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This picture shows a 16 second exposure of Jupiter's moons taken on Nov. 28, 2002 at 2:10 PST. Since the dynamic range of the camera and computer display are much less than that of the human eye, to show Jupiter's moons photographically, the planet's disk has to be highly overexposed, bringing out a violet fringing due to chromatic aberration. For clarity, a normally exposed image of a circular region around Jupiter's disc has been pasted over the original. The violet fringing is not nearly as apparent to the human eye as it is to the camera. Both the moons and Jupiter's disk are shown at their original scale of 0.726 arc-seconds per pixel. Jupiter was 5.29 astronomical units (791 million kilometers) from Earth and 40.2 arc-seconds in apparent diameter when this photograph was taken.
Astronomers describe the brightness of objects using a system of visual magnitudes. In this photo, according to the JPL Horizons ephemeris system, Europa, 3.1 arc-minutes to the left of Jupiter, shines at visual magnitude 5.7. Callisto, second from the left, is 2.0 arc-min from Jupiter at Vmag 6.4. Io, 1.1 arc-min to the right, is at Vmag 5.6; while Ganymede, 4.1 arc-min to the right of Jupiter, is Vmag 5.2. Jupiter was at Vmag -2.3. The difference of about 8 magnitudes means that Jupiter produces some 1600 times more light than any one of its moons. These differences in brightness are largely a result of the differing sizes of the objects, although Callisto is less reflective as well. The four Galilean moons appear to have finite disks in this photo, but this is entirely an artifact due to diffraction in the telescope and blooming in the CCD. The actual disks of the moons (on the order of 1 arc-second in apparent diameter) are much too small to be resolved by a 1-inch aperture telescope.
Since the moons revolve around Jupiter with periods of 1 to 16 days, their pattern is constantly changing. Galileo embarked on a many years long program of extremely careful measurements of the spacings between Jupiter's moons believing that this astronomical clock might provide a practical means for determining the longitude of ships at sea ( Drake, 1979). To make these measurements Galileo is believed to have looked through his telescope with one eye while gazing with the other at a ruled scale fixed to the telescope tube. It is believed he slid the scale towards and away from his eye until the diameter of Jupiter as seen through the telescope matched one division on the scale viewed with the other eye; then noted the positions of the moons in the same units. This is actually surprisingly easy to do as you can verify for yourself looking at Jupiter through any telescope stopped to 1 or 2 inches around twilight. A possible model of such an instrument is on display in the museum at Florence; other investigators (see the Scientific American article referenced below) have slightly different impressions of how it may have looked.
Galileo's observations of the moons of Jupiter were so meticulous that American astronomer Charles Kowal and Galileo scholar Stillman Drake, inspired by an article by Steven Albers in the March 1979 issue of Sky and Telescope predicting that Jupiter must have passed over (occulted) Neptune on January 4, 1613, examined Galileo's manuscripts and found evidence that Galileo had indeed recorded the location of Neptune in his notebooks, although not on the day of the occultation. Another possible sighting was later located by E. M. Standish and A. M. Nobili. Neptune, which was not recognized as a planet until 1846, shining at about magnitude 8, would have been much fainter than the four moons shown here, yet much brighter than any of the many other moons which Jupiter is now known to possess. The next most prominent moon in the solar system is Saturn's moon Titan, which is at a similar apparent distance from its parent planet as the moons of Jupiter, but is only of magnitude 8.4. Titan was first reported by Christian Huygens in 1655. Huygens was using a 2.25 inch diameter singlet objective with a focal length of 12 feet. It is actually a little surprising that Galileo missed Titan, since according to Drake and Kowal he would occasionally record stars as faint as 9th magnitude, and, after his discovery of Jupiter's moons, must have looked very carefully for moons around any of the other planets. As shown on our Saturn Page, we have been able to photograph Titan through our Galilean telescope, and suspect that a younger person would be able to see it visually. Also as shown on our Pleiades Page, in portions of the sky far from the glare of a bright planet Galileo was obviously able to see stars to near magnitude 9 even with his earliest telescopes. But neither of these observations in any way proves that Galileo should have been able to see Titan. Jupiter itself has many more moons, but the next brightest one after the four discovered by Galileo shines only at around magnitude 14, far beyond the range of Galileo's telescope.
Our 16-second exposure, especially as processed above, makes Jupiter's moons appear more prominent than they do to the eye. Since the telescope is unable to resolve the moons, they appear as tiny pinpoints of light on the retina; and their brightness is a function of the light gathering power of the telescope, which is in turn a function of the area of the entrance lens. Compared to an unaided eye with a pupil of 4 mm diameter, the 23 mm aperture of our 1-inch lens should increase the number of photons reaching the retina by a factor of about (23/4)2 = 33X. This amounts to an advantage of about 4 magnitudes (5 magnitudes = 100X in intensity). The telescope also somewhat darkens the disk of Jupiter and the sky background against which the "stars" are seen. The apparent brightness of an extended source, such as the Moon or the sky, as seen through a telescope, is determined by something called the exit pupil of the telescope. The diameter of the exit pupil is equal to the diameter of the objective lens divided by the magnification (power) of the telescope. If the area of the exit pupil is larger than the area of the pupil of the observer's eye, the object will be seen with its normal brightness. If the area of the exit pupil is less, the brightness of the object will be dimmed in proportion to the ratio of the areas. In the present example, with an objective diameter of 23 mm at 20 power, the diameter of the exit pupil is a mere 1.15 mm. For an observer with a pupil of 4 mm diameter, this means that the apparent brightness of the Moon, sky, and other extended objects, as seen through the telescope, will be reduced by a factor of (4/1.13)2 = 12.5X, compared to the brightness that would be seen directly with the naked eye. Because Jupiter, with an apparent diameter, to the naked eye, of a little under one minute of arc, is at the borderline between a point and an extended object, the effect of the telescope on its apparent brightness will be somewhere between these two extremes. Hence, the telescope helps to improve the contrast between Jupiter and its moons, but, just as for the camera, the bright glare from Jupiter still makes the tiny moons more difficult to see than they would be by themselves in a clear patch of sky.
With our Galilean replica under a hazy and light-polluted urban sky in conditions where the unaided eye cannot see much beyond 3rd or 4th magnitude, we often find Jupiter's moons rather difficult to see, and Callisto, especially, is often near our limit of visibility. Although a clearer and darker sky (as Galileo undoubtedly enjoyed in seventeenth century Italy) would undoubtedly make the moons much more visible, experience and expectation also play a role. It is probably not surprising that some of Galileo's contemporaries, being unable to see the moons on looking through his telescope, were dubious of his claims. Rice University's Dr. Albert van Helden, notes that even some modern college students, fully convinced of the reality of the moons, are unable to see them when looking through the eyepiece of a replica of Galileo's telescope. More recently, Italian astrophysicist Costantino Sigismondi, repeating this experiment with a group of novice observers at Yale University, and using what seems to us a not-very-accurate recreation of Galileo's telescope, reported a similar experience. In his presentation, Sigismondi says repeatedly that part of the problem was that, due to chromatic aberration, the apparent diameter of Jupiter as seen through Galileo's telescopes was five times the diameter it would have had with no aberration. We hope the present photograph does not reinforce this highly misleading view. The human eye is much more tolerant than the digital camera to handling extreme ranges of brightness. Although the camera sees a haze of violet light extending to nearly four times the true diameter of Jupiter, this does not mean the human eye sees a disk of that size. In other words, although the haze of violet light does interfere with the eye's ability to detect the satellites when they are very close to Jupiter, it is much less noticeable to the eye than the camera makes it seem. In fact, the disk of Jupiter appears much more like the pasted in normal exposure, with a well defined edge (limb). To get a better impression of how the appearance of the photographs changes as the length of the exposure is increased, please see our photos of the moons of Saturn. According to Standish and Nobili, Galileo overestimated the true diameter of Jupiter by at most 10%; and Stillman Drake says that by 1612 Galileo had determined the apparent diameter of Jupiter to vary during the year (as the Earth moves nearer and farther from it) from 39.5 to 41.5 seconds of arc (compared to the modern value of 32 to 48 arc seconds). We can find no evidence that the chromatic aberration in Galileo's telescope caused him to see Jupiter five times its actual size, as Sigismondi seems to be suggesting.
In addition to the many later and extremely accurate manuscript records referred to by Standish and Nobili, Galileo published a series of schematic diagrams showing the observed positions of the moons of Jupiter, for January 7 through March 2, 1610, in his early book Sidereus Nuncius (printed within days of the final observation). The moons depicted in the first few of these diagrams were identified by the famous Belgian meteorologist and amateur astronomer Jean Meeus in a classic paper in the February 1964 issue of Sky and Telescope (pp. 105-106), in which he compares the drawings to the positions calculated by modern astronomical software. Meeus concluded that the glare from Jupiter in the Sidereus Nuncius telescope prevented Galileo for seeing moons closer than about 1.5 Jupiter radii (approximately 1 minute of arc) from the planet's edge, and that he sometimes saw two moons merged as a single dot of light when they were, in reality, as much as one Jupiter radius (or about 20 arc seconds) apart. Again, the failure to see satellites close to Jupiter does not mean that Jupiter itself appeared distorted, but only that the glow in the sky near Jupiter exceeded the feeble brightness of the moons, just as the normal brightness of the sky prevents us from seeing stars with the naked eye until after the Sun sets. It should also be noted that in Galileo's numerous later observations of Jupiter there are many examples of him recording satellites both closer to Jupiter and closer to one another than in the early examples studied by Meeus. Highly impressed by Meeus' work, Stillman Drake, in an appendix to his 1983 translation of and commentary on Sidereus Nuncius, analyzed all 65 Jupiter drawings appearing in that book, comparing both the verbal and pictorial descriptions of the moons' positions to their positions as calculated by a modern ephemeris. Drake concluded that even with this early telescope Galileo was generally able to resolve two moons when they were separated by more than about 10 seconds of arc. Unfortunately, it is difficult to verify Drake's results because the moons move relatively rapidly, and Drake is not explicit about either the ephemeris he used or the exact universal times of observation he assumed. The publicly available verion of the benchmark JPL Horizons ephemeris of planetary positions refuses to predict positions for the Galilean satellites of Jupiter prior to 1925, even though we know their positions in earlier eras can be estimated with considerable precision.
In his Discourse on Bodies Floating in Water (published in 1612), Galileo asserts that the positions of the Galilean satellites shown in Sidereus Nuncius were estimated by eye using Jupiter as a size reference, and that he had since developed a new system precise to a few seconds of arc (see p. 19 of Drake, 1981). The new system is believed to have involved visually superimposing the image seen by the eye looking through the telescope onto a graph-paper-like grid viewed with the other eye. According to Standish and Nobili, after correcting for the systematic 10% error in scale, the positions of the moons indicated on the drawings made using this later method are usually accurate to within the width of the dot of ink used to represent them.
The present photo shows a tighter than normal clustering of the moons of Jupiter. The moons are also not always seen in so straight a line. At Jupiter's average distance of about 5.2 astronomical units from Earth, the apparent radii of the orbits of the four satellites are approximately 1.9 arc-min (Io), 3.0 arc-min (Europa), 4.7 arc-min (Ganymede) and 8.3 arc-min (Callisto). Less than half the time will all four moons fall simultaneously within a span of 7 arc-min or less, as shown here; and when Jupiter is closest to Earth (making the orbits appear larger) the span of the moons may occasionally exceed the 14 arc-minute diameter field of view of the Galilean telescope. Even then, however, all four moons should be visible by moving the eye around the eyepiece while pointing the telescope at Jupiter. Our Photo-Drawing Comparison page shows an example of one of Galileo's many drawings of a grouping similar to that shown here.
Although two belts are easily visible in the contrast-enhanced photo of Jupiter on our Photo-Drawing Comparison page, we are unaware of any evidence that Galileo ever reported seeing surface markings on Jupiter or any other planet. The belts' small size (compared to the resolution of the telescope) and low contrast make them very difficult for the unprepared eye to perceive in an instrument of small aperture. Jupiter's famous Great Red Spot, if it even existed in the early 1600's, would have been even more difficult to see. The normally exposed and un-enhanced photo of Jupiter at the top of this page gives a clearer idea of the difficulty of seeing Jupiter's belts through the eyepiece of the Galilean telescope.
For those interested in early telescopic observations of Jupiter's belts and the history of the Great Red Spot we can recommend John Rogers' meticulously researched 1995 book, which contains copious references to his original sources, many of which are available on-line. According to Rogers, the first known mention of belts on Jupiter is that by Niccolo Zucchi in 1630. Should Galileo have known of these observations, he may not have believed them, for he had a rather unpleasant habit of rejecting out-of-hand all discoveries made by others.
Jupiter References :
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Last modified: May 16, 2008