallax and not be absurdly large.  However, Galileo did not know that the sizes he was measuring were spurious.

 


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