JUPITER AND ITS MOONS By Rob Ochs, Norwich Free Academy, Norwich, CT Through this exercise, students will read a historical account of the discovery of JupiterÕs moons, observe them using MicroObservatory, perform image processing techniques to enhance their images of the planet and moons. Students will then carry out excercises through which they will track the moons, identify which moon is which, track their periods, and determine the mass of Jupiter using their MicroObservatory images and a number of calculations. The Sky software is recommend for part of this activity, however, the information from The Sky can be found elsewhere, or by using the software program Voyager. The simulation part of the activity requires a software program, such as The Sky or Voyager, that can simulate orbits. If any such programs, or ones like them are unavailable, students may be advised to consult reading materials, electronic or print, to explore the orbits further. BACKGROUND Sir Isaac Newton (1642-1727), in a letter to Robert Hooke wrote, If I have seen further (than you and Descartes) it is by standing upon the shoulders of Giants No scientist works in isolation, all utilize the works of those who have gone before. The Italian physicist Galileo Galilei was not the inventor of the telescope, nor was he the first to observe the heavens through a telescope. The telescope was actually invented in Holland, but some controversy exists over the actual inventor. The invention is usually ascribed to Hans Lippershey, a Dutch spectacles maker, about 1608. In 1609 the Italian astronomer Galileo exhibited the first telescope on record. The German astronomer Johannes Kepler discovered the principle of the astronomical telescope with two convex lenses. This idea was employed in a telescope constructed by the German Jesuit astronomer Christoph Scheiner about 1630. Because of the difficulties caused by irregularities in the curvature of the lenses, early astronomical telescopes had to be of considerable focal length—some of them up to 61 m (200 ft). Galileo is remembered today because he was the first scientist to make careful, systematic observations of the heavens with a telescope and to publish the results of those observations in a small booklet called Siderius Nuncius (“The Starry Messenger”). In this book, published in 1610, Galileo described the phases of Venus and argued that they proved the planet orbited the Sun instead of the Earth. He saw mountains on the Moon, proof that it was a real planet like the Earth, rather than an ethereal heavenly ball. Galileo was able to make out the many,many stars which make up the Milky Way, stars which are too faint and distant to be seen individually from the Earth, but whose light blends to produce whte white band of light visible today only from very dark sites. By December 1609, Galileo had built a telescope of 20 times magnification, with which he discovered mountains and craters on the moon. He also saw that the Milky Way was composed of stars, and he discovered the four largest satellites of Jupiter. He published these findings in March 1610 in The Starry Messenger (trans. 1880). His new fame gained him appointment as court mathematician at Florence; he was thereby freed from teaching duties and had time for research and writing. By December 1610 he had observed the phases of Venus, which contradicted Ptolemaic astronomy and confirmed his preference for the Copernican system.# The most famous of GalileoÔs discoveries with his first telescope were the four satellites of Jupiter which today we call the Galilean satellites. (He called them the Medician Stars, in hopes of financial support from the powerful Medici family, but they have rightly become known by his name). Night after night he observed them and sketched the changing alignments he saw. Gradually he realized that there was a pattern to the motions, and that the four small stars were actually moving around Jupiter. This was to become one of the most conclusive proofs that the Earth was not at the center of the Solar System, as was commonly believed in Galileo s time. After all, if these four stars could travel around something other than the Earth, could not other planets as well? Galileo's final book, Discourses Concerning Two New Sciences (trans. 1662-65), which was published at Leiden in 1638, reviews and refines his earlier studies of motion and, in general, the principles of mechanics. The book opened a road that was to lead Newton to the law of universal gravitation that linked Kepler's planetary laws with Galileo's mathematical physics. Galileo became blind before it was published, and he died at Arcetri, near Florence, on January 8, 1642. Galileo's most valuable scientific contribution was his founding of physics on precise measurements rather than on metaphysical principles and formal logic. More widely influential, however, were The Starry Messenger and the Dialogue, which opened new vistas in astronomy. Galileo's lifelong struggle to free scientific inquiry from restriction by philosophical and theological interference stands beyond science. Since the full publication of Galileo's trial documents in the 1870s, entire responsibility for Galileo's condemnation has customarily been placed on the Roman Catholic church. This conceals the role of the philosophy professors who first persuaded theologians to link Galileo's science with heresy. An investigation into the astronomer's condemnation, calling for its reversal, was opened in 1979 by Pope John Paul II. In October 1992 a papal commission acknowledged the Vatican's error. Galileo's lifelong struggle to free scientific inquiry from restriction by philosophical and theological interference stands beyond science. Since the full publication of Galileo's trial documents in the 1870s, a telescope of 20 times magnification, with which he discovered mountains and craters on the moon. He also saw that the Milky Way was composed of stars, and he discovered the four largest satellites of Jupiter. He published these findings in March 1610 in The Starry Messenger (trans. 1880). His new fame gained him appointment as court mathematician at Florence; he was thereby freed from teaching duties and had time for research and writing. By December 1610 he had observed the phases of Venus. We can deduce some properties of celestial bodies from their motions despite the fact that we cannot directly measure them. In 1543 Nicolaus Copernicus hypothesized that the planets revolve in circular orbits around the Sun. Tycho Brahe carefully observed the locations of the planets and 777 stars over a period of 20 years using a sextant and compass. These observations were used by Johannes Kepler, a student of Brahe s to deduce three mathematical laws governing the orbit of one object around another. Kepler s third law states a relationship between the size of a planet s orbit and the time the planet takes to go once around the sun. This law equally applies to a moon orbiting a much more massive parent planet. The law can be stated mathematically: Where: M is the mass of Jupiter, in units of the solar mass. a is the radius of the orbit T is the period of the orbit in Earth years. The period is the amount of time required for the moon to orbit the parent body once. In this exercise you will observe Jupiter with the MicroObservatory at least once a day for up to three weeks. An image archive is provided in case you have trouble with the weather. The moons appear to be lined up because we are looking edge-on to the orbital plane of the moons of Jupiter. As time goes by, the moons will move about Jupiter. While the moons move in roughly circular orbits, you can only see the perpendicular distance of the moon tothe line of sight between Jupiter and Earth. Therefore, the perpendicular distance of the moon should be a sine wave if you plot it versus time. By taking enough measurements of the position of a moon, you can fit a sine curve to the data and determine the radius of the orbit (the amplitude of the sine wave) and the period of the orbit (the period of the sine curve). Once you know the radius and period of the orbit of that moon and convert them into appropriate units, you can determine the mass of Jupiter by using Kepler s Third law. You will determine Jupiter s mass for each of the four moons; there will be errors of measurement associated with each moon, therefore your Jupiter masses may not be exactly the same. ACTIVITY In this activity you will: Observe Jupiter and its moons at least once a day. Plot the positions of the moons using graph paper or computer Determine which moon is which. Determine how long it takes each moon to go around Jupiter. Use your observations to determine the mass of Jupiter. Part One: Observing Jupiter and its Moons Obtain at least one image each day with the MicroObservatory. If possible (depending on weather conditions) use the same telescope at the same time of the day. You can use the Table of Objects in the Telescope Control Panel to select Jupiter as your target. Use the main telescope, not the finder scope. It is recommended that you refer to Sky & Telescope or Astronomy magazine or to a planetarium computer program (such as The Sky for the PC or Voyager for the Macintosh to find what time Jupiter is highest in the sky (the meridian if possible). When Jupiter is high in the sky you will experience less atmospheric disturbances. Due to the nature of the CCD, Jupiter will always be overexposed on your images. This will cause the planet to look like a bright circle with a vertical line through it. Recommended exposure times for Jupiter are very short, less than 1 second. Try 0.4 seconds first. If the weather is very hazy, you might need to increase the exposure time to see all of the moons. When MicroObservatory has completed your images you will receive an email notification that they are ready. Currently the images are stored as GIF files and FITS files. Since your browser will read GIF files directly, download those files first as you will see the image as it is downloaded. If the image appears to be useful, download both the GIF and FITS files to your MicroObservatory Project directory on your computer. Part Two: Which Moon is Which? Once you have obtained your images you need to identify the satellites on the image. This is not as easy as it might seem at first from MicroObservatory observations. The satellites shift in position from night to night and vary in distance from the planet. The satellites you will be observing are named Io, Europa, Ganymede and Callisto, in order of distance from Jupiter. You can remember the order by the mnemonic I Eat Green Carrots. It is recommended that you use the Jupiter satellite charts in the current issue of Sky & Telescope, or the Jupiter satellite finder program included as a part of The Sky Software. With The Sky software, first set the date and time (data; site information menu) to match the date and time of your image which is included as part of the file name. Then under the tools menu, select Jovian moons. Remember to properly orient your image to match the computer model (you will probably have to invert your image). Point your mouse to the moon in question and it will be identified for you. Annotate the name on your image if you are working with a printed copy. If you are using the computer monitor, measure and record the distance to the moon in your data table at this time. With either method (printed image or monitor) you will measure the distance to the moon in terms of Jupiter diameters. Keep in mind that due to the overexposed nature of the image of Jupiter, your measurement of the diameter of Jupiter will have to be made very carefully. Measure the distance to each satellite to the hundredth decimal place and record the value in the proper column of your data table. Make certain to indicate whether the satellite is east or west of the planet. A sample data value would be 7.35W indicating that the satellite was 7.35 Jupiter diameters west of the center of the planet. You may also use (+/-) to indicate direction from the planet if you desire. The main thing is to be consistent. Include the following on your data sheet: Data Sheet Date Time Day Io Europa Ganymede Callisto Column 1: Local Date Column 2: Universal Time Column 3: Day number of day (e.g. 1.0, 1.5, 2.0, & ) NOT counting cloudy days. Enter cloudy days in the space provided at the bottom of the sheet. Columns 4-7: Record each moon s position under the column for that moon. Use + for west and - for east. If Europa were selected and had an X=2.75W, you would enter that in column 5 as +2.75.; Data Analysis: You now need to analyze your data. By plotting position versus time, you will use the data to obtain a graph. You will need to determine the sine curve that fits your data best in order to determine the orbital properties of each moon. Here are a few hints: The orbits of the moons are regular, that is they do not speed up or slow down from one period to the next. The sine curve that you draw should therefore also be regular. It should go through all of the points, and not have a varying maximum height nor a varying width from peak to peak Using the data from each satellite, it is possible to determine the radius and period of the orbit. The period is the time it takes to get to the same point in the orbit. Thus the time between two maxima is the period. The time between crossings at 0 J.D. (Jupiter Diameter) is equal to half of the period because this is the time it takes to get from the front of Jupiter to the back of Jupiter, or half way around. For your moons, you may not get enough observations for a full period, so you may find thetime between crossings at 0 J.D. to be of use to you in determining the period, even though the satellite has not gone though a complete orbit. On the other hand, if you have enough observations for several cycles, you can find a more accurate period by taking the time it takes for a moon to complete, say 4 cycles, and then divide that time by 4. The y (vertical) axis for all satellites is the distance from Jupiter in Jupiter Diameters. For Ganymede the max y value would be 12, for Callisto the max value is 16, for Io 5 and for Europa 6. After you have plotted your data and determined the period in Earth days, you must convert your units to Earth years by dividing by 365 to use Kepler s Third Law. For example, if you determined the period to be 14 days, T=0.038 years. Now use your graph to determine the greatest distance from Jupiter that the moon travels. This distance must be converted to AU to use Kepler s Third Law. There are 1050 Jupiter widths. As an example, if the distance to a satellite was 3 J.D. the conversion would be: The value would then be 0.0029 A.U. = a Now that you have a value for distance (a) and time (P), you can plug your values into Kepler s Third Law: Remember that the value for mass obtained by this method will be in solar mass units. Calculate a mass of Jupiter in each of the four cases. If one of the values is very different from the other three, look for a source of error. For all satellites the x (horizontal) axis is Time in Earth days. The y (vertical) axis for all satellites is the distance from Jupiter in Jupiter Diameters. For Ganymede the max y value would be 12, for Callisto the max value is 16, for Io 5 and for Europa 6. Satellite Used Mass of Jupiter (MJ) in Solar Mass Units Callisto Ganymede Europa Io Average MJ Questions and Discussion: Express the mass of Jupiter in Earth units. The mass of Earth in solar mass units is 3.00 x 10-6. There are moons beyond the orbit of Callisto. Will they have larger or smaller periods than Callisto? Why? Which do you think would cause the larger error in MJ: a ten percent errror in T or a ten percent error in a? Why? The orbit of Earth s moon has a period of 27.e days and a radius of 2.56 x 10-3 A.U. (=3.84 x105 km). What is the mass of the Earth? What are the units? Show your work. Activities Page |