Teaching Manual for 653-3120 (SOL-100) and 653-3110 (SOL-300)

Trippensee® Planetariums Worlds in Motion

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Function of Science The Earth is Round Ptolemy knew that during the We are so accustomed to think- The first thing Ptolemy explained course of one night the planets moved ing of the earth and the universe in was the earth itself. Ptolemy, like westward; but, as prior observers our kind of scientific ideas that any other scientists before him, used had noticed, during the course of a other form seems childish and even eclipses to help determine the shape week, these planets moved eastward unintelligent. But transport yourself of the earth. He theorized that if the as measured against a background of backward in time some 2,000 years earth were really flat, a popular notion fixed stars. Fascinated with "motor" ago and place yourself in someone of his day, then an eclipse ought to explanations, he pictured a motor ro- else's scientific shoes. How childish be seen by all the people of the earth tating the celestial sphere once every would it then seem to imagine the at the same time. Since the records 24 hours. The planet motion was east- earth as flat and floating in a great sea clearly indicated that this was not ward about the earth according to this of water? How childish would it then so, Ptolemy claimed the earth to be "motor" theory, because it was geared seem to picture the stars as fixed on spherical or round in shape. slower than the machinery operating a big sphere and rotating about the the celestial sphere. earth? Would you have been ashamed The Geocentric Earth Ptolemy theorized that Mercury 2,000 years ago to admit you did not At the same time, however, and Venus were inferior planets lying understand the motions of the planets Ptolemy was committing an error in between the earth and sun. Since nei- or how they differed from the stars reasoning that was to prove a difficult ther Mercury nor Venus can ever be on the inside of the celestial sphere? hurdle for scientists who would fol- seen far from the position of the sun, When you put yourself in another low. He placed the earth at the center a maximum of 48° for Venus, it was time you are amazed at how much of the universe (a geocentric system) assumed by Ptolemy that the earth, they knew rather than how little. and had everything revolve about it. Mercury, Venus, and the sun were all As you study the story of science, The earth, according to ptolemy, had connected by some central axis. Two you will probably be impressed with no local motion; it neither rotated on thousand years ago this was the most the number of times our explanations an axis nor revolved around the sun. logical explanation available. of things and their behavior have This method of proof was simple Observations had taught men changed in a few short centuries. You observation. If the earth were not another interesting fact about the will find people believing the truth stationary in space, birds would be planets and their motions as viewed one century, denying it the next, and left behind in their flight and rockets against a "fixed" background of stars. then rediscovering it a century later. would fall sideways rather than down. Although the motion of the planets Before you criticize science harshly was generally eastward, there were for this behavior, remember that one of the basic functions of science is Celestial Sphere to replace old theories with new. Saturn Sometimes the new theories are not Jupiter correct, but the fact that we are free to Mars Sun develop new theories means that we Venus will sooner or later arrive at that posi- Mercury Moon tion which is most true. Earth

Geocentric Universe of the Greeks One of the longest lasting explanations of the earth and universe was developed by Claudius Ptolemy who studied in Alexandria, Egypt between 85 A.D. and 165 A.D. Ptolemy developed an explanation for the motions that man saw about him everywhere Figure 1 - Primus Mobile in his wonderful universe. This explanation was honored as truth for 1,200 years and was called the "Ptolemaic Figure 1 - Primus Mobile. Ptolemaic idea of the known universe showing the System." machine relations of objects in motion. Notice that the earth is the only body not controlled by gears and motion arms.

such long-lasting popularity. Each Fig 2 step in his theory accounted perfectly, or almost so, for every motion that many could observe in the morning and evening sky. It is understand- able also that when Ptolemy's book, Mathematical Systems of Astronomy, was translated by the Arabs, it was referred to as the Almagest, or the great system. The fact that Arab astronomers added cogs and wheels to the Ptolemaic machine, eventually winding up with over eighty circles to Figure 2 - Deferents and Epicycles. The large circle on which the planet revolves is called explain the motions of their universe, the deferent. Also to be seen here are the smaller circles or epicycles that Ptolemy used to describe retrograde motion and the dimming and brightening of the planet's light. does not detract from the simple fact that his position in scientific history, the work he produced to explained many occasions when the planets, another observed phenomenon as observed phenomena of the sky, was particularly Jupiter and Saturn, moved well. It has been observed that planets the greatest. backward or westward among the changed in brightness as they were stars. This regression of the planets observed over a period of time. The presented a real challenge to Ptol- Ptolemaic theory explained this by Copernicus emy, who, in designing a machine saying that when the planet was at the At the beginning of the 16th to explain the motions of things in top of the epicycle, outside the defer- century, a Polish astronomer named space, had to take every motion into ent, it was further from the earth and Nikalaus Kopernik (Copernicus) consideration. consequently its brilliance would be published a book called De Revolion- diminished. On the other hand, when ibus Orbium Coelestium. The book Deferents and Epicycles the planet reached its bottom position revolutionized the world of science in According to the final diagrams on the epicycle, it would be closer to that it assumed just the opposite posi- of the universal machine, the moon, the earth and consequently appear to tion that had been taken by Ptolemy. the interior planets, the sun and the be brighter. Instead of placing the earth at the stars had single circular rails on which Perhaps you can now see why the center of the universe and allowing to revolve about the earth. These work of Claudius Ptolemy enjoyed everything to move about it Coperni- cir-cular rails were called deferents. cus placed the sun at the center and The retrograde (regression or west- allowed the earth and the other five ward motion of the outer or superior known planets to revolve about it. planets) could only be explained by The introduction of this new theory building a series of smaller circles on Fig 3 moved us from a geocentric system the deferents. These smaller circles - earth centered - to a heliocentric were called epicycles. Each epicycle system - sun-centered. contained two objects: the planet seen It is easy to forget the battles in the evening sky and another unseen fought in order to accept this theory point called the fictitious planet. as fact. People objected to the Co- When the real planet Mars, Jupiter, pernican theory on the grounds that or Saturn moved to the top of the is was antireligious. Many felt it was epicycle, its eastward motion quick- against religion to allow the earth ened. When the real planet moved to orbit about the sun. Still others inside the deferent, the bottom of the refused to accept the new theory because they could not understand how epicycle, the planet slowed down its Figure 3 - Path of Jupiter in Retro- visible motion and appeared to move grade. This shows four observational such great speed could keep from westward (in retrograde motion) as sightings of Jupiter as made by someone tearing the earth to pieces. viewed from the earth. on earth. Position 3 shows the beginning The new theory did not answer all of the retrograde. It is more pronounced the observed facts, however. If the Not only did the construction of in position 4 as the earth has moved deferents and epicycles solve the farther in its orbit around the sun. This is planets really moved in a circle about problem of the motion of the plan- a typical retrograde motion of a superior the sun, their observed speeds should ets, it also provided the solution for planet as observed on an inferior planet. be constant at all times as measured

against a background of stars. Simple Johannes Kepler, this way, a little arithmetic will show observation proved that this was not Astronomer/ Mathematician you that our earth is actually travel- so. There were times when the planets The final work in establishing the ling over 2,000 miles per hour faster appeared to speed up in their courses current view of the solar system was when we are closer to the sun than it and other times when they slowed. done by Johannes Kepler, a student is when we are farthest from it. If you The first visible support for the of Brahe's. In 1609, at the age of 45, think of the two shaded areas as being basic theory of Copernicus came from after many years of research and ex- pieces of pie, you will see that both Italy in 1609. An astronomer named periments, Kepler published the first are exactly equal in the amount of pie Galileo Galilei was using a telescope two laws of planetary motion. These they contain. This is in keeping with for the first time when, in scanning laws not only established Copernicus' Kepler's second law of equal areas. the planet Jupiter, he discovered heliocentric system as fact but also four bright objects revolving about provided answers to questions that it. These he correctly assumed to be Kepler's Third Law troubled people about their observa- Kepler's third law was published moons, and since they obviously were tions of sky and space. going about Jupiter rather than the several years after the first two. It is called the harmonic law and is usu- earth, it proved to him that the earth Kepler's First Law was not, as Ptolemy had said, the ally expressed mathematically as: The first law describes the shape 3 3 2 2 center of everything. A1 : A2 :: P1 : P2 or of the orbital path of a planet about p2 = R3 Tycho Brahe the sun. Instead of a circle, Kepler p2 r3 substituted an ellipse. He found that Tycho Brahe, a Danish nobleman Expressed in words, the square planets described this kind of path interested in astronomy since the age of the time of a planet's revolution is with the sun acting as one of the foci of 14, believed that at least some of proportional to the cube of its aver- of the ellipse. the planets revolved around the sun, age distance from the sun. Expressed particularly the inferior planets of as symbols, letters A or R equal the Mercury and Venus. He knew that if Kepler's Second Law average distance from the sun, with Venus and Mercury revolved as Co- The second law is often referred to A and R standing for area and radius pernicus said then they ought to show as the law of equal areas. As Kepler respectively. The letter P in both phases like the moon. Since they did stated, "The radius vector of each instances stands for the period or time not appear to do so, his findings did planet passes over equal areas in of the planet's revolution. not change the scientific thinking of equal intervals of time." The third law is an important his time. Although Brahe believed As seen in Figure 5, a planet will formula because it means that, by these planets revolved around the sun, sometimes be closer to the sun than knowing only the radius of one planet, he still believed the sun in turn went at other times. When it is closer, we can calculate the orbital radius of around the earth. or perihelion, it will travel faster every other planet. It also enables us thereby covering a short but wide to understand how rapidly a particular Galileo, Telescope Maker part of the ellipse. When the planet planet moves in its orbit. In 1610-1611 Galileo Galilei, is farthest from the sun, or aphelion, Not only did these laws answer the while studying the planet Venus it will move more slowly. Our own question about variation of speed in through his telescope, discovered that planet earth, for example, travels at the planet motion about the sun, they the planet did go through phases like 18.3 miles per second at aphelion and also answered the old problem of ret- the moon. These phases go unnoticed 18.9 miles per second at perihelion. rograde motion in a simple and logi- to the naked eye, but in they are dis- Although this does not seem to be cal fashion. The epicycles of Ptolemy tinguished through the telescope. a great difference when expressed were no longer needed. Since the earth moves faster than Mars, Jupiter, or Saturn, our rapid motion would make them appear to move backward even though their real course remained unchanged. When you pass a slower vehicle on a highway, there is a point in passing when the slower vehicle seems to stand still, then move Figure 5 - Kepler's First and Second Laws. The solid line represents a highly exaggerated ellipse (Kepler's first law). The shaded sections represent the area swept out by a planet in an backward, and then, after the faster equal amount of time (Kepler's second law). Both aphelion and perihelion positions represent vehicle is going the opposite way, an equal area. Only the shapes of the shaded areas are decidedly different as the angle con- the other object seems to be moving verges on the sun at one focus of the eclipse. unusually fast.

The planets "Bode's Law" this is clearly in error, the figures for From the very beginning of time The astronomer Bode is remem- Neptune are usually ascribed to Pluto man had known of the existence of bered principally because in 1772 he as shown in the Table 1. five planets other than his own earth. had published a "law" relating to plan- Asteroids He had watched their motions, and he et positions within the solar system. On the first day of the 19th century had ascribed to them the power of the In actuality Bode did not discover the Sicilian astronomer Piazzi noticed gods that ruled over him his daily life. it, nor is it a law. It is an exercise in something unusual at the distance of Even as late as the 17th century, when arithmetic that happens to apply with Bode's unknown planet. He thought the telescope was invented and when some degree of accuracy. he had discovered the mystery planet Kepler published his 3 famous laws If you take a series of numbers: and named it Ceres after the mother of motion, these 6 objects (including 0, 3, 6, 12, 24 etc. and add 4 to each goddess of Sicily. Later observations the earth), represented the limits of number and divide by 10, you arrive proved Ceres was not a planet but a man's solar system. at a fairly good approximation as to minor planetoid with a diameter of the location of the planets measured some 480 miles. In the years follow- Uranus in astronomical units or AU's. One ing, so many thousands of these frag- In the year 1781 an English as- astronomical unit equals 92,956,000 ments were found that astronomers tronomer and telescope builder named miles, the mean distance from the engaged in space research consider William Herschel added to our knowl- earth to the sun. them to be nuisance objects. edge of the solar system by discover- The system works well in theory ing the seventh planet - the first one to until the planet Mars, where Bode's Neptune be discovered in historical times. He "law" suggests another planet should The eighth planet of the solar promptly named the planet Georgium exist between Mars and Jupiter. Since system was predicted before it was Sidus in honor of King George III of none exists, many scientists doubt the found. You have seen how astrono- England. usefulness of these figures. mers predict the paths planets will Later, the planet was to be renamed If you carry the figures out to the follow and the speed at which they Uranus by Bode of the Berlin Obser- correct place, Pluto's distance should move. Suppose you were able to pre- vatory. be 77.2 AU's from the sun. Since dict the path and velocity of a planet only to find it did not act as expected. Table 1 Either your facts were wrong or there Bodes' Law Actual were additional facts not taken into Mercury 0.4 Mercury 0.39 consideration. Venus 0.7 Venus 0.72 Astronomers observing the path Earth 1.0 Earth 1.00 of Uranus were disappointed with Mars 1.6 Mars 1.52 their predictions. Before 1822 the Asteroids 2.8 Asteroids 2.8 planet moved faster than expected, Jupiter 5.2 Jupiter 5.20 while after 1822 it seemed to slow. Saturn 10.0 Saturn 9.54 Rather than scrap the work of Kepler Uranus 19.6 Uranus 19.19 and Newton, scientists began looking Neptune -- Neptune 30.07 for an undiscovered force that would Pluto 38.8 Pluto 39.46 explain Uranus' behavior. This outside force on another object is called perturbation. Two mathematicians - Adams, an Fig. 6 Englishman and Leverrier, a French- man -began to work on the problem independently. Both came to the conclusion that there must be another planet, as yet undiscovered, disturbing the path of Uranus. Adams had difficulty getting an astronomer to verify his prediction. Leverrier met with better luck, and in 1846 the German Figure 6 - Perturbation. The inner planet in order represents the planet Uranus. The outer astronomer, Galle, discovered Nep- planet represents Neptune. The dash lines between the inner and outer orbits show lines of tune almost exactly where Leverrier force existing before 1822 and after 1822. had predicted it would be.

Pluto Morning/ Evening "Stars" Why? How can the same planet be Lowell questioned whether Ura- We know much about the plan- seen in both morning and evening? nus' great perturbation was caused by ets and how people over centuries Imagine you are out of doors and a planet Neptune's size. In the early developed the idea of the solar or sun facing directly south with a great 1900's, he and his associates at the system. The struggle for truth was not hoop running over your head from Flagstaff Observatory began an inten- an easy one. The story of the science due south to due north. This line, sive search for planet X. of astronomy shows that "common called your local meridian, will be About 25 years later, Clyde Tom- sense" based on simple observations is helpful in the study of astronomy. bough, a young astronomer, came not always considered truth. Since you are imagining it above you, across a suspicious object in photo- One of the most easily misun- consider it an upper meridian. graphs taken of the stars in the con- derstood observations involves the Now imagine your hoop passes stellation of Gemini. The announce- planets and their relationships with underneath you all the way around the ment of the discovery was made on the earth and sun. There was a time, earth. This line is your lower merid- March 13, 1930, the day of Lowell's not many centuries ago, when man be- ian. (This kind of scientific thinking birthday celebration. lieved he could see more planets in the helps explain such concepts as time A contest conducted to select the evening sky than there actually are. and planet positions). name for the new planet was won by For example, when the Greeks saw the Now imagine that we can hold the an 11-year-old English girl. "Pluto" planet Mercury in the sky before the earth stationary, thereby keeping the combines Lowell's initials with the sun rose in the morning, they called it sun on your noon line (local meridi- name of the ancient god of eternal "Apollo". Likewise, the planet Venus an). In addition, allow the two inferior darkness. A good choice for a planet was called "Phosphorus" in the early planets, Mercury and Venus, to follow that lies some 3,664 million miles morning sky but "Hesperus" in the their natural course and see what posi- from its source of light and heat! evening sky. tions they might assume.

Fig 7 - Planetary Data Chart Superior and Inferior

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Conjunction When either Mercury or Venus Astrological is directly between you and the sun, Symbol the planet is at a position of inferior Distance conjunction. When it has reached its from sun 0.387 .723 1.000 1.524 5.203 9.55 19.191 30.071 39.457 furthest angle from the sun, it is at in AU's greatest elongation. This is par- Distance ticularly important with tiny Mer- from sun 36 67 93 142 483 886 1,783 2,794 3,664 cury which is seen only when it has million miles reached its greatest eastern or western elongation, some point between the Revolution period of 88d 225d 365d 687d 11.86d 29.46y 84.02y 164.8y 284.4y 18° and 28° maximum positions. Note planet also that either of the two inferior planets may stand on your meridian Rotation line if that line is extended from the period of 59+5d 243 23h56m 24h37m 9h50m 10h14m 10h49m 15h40m ? sun to the earth. When a planet is in Diameter a straight line with, but on the other in miles 3,008 7,600 7,918 4.215 865,800 71,500 29,400 28,000 ? side of, the sun from you, it is at superior conjunction. Mass in terms of 0.053 0.815 1.0 0.107 318.0 95.2 14.3 17.6 ? Those planets that lie beyond the earth's mass earth in our solar system can never, of course, assume a position of inferior Density in conjunction. They can, and often do, terms of 5.3 5.0 5.5 4.0 1.3 0.7 1.6 2.3 ? water however, assume positions of superior conjunction. Inclination The outer or superior planets can to ecliptic 7°.0 3°.4 0°.0 1°.8 1°.3 2°.5 0°.8 1°.8 17°.1 assume other positions in the solar plane system which the inferior members of Termper- +640°F 800°F var var -220°F -243°F -300°F -330°F -348°F the solar family cannot assume. ature -450°F

tion, you will know you cannot see it Fig 8 because it will be in the middle of the sky at the same time as the sun. If, on the other hand, a planet is said to be in opposition, you will need to look for it at midnight if you wish to see it on your imaginary meridian line. Assume you read in the paper that Mercury has reached its greatest eastern angle of elongation. You know automatically that you will look for it in the western sky shortly after sunset.

Figure 8 - Meridian Lines. The upper meridian line is indicated. The lower meridian line ® is not indicated, but it extends below the observer and connects to the two ends of the upper Trippensee Solar System meridian line. Models Science First® produces 2 hand- operated Trippensee® planetarium A Greatest eastern Superior Conjunction elongation models specifically designed for Orbit of superior school use. They are characterized planet B Inferior by simple design, easy maintenance, conjunction attractiveness and ability to withstand C Greatest years of hard use. western The 653-3120 Copernican Sys- Orbit elongation D of inferior tem Model is a hand operated model planet of the complete solar system with the D Superior Sun heliocentric (sun-centered) design of conjunc- Earth's tion orbit Copernicus. The 653-3110 Ptolemaic System A C Model is a hand operated model of B the geocentric solar system described by Ptolemy and others. Besides its Eastern Western historical use, it serves as a conve- Earth quadrature quadrature nient model for demonstrating the movements of planets, the sun and the moon. It serves as a constant reminder of what these heavenly bod- Fig 9 Opposition ies look like when viewed with the unaided human eye. After all, without Figure 9 - Conjunction and Quadrature. This diagram illustrates the astronomical terms a telescope, Saturn has no rings and used to describe the relative locations of the planets with respect to the earth. appears to be similar to Jupiter and Venus in size and color.

Quadrature Since a planet that is at conjunction Why use models? Notice that in this drawing three is on our meridian at noon, and one Models have always been a suc- new positions have been added. The that is at opposition is on our meridian cessful device used by scientists and position left of the earth is called at midnight, and since quadrature rep- engineers to understand and explain eastern quadrature and the position resents a halfway point between these many complex or difficult ideas, to the right is western quadrature. two extremes, it is logical to assume concepts, or theories. The Trippensee® A superior planet may, as you can that quadrature point represents a six solar system models can be used in see by this diagram, stand behind the o'clock position. Whether a planet that this manner. earth on the line drawn from the earth is at quadrature is a 6 AM or 6 PM These models allow you to "see" through the sun. This places the planet planet depends once again on which and "feel" what the solar system looks on the lower meridian at midnight, a side of the sun it is located. like and appears to look like. Many point referred to in astronomy as op- people have trouble comprehend- position. ing spacial relations. Without such If you know that a planet is at models, they would be lost trying to either superior or inferior conjunc- 7 SCIENCE FIRST® | 86475 Gene Lasserre Blvd., Yulee, FL 32097 | 800-875-3214 | www.sciencefirst.com | [email protected] SCIENCE FIRST® | 86475 Gene Lasserre Blvd., Yulee, FL 32097 | 800-875-3214 | www.sciencefirst.com | [email protected] ©2002 - v 4/15

visualize the physical relationships Since it is not practical to build a model complex, will show all planets mov- between the planets and the sun and the length of 7 football fields, models such ing in the same plane. Actually this the various motions of the planets. as this are useful for the classroom. is not the case - the orbital planes of C. For a solar system model suitable all the planets except Pluto and some Scale of the Solar System for a classroom, the following scale asteroids lie within 7° of the ecliptic. A. For this class activity, a compass may be used: Remember, however, that the Coper- and highway map are needed. • Mercury - 5" from a point which nican model examines the entire solar Locate the site of your school or we will call the sun system at once and therefore even some other landmark. By setting • Venus - 8-1/2" from the sun large distances seem relatively small. the compass point on this site, the • Earth - 12" from the sun For all practical purposes, the earth planetary orbits can be drawn to • Mars - 18" from the sun and its sister planets appear to be scale. The scale of miles is given • Asteroids - 2'9" to 2'10" from the moving along a completely flat plane. somewhere on the highway maps. sun • The globe would be 600 feet sun • Jupiter - 5 feet from the sun ® in diameter; • Saturn - 9-1/2 feet from the sun Trippensee Ptolemaic • Mercury - 2 feet in diameter, • Uranus - 19 feet from the sun System 4-3/4 miles away; • Neptune - 30 feet from the sun This model is designed to demon- • Venus - 5-1/3 feet in diameter, 9 • Pluto - 40 feet from the sun strate the basic concepts of the solar miles away; It would be impossible to see most of the system as described by Ptolemy. • Earth - 5-1/2 feet in diameter, planets on the same scale if you were to Since Ptolemy was convinced that 12-1/4 miles away; look at them from across the room. the earth occupied the center of all • Mars - 3 feet in diameter, 18-1/2 • You may use your own scale for things, the model has been construct- miles away; making a series of circles which ed so that the earth no only occupies a • Asteroids - tiny globes ranging can be taped to the wall in the central position in the model but also from under a millimeter to three above orbits. Use the data in this dominates the other bodies by being inches in diameter, an average book to make an appropriate scale. larger than all the others, including distance of 30 miles; the sun. Even this representation, ® • Jupiter - 60 feet in diameter, 64 Trippensee Copernican however, is not as extreme as the ideal miles away; System held by Heraclitus of Ephesus, about • Saturn - 52 feet in diameter, 117 This is a highly simplified model 500 B.C., who believed the sun to be miles away; of the solar system as we know it. Not only one foot wide and recreated new • Uranus - 20 feet in diameter, 234 only does it demonstrate the knowl- every morning. miles away; edge gathered by pioneers such as The constellations of the Zodiac • Neptune - 19 feet in diameter, 367 Galileo, it also clearly demonstrates can be traced back as far as the writ- miles away; much of the knowledge gathered in ten history of man himself. Although • Pluto - 2-1/2 feet in diameter, 485 the first half of the 20th century. the ancients had no understanding of miles away; As we have already seen, the plan- such complex terms as "obliquity of B. The following scale would be in ets of our solar system travel about the ecliptic", and although they were proportion to the 6" sun globe on the sun in ellipses rather than circles. completely unaware that the polar the Trippensee® Copernican Solar The eccentricity of an ellipse - ap- axis of their own planet was inclined System Model SOL-100. proximately 3,000,000 miles in the at 23-1/2° to the perpendicular of • Mercury - 7 yards away; case of our own earth - may sound its own plane, they were aware of • Venus - 13 yards away; tremendously large when we speak of the sun's rise and fall against a fixed • Earth - 18 yards away; a planet orbit, but to a space voyager background of stars. The Ptolemaic • Mars - 27 yards away; far enough away to see all the planets model has been designed so that the Note that none of these planets would be at once, the earth would appear to earthbound observer might be able to larger than a pin head. move in a circle about its star. When see how this seasonal phenomenon • The orbit of the asteroids would be you use a model of the solar system occurs. 50 yards away and they would be to explain motions and relationships, You will also notice that the defer- too small to see on this scale. you must adopt a space-eye view. ent arms holding Mercury, Venus and • The great planets Jupiter, Saturn, When the orbits are reduced to cor- the sun are held together by a slip Uranus and Neptune are the size respond with this point of view, the ring. This grouping represents the of small peas and are 93, 171, 344, ellipses will appear as circles. central axis that Ptolemy believed and 539 yards away, respectively. At the same time there is a prob- connected the two inferior planets • Pluto is a speck of silver 707 yards lem with the plane of the planetary to the sun. Because of space limita- away. orbits. Any model, unless specially tions, the epicycles are not as large

the earth. Mercury Venus The constellations of the Zodiac no Earth Mars longer appear where the signs of the Uranus Neptune Pluto Zodiac are, because of their preces- sion. The Zodiac signs are used on the Zodiac plates as they were originally set up over 2,000 years ago. The signs Handle of the Zodiac are points on the ecliptic, not the location of the constella- Base Asteroids Jupiter Saturn tions of the same name. Zodiac and degree plate (Hold the Copernican model in Copernican system, 653-3120 one hand and move the earth about the sun. Note that when viewed from the morning earth, the sun appears to Moon Mercury Jupiter Saturn move on a line about the room. This Ptolemaic system, line is called the ecliptic.) Venus Sun The data for locating the planets 653-3110 on the Copernican model is given in This unique model dra- matically demonstrates the Appendix I and III. Follow the move- planetary motions involving ment of all the planets for a year or deferents and epicycles Epicycle two to see how the planets move. Handle described by Ptolemy. It arms The Trippensee® Ptolemaic System explains apparent motions of the planets more clearly Zodiac and degree plate is much easier to read, as only one than the Copernican Model. view point, that of the earth, need be Base considered. All data is read under the appropriate wire arm. Notice that the sun's location on the ecliptic, the sign of the Zodiac, and the date are all read as Ptolemy conceived them to be, actual maximum number of eclipses under the sun's wire arm. but they do allow you to demonstrate which can occur in one year is seven. Remember, real planetary loca- the particular planetary motion that This would include four solar and tions are the sun's view on a Coper- appears to be only a swinging motion three lunar or five solar and two lunar nican (heliocentric) system. Appar- between us and the sun. eclipses. ent planetary motions are an earth Again there is a problem with the observer's view (geocentric) as on the Trippensee® Ptolemaic system model. plane of planetary orbits as indicated Reading the Zodiac Plates by the moon in this model. The moon When attempting to read the loca- is usually much higher (or lower) than tion of a planet in space, the actual ® the plane of the ecliptic and does not Care of your Trippensee reading is done on the ecliptic. The cause one solar eclipse and one lunar Solar System Models ecliptic is an imaginary line drawn every lunar month. Our models are designed to give through the background of stars. This Since the sun is continually on the many years of trouble-free service. imaginary line is generated by the sun ecliptic, and since the moon crosses However, any mechanical device can as the earth moves about it. the ecliptic twice a month, it would eventually give difficulty in operation. There are two view points to be appear that we might expect one solar If the stainless steel wire arms considered. In the heliocentric (Co- and one lunar eclipse every month. become difficult to move, a light ap- pernican) models the planet locations The fact that keeps this from occur- plication of machine oil should enable are given on the ecliptic as viewed ring at this frequency is that ours is them to move much easier. from the sun. Even though their speed a solar system in constant motion. The models are designed to be may vary a little, the planets move Both sun and moon must be close to held in one hand and the wire arms regularly through the sky (Appendix a node, a crossing of the equator, at moved with the other hand. If the I). The date is read under the earth the same time. A solar eclipse always handle wants to turn when the wires wire arm. The sign of the Zodiac in occurs if the sun is within less than are moved, then the nut at the bottom which the sun is rising and setting is 15°21' of a node at the line of the new should be tightened so that the handle 180° away from the calendar date, moon, and a lunar eclipse always oc- does not move while the wire arms that is, the sign is where the sun ap- curs if the moon is less than 9°31' of are being moved. pears on the ecliptic as viewed from a node at the time of full moon. The If the wires become loose on the

steel standard, the nut which holds Fig 10 them may be tightened. There is a wave washer between the top washer and the nut which supplies the tension for keeping the stainless steel wire arms taut. If this nut should work loose, it is a simple matter to tighten it down again. The plastic balls are fused to the stainless steel wire arms. If any should be lost, they can be replaced. The ring of Saturn is also available. When inquiring about replacement balls, refer to part numbers and pric- ing are list on page 12 - Remember that on the Copernican system the wire for the asteroid orbit contains Zodiac and degree plane of 653-3120 Zodiac and degree plane of 653-3110 no ball.

How to use 653-3120 and North celestial pole 653-3110 solar Fig 11 Celestial sphere system models These models will help explain 0° many complex concepts related to Vernal equinox the motion of planetary bodies. They allow you to control time, since it will be you who will move the planets a predetermined distance in their orbits 270° about the sun. You will also be able to 90° Winter Summer solstice demonstrate eclipses, changing sea- solstice sons of the earth, retrograde motion, planetary changes in the sky outdoors, Ecliptic and problems of motion that confront 180° our scientists as they prepare to visit Autumnal Celestial equator equinox our interesting neighbors in the solar system.

locations. These planetary locations are also found in The American South celestial pole Ephemeris and Nautical Almanac under the date for each planet titled "Oh Ephemeris Time" under the column Apparent Right Ascension; this data can be given in eight degrees or Figure 11 - Ecliptic and celestial equator with degrees. The earth revolves around the sun hours. The person using The Ephem- in an orbit which is almost circular. The path the sun appears to follow through the back- eris to determine Apparent Right ground of "fixed" stars during one revolution is called the ecliptic. It is represented as a great Ascension will find the translation of circle located on the celestial sphere. The earth's equator projected out to the celestial sphere becomes a great circle called the celestial sphere. The points of intersection of the ecliptic time into degrees considerably simpli- and celestial equator are called the vernal and autumnal equinoxes located on 0° and 218° fied by using the table, also included respectively. The location in space of the planets is determined from the degree markings of in The Ephemeris, under the heading the ecliptic. "Conversion of Time to Arc."

a. Planetary Locations more than two revolutions. Be certain should clear up any misunderstanding Information regarding the loca- that Mercury, as well as the other as to how the same planet can, on tion in the sky of any of the planets planets, is moved in a counterclock- different occasions, appear to be both can be obtained from The American wise direction around the sun (as morning and evening objects. Ephemeris and Nautical Almanac. viewed from the top of the model). The data for the planetary motions is Correct settings for the planets can c. Planes of the celestial given as the "Heliocentric Position for be made for any date, past or future, Equator and Ecliptic h o Ephemeris Time" and the locations by consulting The American Ephem- The ecliptic is a circle generated are given in degrees of longitude, eris and Nautical Almanac. The by the apparent motions of the sun as which correspond to the degrees settings are listed under the longitude it moves through the sky during the ® on the Zodiac plate for Trippensee column of heliocentric positions. course of the year. All the planets ap- Copernican system model 653-3120. pear to move within 7° of this gener- This information has been summa- ated circle. Consequently, all the ref- rized in Appendix I. b. Morning and Evening Star Demonstrations erences to planetary motion are made When using the Ptolemaic sys- from the ecliptic. Since any circle can Whenever an inferior planet ap- tem, the above data does not apply. form planes, we can use this plane pears to the west of the sun (when Remember that the Ptolemaic system as a reference guide throughout the looking at the sun from the earth), it does not show real motions and real entire universe. will appear as a "morning star", unless locations but apparent motions and The equator of the earth is a circle By comparing the revolution it is obscured by the sun. From the and can be projected in space to create period of each planet (note the plan- Earth, the only inferior planets are the celestial equator. The position of etary tables in Table II, below), we Venus and Mercury. An inferior planet the stars in the sky is usually calcu- can make mathematical comparisons is seen as an evening star when it is lated along this imaginary line. In of the earth's motion to that of other in the east. The evening stars appear the spring, when the sun first starts to planets. In other words, one complete shortly after the sun sets and generally cross one of the two intersections of revolution of the earth equals 4.1 remain visible for 2 or 3 hours. these planes, the first day of spring revolutions of Mercury, 1.6 revolu- Both evening and morning stars occurs. Similarly, when the sun re- tions of Venus, 0.53 revolutions of can be demonstrated on all the Trip- crosses the intersection in September, Mars etc. pensee® solar system models. Just set the autumnal equinox occurs. Arbitrarily select a six-month Venus or Mercury west of the earth Since most people prefer to mea- period in which to show the relative when looking a the sun or set them sure positions in space with a system motion of each of the planets. If you to the east so they may appear as common to both distance and time, are using the Copernican model, you evening stars. they refer to an equatorial system - will move the earth arm so that its The person using the model should that system that uses the earth's equa- reading becomes 0° instead of the review the material included in sec- tor extended into space. In this way, original 180°. The same concept may tions "Morning and Evening Stars" it is possible to divide the circle into be emphasized by using the Ptolemaic and "Superior and Inferior Conjunc- 24 hours with each hour having 60 Model by moving the sun arm rather tion." This information will permit the minutes and each minute 60 seconds. than the earth arm. planets to be set to any desired posi- Degrees are easily converted into The only planet to complete a total tion corresponding to earth observa- hours by dividing the degrees by the revolution during a six-month period tions of day or night. These observa- number 15. is Mercury. It will complete slightly tions of earth-planet-sun relationships d. The Selection of Zodiacal Signs Table II- Positions of planets on equinoxes in 2002 It is well known that the constellations of the Zodiac do not appear Position of Planets on March 21, 2002 Position of Planets on September 22, 2002 where they once did thousands of Planet Longitude Distance/AU Sun Planet Longitude Distance/AU Sun Mercury 304.8° 0.43 Mercury 344.7° 0.37 years ago. In fact, the constellations Venus 38.8° 0.72 Venus 336.7° 0.73 of the Zodiac have moved eastward Earth 180° 1.0 Earth 0° 1.0 about 30° in the last 2,000 years. In Mars 70.3° 1.52 Mars 156.8° 1.67 Figure 11, the ecliptic is shown di- Jupiter 107.0° 5.20 Jupiter 122.3° 5.27 Saturn 75.2° 9.05 Saturn 82.1° 9.03 vided into 360°. One-twelfth of 360° Uranus 326.0° 20.00 Uranus 328.0° 20.02 is 30°. About 2,000 years ago, the Neptune 308.0° 30.15 Neptune 309.1° 30.15 constellation Aries was found in that Pluto 246.6° 30.11 Pluto 247.7° 30.15 part of the sky, which is indicated on

the ecliptic from 0° to 30°. about half the size of the earth, but students are outside the model, this The constellation Taurus was scientists theorize that the great gravi- means they are no longer earthbound. found in the space from 30° to 60°. tational pull of Jupiter may alter the They can watch the moon's motion as Gemini, Cancer, Leo, Virgo, Libra, arrangements of the asteroids, leaving if they were half million miles away. Scorpio, Sagittarius, Capricornus, gaps in the belt itself. These probably Move the moon slowly around Aquarius and Pisces follow at 30° in- empty areas are called Kirkwood the earth, being careful to keep the tervals. These areas represent regions gaps. chalked side toward the earth. of space which today are called the Give the students the opportunity signs of the Zodiac. The constellation f. Eclipses to discuss how much of the moon's Aries is no longer found between 0° Both Ptolemaic and Copernican surface they have seen. Each stu- - 30° but occupies a space approxi- models explain why lunar and solar dent, after one complete revolution, mately 30° - 60°. Likewise, all other eclipses occur. The complete solar will have seen the entire surface of constellations have moved about 30° eclipse is more easily observed with the moon. This raises the interesting in the last 2,000 years. Since this is all the Ptolemaic than with the Coper- question as to how much of the moon very confusing and can easily lead to nican because of the moon's position people on earth could expect to see if errors, it is much simpler to refer to a in the orrery. By placing the moon it did not rotate on its axis. location along the plane of the ecliptic directly between the sun and earth, Repeat the experiment with the in degrees. These are called celestial you can see how the light from the moon held stationary on its support longitude. sun can be obscured by the moon as arm. Students watching the demon- it moves between us and the sun. The stration will easily understand that if same effect can be achieved with the the moon did not rotate at the same Copernican system by substituting the rate it revolved, we would be able to planet Venus for the moon. see all of its surface during the course of one lunar month. e. The Asteroid Orbit Observations of the motion of the The 653-3120 has a stainless steel g. Retrograde Motion noon line will allow you to under- This backward motion of some wire arm to indicate the orbits of the stand why it is afternoon in New York of the planets was discussed earlier vast majority of the asteroids. Many while people in California have just and illustrated in Figure 3. Since thousands of these tiny rocks revolve finished breakfast. Since evening retrograde motion is only an apparent around the earth between Mars and would also come earlier for those on motion, not a real one, it can be best Jupiter. The wire arm is used to indi- the east coast than for those on the illustrated on the Ptolemaic System. cate their orbit, rather than trying to west coast, students in Florida could Ptolemy's concept of the epicycle show each individually. be studying evening stars and planets was so successful simply because he The asteroids or planetoids were while astronomers in Seattle could be did not know, and could not know, discovered on January 1, 1801 by the counting sunspot numbers. Sicilian astronomer, Piazzi. The ob- that he had confused the real and ap- ject he discovered was the largest of parent motion of the planets. the asteroids - Ceres, a single piece of solar system material with a diameter h. Motions of the Moon j. When to use Copernican of 480 miles. A simple yet difficult concept to and Ptolemaic systems Since then, thousands of these explain is how the moon manages to The Trippensee® Copernican sys- objects have been discovered on rotate and revolve and yet keeps the tem is used to show the solar system astronomical photographs. Obviously, same side facing the earth at all times. as it really is. The heliocentric view these pieces of material do not occupy Astronomers tell us that both motions shows the real positions and motions a single position within the solar sys- take place in exactly the same amount of the planets as viewed from the sun. tem as the planets do. Rather, they are of time, and yet, only the moon's rev- Data is given in Appendix I. spread somewhat uniformly around olution about our planet is obvious. People do not, however, view the the sun. The wire arm indicates the The Ptolemaic model is constructed planets, moon and stars from the sun. orbit of these pieces of material rather so that the moon can be rotated about We are on the third planet - quite than to try to show each of them a center axis. This rotation is helpful different. When locating a heavenly individually. in making this astronomical principle object in the sky, we need to know its As shown by the model, the orbit understood. apparent location and motion. Which of these minor planets lies between Mark the side of the moon facing brings us back to Ptolemy. Mars and Jupiter. Mars would prob- the earth lightly with colored chalk. The Ptolemaic system illustrates ably have little effect on the grouping Ask students to form a ring around the apparent motions better than the of the asteroids since Mars is only the model to observe it. Since the heliocentric models.

k. Demonstration of planetary A class project could include a k. Demonstration of seasons nomenclature wraparound mural, about one foot Everyone in the north temperate While this model has many advan- high, on which various constellations zone has experienced cold, blustery tages, chief among them is the fact of stars are painted. By placing this winters and hot, sticky summers. that it lends itself to an almost infinite around the solar system, you can Obviously the sun does not increase number of planetary configurations. show planetary position. You can also and decrease its heat to mesh with the You can see for yourself what astro- demonstrate in what constellation a dates on our calendar. To understand nomical terms mean as they apply particular planet is found. the reasons for the seasons, we must to our solar system. Once the model Once a constellation mural has look to a world in motion. has been set for the correct date, you been created to be used in conjunc- Ptolemy had no idea that the world ® can also determine what planets we tion with the Trippensee solar system was not perpendicular to the almost will find in the evening sky and what models, it will be possible to com- flat plane in which the planets move. planets we will not be able to see at bine the many demonstrations with Modern astronomy, however, shows all because of sunlight. observational astronomy in which all that the polar axis of the earth's equa- Photographs of the Copernican students can participate. tor is inclined 23-1/2° to the plane of model can illustrate several distinct Select a conspicuous planet or the ecliptic. This simple fact is the planetary positions. The student planets. Arrange the planets of the reason for our seasons. should learn to recognize these posi- model so that they appear to stand You will notice that in the fall and tions easily. [The figure below shows in front of the appropriate constella- spring the light of the sun falls equally the heliocentric view of planets, sun tion. Over a period of several weeks, on the northern and southern hemi- and moon on - what date]. When observe the planets and chart any spheres. In the northern hemisphere's viewed from the earth, Mars is near changes. These changes can then be winter, the sunlight is falling more superior conjunction. Jupiter and made on the solar system model. directly on the southern hemisphere, Venus at eastern quadrature, Saturn If the charted motion of the planet and in the northern hemisphere's sum- and Uranus at western quadrature, and is eastward, you will know that you mer, the sunlight falls more directly Neptune and Pluto have just been in are following the real counterclock- on the northern hemisphere and less opposition. wise motion of the planets about the directly on the southern hemisphere. sun. If, on the other hand, the planet The Copernican model of the solar seems to be moving westward, you system shows the earth's polar axis will know that you are observing a i. The sun and time of day clearly. By revolving the earth slowly planet in retrograde. This observation about the sun, the change of seasons We know the sun is no fiery chariot can be used to review and reinforce due to the difference in the angle of crossing the sky behind invisible the material covered in this booklet. the sunlight falling on the earth can be horses. These myths of sky and space easily understood. Stop at either polar have been dead for centuries. There extreme or at either equinox period are even those who realize that the ro- in order to demonstrate the changes tation of our planet causes the sun to taking place. appear to move westward at approxi- mately 15° per hour. But how many understand the simple but important role the rotation of the earth plays in 23-1/2° 23-1/2° Night ordering our lives through a process North Pole North Pole called time? Night Arctic Circle Tropic of The Ptolemaic model is designed Cancer so that rotation of the earth can be Day Equator demonstrated. The student can learn Tropic of Cancer Tropic of Cap how time is measured by establishing Plane of ricorn a line relationship between the earth Equator Ecliptic - and the sun. This relationship can be Antarctic Circle shown by holding a pencil or piece of Tropic of South wire stationary against the sun. Then, Capricorn Pole very slowly, rotate the earth counter- clockwise on its axis. The pencil or Summer Solstice Winter Solstice wire represents the most direct rays of Figure 12 - Seasonal Changes. As the earth orbits about the sun, it is lighted evenly. The the sun as they fall on the earth; that angle of the polar axis of the earth provides us with days of various lengths and thus with is, they represent the noon line. our temperature extremes.

Glossary mining an ellipse. object around another body. Albedo - The percentage of light Geocentric - Earth centered. Rotation - The turning of an object on reflected from the planet Heliocentric - Sun centered, as a solar a central axis. Apparent motion - Any motion not system. Spherical - Globular in shape. based on real causes. Hour angles of right ascension - Per- Solstice, summer - The position when Aphelion - The point of an object's pendicular measurement from the the sun appears to reach its highest orbit farthest from the sun. celestial equator. position. Antarctic circle - An imaginary circle Hyperbola - A curve formed by the Solstice, winter - The position when 23.5° north of the south pole. section of a cone cut by a plane the sun appears to reach its lowest Arctic circle - An imaginary circle that makes a greater angle with position. 23.5° south of the north pole. the base than the side of the cone Superior - Term used to designate Area - Used to describe a specified makes. objects farther from the sun than amount of distance within a deter- Inferior - Term applied to Venus and the earth. mined plane. Mercury, lying between earth and Transit - The passage of any object Asteroids - "Star like", name applied sun. across any given meridian. to the minor planets. Kirkwood gaps - Possible vacan- Tropic of Cancer - Position 23-1/2° A.U. - Astronomical unit, a distance cies in the asteroid belt due to the north latitude. of 92,956 miles. gravitational attraction of Jupiter. Tropic of Capricorn - Position Autumnal equinox - Point where the Meridian, lower - An imaginary 23-1/2° south latitude. sun crosses below the celestial north-south line running below the Velocity - Rate of motion in a particu- equator. observer on the other side of the lar direction. Axis - A real or imaginary straight earth. Vernal equinox - The position where line relationship. Meridian, upper - An imaginary the sun makes its upward passage Celestial equator - The equator of the north-south line running above the across the celestial equator. earth extended to infinity. observer and bisecting the sky into Celestial longitude - An imaginary two parts. line perpendicular to the ecliptic. Oblateness - A polar flatness more Celestial pole - Imaginary north-south pronounced with rapidly rotating axis of earth extended into space. objects. Coma - The gaseous envelope of the Orbit - The path of any object around nucleus in a comet. a primary object. Conjunction, inferior - Between earth Parabola - Curve formed by the and sun on direct axis. intersection of a cone with a plane Conjunction, superior - Opposite the parallel. sun on an earth-sun axis. Perihelion - Point of an object closest Constellations - Imaginary figures to the sun. composed of stars. Period - The time taken to complete Copernican - Adjective indicating any cyclical action. influence of Nikalaus Kopernik. Perturbation - An irregularity in the Corona - Crown halo of the sun. motion or orbit of a heavenly body. Deferent - Major circle of revolution Phases - Stages of variation in illumi- in the Ptolemaic planetary system. nation. Eclipse - A complete or partial block- Planetoids - Planet like; name given age of light, applied to sun or to small objects between Mars and moon. Jupiter. Ellipse - The path of a point that Ptolemaic - The adjective applied to moves so that the sum of its the ideas of Claudius Ptolemy. distances from two fixed points is Quadrature - The relative position constant. of two heavenly bodies when 90° Elongation - The distance of a planet distant from each other. from the sun measured in degrees. Regression - Movement backward, Epicycle - Circles designed by Ptol- westward with the planets. emy to explain planetary motions. Retrograde - Movement backward. Foci - Two fixed points used in deter- Revolution - The movement of an

Appendix I

Average daily, monthly, yearly planetary motions Heliocentric System

Planet Average Average Average Daily Motion Monthly Motion Yearly Motion

Mercury 4.1° 123° 4 revolutions + 36°

Venus 1.6° 43° 1 revolution + 216°

Earth 1.0° 30° 360°

Mars 0.53° 15.8° 190°

Jupiter 2.5° 30.1°

Saturn 1.0° 12.2°

Uranus 0.4° 4.3°

Neptune 2.2°

Pluto 1.45°

653-3110 Parts List, Ptolemaic Solar System* 653-3120 Parts List, Copernican Solar System 017838 Earth Wire 000355 Mercury Ball 006625 Earth Globe 000382 Venus Ball 001130 Base 000352 Earth Ball 033252 Zodiac 000362 Mars Ball 017955 Moon Wire 000410 Jupiter Ball 017920 Mars Wire 032154 Saturn Ball 017985 Jupiter Wire 033112 Uranus/Neptune Ball 017900 Saturn Wire 000387 Pluto/ Moon Ball 033112 Jupiter Ball 017975 Pluto Wire 033112 Saturn Ball Same as Jupiter 017970 Neptune Wire 033112 Venus Ball Same as Jupiter 017995 Uranus Wire 000362 Mars Ball 017985 Saturn Wire 015325 Sun Ball 017940 Jupiter Wire 000387 Mercury Ball 017930 Asteroid Wire 000410 Moon Ball 017945 Mars Wire 017840 Epicycle Casting 017935 Earth Wire 011950 Nylon Retainer, pair 018000 Venus Wire For epicycle casting, set of 2 017855 Mercury Wire 033862 Mercury, Venus, Sun wire together 033254 Zodiac * Big earth, small planets 017854 Main Shaft 001130 Base 017205 Wire Guide 033850 Sun Globe ass'y

Appendix II

653-3120 Ephemeris 2003-2010 Planetary Heliocentric Longitude as of January 1 (Degrees)

Planet 2003 2004 2005 2006 2007 2008 2009 2010

Mercury 50.9 125.7 193.5 236.7 269.3 308.5 11.3 84.8

Venus 138.3 2.4 230.2 93.7 318.8 184.3 49.3 275.3

Earth 100.8 100.5 101.3 101.0 100.7 100.5 101.2 101.0

Jupiter 130.5 159.1 186.8 214.2 242.3 271.5 302.3 334.4

Saturn 85.8 99.4 113.0 126.4 139.7 152.8 165.7 178.3

Uranus 329.1 333.0 336.9 340.8 344.7 348.6 352.5 356.4

Neptune 309.7 311.9 314.1 316.3 318.5 320.7 322.8 325.0

Pluto 248.3 250.4 252.6 254.7 256.8 258.9 261.1 263.2

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