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The image at left below is a 4 second exposure at ISO 400 of the Trapezium in Orion taken at 11:54 pm PST on December 30, 2004. This well-known star system, located in Orion's sword and known more formally as Theta 1 Orionis (or 41 Ori), consists of a large number of components, the four brightest of which are identified in the center diagram, along with their relative spacings in arc-seconds. The original photo clearly shows all four components, but depending on the contrast and brightness of your monitor, Theta 1 Ori B may be very difficult to see. For this reason, an enhanced version of the photo is shown at right, in which the photometric curve has been adjusted to emphasize faint features and de-emphasize the brighter ones. The bright features immediately to the right of star "C" are believed to be fragments of the diffraction rings around that star.
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The photos are shown at a scale of about 0.24 arc-seconds per pixel, three times their original size. 8-th magnitude Theta 1 Ori B is well separated from its 7-th magnitude neighbor Theta 1 Ori A, some 9 arc-seconds away. Since the Rayleigh limit of a perfect 23-mm telescope in green light is around 6 arc-seconds, it is evident from this photo, as well as from test photos of terrestrial objects, that telescopes of the Galilean design can work very well. The spacings listed in the diagram are the values for 1965 extracted from the charts of ground-based Trapezium measurements, 1835-1965, given in an article by Allen, Poveda and Worley.
This region is of particular interest because on February 4, 1617 Galileo made a careful drawing in his notebook of a star field including the Trapezium. The stars Galileo labeled c, g and i correspond to what are now known as Theta 1 Ori D, C, and A. Galileo does not show Theta 1 B, which was evidently either too dim or too close to Theta 1 A for him to see. With the exception of Theta 1 Ori B, it appears from the drawing that the view of the Trapezium through Galileo's telescope was very similar to what we see through the modern replica. We conclude from this that Galileo's telescope worked very well.
This picture shows a larger section
of our photo, including two more distant field stars
(that Galileo labeled a and b), superimposed on Galileo's drawing.
The photo is at its original scale of 0.73 arc-seconds per pixel.
Galileo's drawing was enlarged until the spacing between his stars b and g matched
those two stars in the photo.
The exactness with which the remaining stars register is truly remarkable.
Galileo's b is the 5th magnitude star Theta 2 Orionis (43 Orionis); while a
is a 6th magnitude star sometimes
regarded as a widely-spaced double with b, in which case it is referred to as Theta 2 Orionis B.
As pointed out by Czech amateur Leos Ondra,
Galileo's text accompanying the drawing states that the apparent spacing of stars
a and g, as seen through his telescope,
exactly matched the apparent spacing of two of the stars in Orion's belt as seen with the unaided eye.
This implies a power of about 27 for his telescope.
Ondra appears to have learned about Galileo's observation of the Trapezium from a 1949
article by Umberto Fedele, but the
calculation of the power of Galileo's telescope seems to be original to him.
An English language translation of Galileo's Latin notes (which appear, along with his drawing, on Volume 3 and Page 880 of the National Edition) has been most kindly provided to us by University of Nebraska Classics Professor Thomas N. Winter:
The arrangement of fixed stars pictured here was discovered by me near the point of Orion's sword, from which they arise toward the north and lean a bit to the east; and g and b appear equal in magnitude, a smaller really by little, but two, c, i, rather faint, scarcely a fourth or fifth part of g itself. Three, a, b, g, form a very obtuse angle. The lines through b, a, and through i, c, are almost parallel, but will [eventually] meet [in a direction] towards c, a. Two, c, i, are equidistant from g, which they practically touch. The distance between a and b is adjudged three semidiameters of Jupiter, to which the distance b-g seems triple. These things were observed by me the fourth day of February 1617 at Bellosguardo.
The point of Orion's sword falls on the 18th degree of Gemini with latitude 30 degrees south. The angle cgi is barely obtuse. And a, g themselves, carried across by means of the telescope which I customarily use, towards Orion's belt, fall upon and are congruent with two of the belt itself, i.e., with the middle and the other of the sides, so that a straight line through a, g, is parallel to those which are in the belt. Further, the interval between g and whichever one of them you like, c or i, would scarcely take another g.
Note that although in the first paragraph Galileo implies that stars c and i nearly touch star g, in the final sentence of the second paragraph he may be saying he actually sees a gap between them roughly equal to the apparent size of star g. This would imply his resolution was a little better than that achieved in our modern photograph. His use of the Latin word "intercapedo" for "interval" is a little ambiguous, however, and more likely means, as his ink drawing seems to indicate, that the distance between centers of c-g and i-g is about the same as the apparent diameter of g. In that case his resolution would have been slightly worse than that of the present replica telescope. Galileo seems to have achieved a cleaner separation of similarly-spaced double stars in his observation of Mizar. Seeing conditions, a less perfect telescope, and the dimness of the target stars all could have contributed to poorer visual separation.
Some have expressed puzzlement that in his text Galileo does not mention the nebulosity (known in modern nomenclature as M42) enveloping these stars. There are two likely reasons for this. First, we have become accustomed to seeing deeply-exposed images of M42 taken through faster and larger aperture instruments. Through a small aperture, long focal length, low power telescope, the unusual pattern of stars is much more striking than the faint nebulosity. This is evident, for example in our larger photo. In such a short exposure the stars are quite striking, but the sky between them appears black. This is also evident in our mosaic photo of the Pleiades, where the well-known nebulosity is not visible. Second, since Galileo believed, as he explains in Sidereus Nuncius, that what looks nebulous to the eye is resolved into stars by his telescope; what looks nebulous through his telescope could presumably also be resolved into stars by a still larger and more powerful telescope. Hence, a diffuse glow would be, more than anything, an indication of the limitations of his telescope and not particularly worthy of special note.
As explained on our Jupiter Page, for a telescope of a given aperture, when the magnification is extended beyond a certain limit (where the exit pupil becomes smaller than the observer's eye), the apparent brightness of extended objects like the planets and the sky are diminished relative to the stars. Modern binoculars (e.g., 36 mm aperture at 6 power giving an exit pupil of 36/6 = 6 mm) operate close to this limit. Increasing the magnification without increasing the aperture would make the view seen through them dimmer. At 20 or 30 power, Galileo's telescopes were well beyond this limit. Since high resolution is not required to see nebulae, some of his contemporaries observing with inferior telescopes having similar apertures but lower power would likely have been much more impressed with M42.
The next known drawing of the Trapezium stars is that of Christiaan Huygens. It appears in his celebrated sketch of the outline of M42 made in 1656 and published on page 8 of his Systema Saturnium (1659). Huygens, like Galileo, noted that the three Trapezium stars appeared to nearly touch, but, like almost every visual observer to follow Galileo, in his drawing Huygens somewhat exaggerates the spacing of the Trapezium stars relative to their neighbors. We believe that Galileo's sketch may well be the most accurately proportioned representation of this star field ever recorded by hand at the eyepiece.
Quite recently, science historian Harald Siebert has re-examined the question of Galileo's early observations of Mizar and the Trapezium, and their relation to the search for stellar parallax. Although Siebert proves himself totally incapable of recognizing the stars portrayed in Galileo's Trapezium diagram, he does seem to have, in the footsteps of Umberto Fedele and Leos Ondra, searched thoroughly through the pages of the National Edition, and has been able to provide some additional interesting footnotes on Galileo's correspondence with Castelli and others on this subject. Siebert believes Galileo's thrill at recording this particular observation to have been heightened by his awareness that this peculiar juxtaposition of bright and dim stars would be ideal for their search for stellar parallax: the apparent motion of near stars compared to distant ones due to our changing perspective as the Earth moves in its yearly orbit about the Sun. In fact, Siebert thinks the Latin word "apposita" with which Galileo starts his Latin description should actually be interpreted as equivalent to the rather obscure English word "apposite" meaning "relevant" or "apropos": that is, Galileo is telling himself he has discovered an arrangement of stars particularly apropos to the search for parallax. However that may be, according to a letter cited by Siebert, Galileo's friend, Castelli, even after being informed of its existence by Galileo, was unable to find the Trapezium. Siebert attributes this to Galileo's faulty directions for locating it. We can find nothing wrong with Galileo's directions as given above (although in fairness we don't know what Galileo said to Castelli). Siebert apparently does not appreciate the difficulty (due to its tiny field of view) of sweeping the sky with a Galilean telescope. Also, Castelli may well have been using an inferior telescope which, due either a smaller aperture or less perfect lenses, was unable to resolve stars c and i with clarity, even when they were within its field of view. Indeed, Galileo seems to have reserved his best telescopes as gifts to people in power, and does not seem to have been overly generous in providing them to working astronomers, perhaps out of fear of competition. Although Siebert, like others, is convinced that Castelli had previously discovered Mizar B and reported it to Galileo, this is not totally obvious from the letter he cites. Castelli had previously pointed out to Galileo the system of Mizar, Alcor and the faint star sometimes called Sidus Ludoviciana (without any mention of Mizar B). In asking Galileo to re-examine "the third star in the tail of the bear," it is not clear that Castelli is doing any more than reminding Galileo that, in Castelli's opinion, the previously mentioned system of three stars is still the best suited for detecting parallax; Castelli having previously thought he detected a change in the position of Sidus Ludoviciana. As with the Trapezium, the first clear description of Mizar A/B is not by Castelli, but by Galileo (see our Mizar Page). Siebert, and others, may have overestimated the capabilities of Castelli's telescope. Indeed, when Castelli announces in a later letter to Galileo that he has discovered a companion to Beta Scorpius, Siebert declares that Castelli could not possibly be referring to its 5th companion, Bet 2 Sco, because the latter, at a separation of 25 arc-seconds (in 1627), is impossibly far away. Instead, Siebert advances the (what seems to us rather incredible) hypothesis that Castelli was reporting to Galileo his discovery of an 11th magnitude companion 9 arc-seconds from the magnitude 2.5 primary star, something that would require a very good telescope indeed! At the same time, he seems to underestimate the accuracy of Galileo's telescope, declaring that the agreement of Galileo's estimate of the separation between Mizar A and B (15 arc-seconds) with the modern value could not possibly be anything but an accident.
In addition to his commentary on Galileo's drawings, Siebert mentions a diagram of a triple star in Orion published by Czech astronomer Anton Maria Schyrleus of Rheita in his 1645 book Oculus Enoch et Eliae; and also the purported sketch of the Trapezium in a 1654 book by Sicilian astronomer G. B. Hodierna. We compare Rheita's and Hodierna's drawings on a separate page. Despite its wide acceptance as such, Hodierna's drawing clearly does not depict the Trapezium. Rheita's unscaled sketch seems far more likely to be an actual drawing of Galileo's stars c, g, and i; although Rheita is known for having made many strange claims.
Almost equally strange (if we understand what he is saying) is Siebert's claim that Galileo's sketch of a cardboard guide for checking the angle between three stars (possibly, but by no means certainly Mizar, Alcor and Sidus Ludoviciana) is an aperture mask to be placed over the front of the telescope. We are unable to understand how placing such a mask over the objective could in any way assist with such a measurement. When Galileo says to place it at on the top of the telescope, we must assume he did indeed mean to mount the guide at the objective end, but a little to one side where, like his Jupiter moon measuring reticle, it could be visually superimposed on the image of the stars drifting over it (by looking at the guide with one eye while looking through the telescope with the other). In this way he apparently hoped to detect small deviations from the original angle. In the case of the three Trapezium stars, because their separation is so slight, it seems unlikely that such a guide would have been used.
The following table provides a cross-identification of Galileo's star designations with the modern nomenclature, and also gives the normal modern visual magnitude of each. Most of these stars are variable. Theta 1 Ori A & B, in particular are noted as eclipsing binaries, the magnitude of A dropping briefly to 7.65 every 65.4 days, while B drops to 8.65 every 6.5 days. Click on the Henry Draper Catalog Number to bring up additional information about each star, including its identity in numerous other catalogs, via the SIMBAD database, operated by the CDS in Strasbourg, France.
| Galileo ID | Flamsteed/Bayer ID | Henry Draper Cat. No. | Magnitude |
|---|---|---|---|
| a | The 2 Ori B | HD 37042 | 6.02 |
| b | 43 The 2 Ori A | HD 37041 | 5.08 |
| c | 41 The 1 Ori D | HD 37023 | 6.71 |
| g | 41 The 1 Ori C | HD 37022 | 5.13 |
| i | 41 The 1 Ori A | HD 37020 | 6.73 |
| -- | 41 The 1 Ori B | HD 37021 | 7.96 |
Since the Trapezium region is both relatively nearby (~1,500 light years from Earth) and extremely young (astronomically speaking) and since nearly 400 years have elapsed between the drawing and the photograph, some changes in the pattern of these stars might be expected.
The relative motions of many of the Trapezium stars over a span of 160 years have been updated in a recent article by Allen, Poveda and Hernández-Alcántara. Although they find other Orion star pairs separating at an easily noticeable 6.6 arc-sec per century, the components of The 1 Ori (referred to in the paper as ADS 4186) are relatively stable. The most rapid motions detected were between components A & B, which were found to be moving apart at 0.18 arc-sec/century; and between components A & C, moving together at 0.11 arc-sec/century. They could detect no systematic change in the spacing between components C & D. Since the total motion in 400 years is under an arc-second, these changes would be undetectable in our comparison. The apparent positions of Galileo's field stars a and b appear to be stable to about the same level. The most rapidly moving star in the field appears to be Galileo's star a. The SIMBAD basic data screen indicates a proper motion in declination of 7.2 mas/yr, which would move its relative position by 3 arc-seconds in 400 years; however, this appears to be a misprint. A direct inquiry to the TYCHO database, from which this number is said to be derived, indicates the correct figure is 2.1 mas/yr. The listed proper motions for the other stars are of a similar magnitude or smaller. Our conclusion is that no relative motion would be expected at the resolution limit of a 1-inch telescope.
Changes in relative magnitude are another matter. Galileo draws and comments on his star a being only very slightly dimmer than stars b and g; yet our photo and the official modern magnitudes indicate a is now noticeably dimmer.
As to the power of Galileo's telescope we are able to confirm Leos Ondra's estimate. The current spacing of Galileo's stars a and g is 2.96 arc-min. If, when viewed through the telescope, these match the spacing between the center and right-hand stars in Orion's belt (Alnilam-Mintaka, current spacing = 83.2 arc-min) the power would be 28.1. If they match the center and left-hand stars (Alnilam-Alnitak, current spacing = 81.4 arc-min) the power would be 27.5. Again, these spacings would have changed by at most a few arc-seconds in 400 years.
Although the camera sees this star field clearly, the Trapezium through a 1-inch 20-power Galilean telescope is an extremely difficult target visually. Its stars are both dim and closely spaced. The senior author's 33-year old son said he could see Galileo's c, g, and i stars with ease, but under the prevailing sky conditions neither of us was able to see g or i.
It is an eloquent tribute to Galileo's skill as an observer that he was able to produce so accurate a drawing. Yet while truly remarkable, the meticulousness of this observation is not unprecedented. Standish and Nobili note that the position of the moons in Galileo's many drawings of Jupiter tend to be accurate to less than the width of dots used to depict them.
The image at left is the raw 4 second exposure shown at its original scale. Unlike most of the photos on this website, which were taken at ISO 100, the camera was set at ISO 400 and, depending on how your monitor is set, you may be able to see a considerable amount of background noise. The effective exposure time is eight times greater than that used for photographing the double star Mizar. The image on the right is the same photo after the background of hot pixels has been subtracted. The background noise was further suppressed to produce the final images shown at the top of the page.
References :
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Last modified: March 15, 2006
