Critical Thinking Questions
(Think about these carefully before you consult the answers below)
QUESTIONS
1) Roemer relied primarily on the motions of the satellite Io for his work on the speed of light. (Refer to the activity.) Why? <answer>
2) There is reason to believe that under rare circumstances, some of the Galilean satellites may be visible to the unaided eye. Which one do you think is most likely to be seen? <answer>
3) Callisto is almost as big as Ganymede, yet it is about 2.5 times dimmer. There may be several explanations. What do you think is the reason? <answer>
4) How would it have affected the course of astronomy if Galileo had not discovered the satellites of Jupiter? <answer>
5) The orbits of the Galilean satellites are almost perfect circles, with eccentricities lower than any planet save Venus. However, the more distant satellites have much greater eccentricities. Why do you think this is so? <answer>
ANSWERS
1) Io is the closest of the Galilean satellites to Jupiter and, as such, moves the fastest (remember Kepler's second law?). Moving the fastest means that its motion is more evident over a shorter period of time, and changes in its position are easier to observe. Since the time differences Roemer was measuring were fairly short, in minutes and seconds, Io was the satellite that was easiest to calculate the differences for -- and is the satellite that has the most eclipses by Jupiter, which was what Roemer was observing in the first place.
2) The magnitudes of the satellites are: Io, 5.0: Europa, 5.3; Ganymede, 4.6; and Callisto, 5.6. Remember that on the magnitude scale, smaller numbers represent brighter objects. Combined with the distances from the planet (you can find this information in your text), it would seem that Ganymede, the largest and brightest of the Galilean satellites, would be the most likely candidate. Although Callisto is nearly twice as far from Jupiter, and hence less affected by the glare of the planet, it is a full magnitude fainter, which means about 2.5 times fainter. Io, which is a bit less bright than Ganymede, nevertheless is much closer to the parent planet, making it much harder to see.
3) Astronomers measure the brightness of planetary (and satellite) surfaces by something called albedo , which is just a ratio of the amount of light reflected off a surface to the amount of light falling on it. A perfectly reflecting surface has an albedo of 1.0, which is unlikely in nature. For instance, freshly fallen snow has an albedo of 0.8 and that of the Earth as a whole is about 0.4. Our moon is very dark on the average, with an albedo of about 0.07. Overall, the Galilean satellites are quite reflective, with albedos of 0.6, 0.6, 0.4, and 0.2 for Io, Europa, Ganymede and Callisto, respectively. From this you can see that Ganymede's surface brightness is twice that of Callisto's, but the question is why is this so?
The currently most popular explanation has to do with tectonic activity (changes in the crust). It appears that Ganymede, having a differentiated interior, also has experienced considerable changes on its surface. Such changes tend to expose new surfaces, which tend to reflect more like. Such a situation has been demonstrated on the Moon. Callisto, with little or no internal differentiation, has had little surface activity. Its surface has not changed much in billions of years, as evidenced by the large number of craters. Older surfaces tend to be darker, as again evidenced on the Moon. This it appears that Ganymede's surface is brighter because it has been more disturbed than that of Callisto.
4) Much of science fiction is built around the question of "What if...." However, in this case there really is no reasonable concern that the course of astronomy would have been different if Galileo hadn't observed the satellites. The fact is that someone else would have, and at least one other Italian may deserve the honor along with Galileo anyway. (There is even some evidence that an astronomer in 4th Century BC China may have recorded them without a telescope.) Jupiter is such a bright and appealing object in the night sky that the discovery of its satellites would not have waited long even if Galileo had never been born. (However, the exact effect on history can never be known, and a mathematical theory known as chaos, which has gained wide acceptance, indicated that relatively small changes in initial conditions could result in major and unpredictable differences in the outcome.
5) The Galilean satellites are large bodies that most likely have been in orbit about Jupiter for a very long time. The gravitational effect of Jupiter is so great that they, like our own Moon, are locked into rotation about the planet, always keeping one face toward Jupiter. Whatever their origin, over billions of years their orbits have evolved into the near circles they are today, an arrangement that minimizes the gravitational differences in different parts of the orbit. (The process is known as "eccentricity damping.") The smaller, outer satellites, however, likely were captured as the passed nearby. Just by the geometry of such capture their resulting orbits are likely to be considerably eccentric. Being farther from Jupiter and taking longer to orbit it, the process of circularization of their orbits has not proceeded as far as that of the Galilean satellites.
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