S ca le M o d e l o f th e S o la r Sy ste m

Transcription

1 N a m e ' D a t e ' S ca le M o d e l o f th e S o la r Sy ste m 6.1 I n t r o d u c t i o n T h e S olar System is large, at least w hen com pared to distances we are fam iliar w ith on a day-to-day basis. C onside r that for those of you w ho live here in O rl ando, you travel 2 kilom eters (or 1.2 m iles) on average to cam pus each day. If you go to M i a m i on weekend, you travel about 375 kilom eters (232.5 m iles), and if you travel to M e p m p h i s T N, t o v i s i t f a m i l y for S p rin g Break, you travel ~ 1,300 kilom eters (N 800 m iles), w here the ~ sym bo l m eans a pproxim ately. Th e se are all distances we can m e ntally com prehen d. N ow, how large is the E a r t h? If you wanted to take a trip to the center of the E a rt h (the very hot core ), you would travel 6,378 kilom eters (3954 m iles) from O r lando dow n th rou g h the E a rth to its center. If you th en continued going another 6,378 kilom eters you w ould pop out on the other side of th e E a rt h in the south ern part of the In dia n Ocean. Thus, the total distance th rou g h the Earth, or the d i a m e t e r of th e Earth, is 12,756 kilom e- ters (N 7,900 m iles), or 10 tim es the O r l a n d o t o M em p his distanc e. O bviously, such a trip is im p o ssib le. T o get to the southe rn In d ia n Ocean, you w ould need to travel on th e surface of th e Earth. H ow far is th a t? Since the E a rth is a sphere, you w ou ld need to travel 20,000 k m to go ha lfw ay aroun d the E a rth (rem em ber the equation Circum ference :. T h is is a large distan ce, but we ll go farther still. Next, we ll travel to the M oo n. T h e M o o n, E a rth s n a tu ral satellite, orbits the E a rt h at a distance of ~ 400,000 kilom eters ( N 240,000 m iles), or about 30 tim es the diam eter of th e Earth. T h is m eans that you could fit rou g h ly 30 E a rths end-to-e nd between here and th e M o on. T h is E a r t h - M o o n distance is N 200,000 tim es the distance you trave l to school each day (if you live within 1.2 mi). So you can see, even th ough it is located very close to us, it is a lon g way to th e E a rt h s nearest neighbor. N o w let s travel from the E a rth to th e Sun. T h e average E a rt h -to-s u n distance, ~ 150 m illion kilom eters ( ~ 93 m illion m iles), is referred to as on e A s t r o n o m i c a l U n i t (A U ). W h e n we look at the pla nets in our S olar System, we can see that th e planet M e rcury, w hich orbits nearest to the Sun, has an average distance of 0.4 A U and Pluto, the planet alm ost always the furthest from the Su n, has an average distance of 40 A U. T hu s, the E a rt h s distance from the S u n is on ly 2.5 percent of the distance between the S u n and planet Plutol! P lu to is very far away! T h e purpose of today s lab is to allow you to develop a better appreciation for the distances between th e largest objects in our solar system, and the physical sizes of these objects relative to each other. To achieve this goal, we will use the length of th e football field in B i l l S p o o n e S ta d iu m as our platform for developing a scale m odel of th e Solar System. A scale 79

2 model is simply a tool whereby we can use manageable distances to represent larger distances or sizes (like the road map of New Mexico used in Lab #1). We will properly distribute our planets on the football field in the same relative way they are distributed in the real Solar System. The length of the football field will represent the distance between the Sun and the planet Pluto. We will also determine what the sizes of our planets should be to appropriately fit on the same scale. Before you start, what do you think this model will look like? Below you will proceed through a number of steps that will allow for the development of a scale model of the Solar System. For this exercise, we will use the convenient unit of the Earth-Sun distance, the Astronomical Unit (AU). Using the AU allows us to keep our numbers to manageable sizes. SUPPLIES: a calculator, Appendix in your textbook, the football field in Bill Spoone Stadium, and a collection of different sized spherical-shaped objects 6.2 T h e D i s t a n c e s o f t h e P l a n e t s F r o m t h e S u n Fill in the first and second columns of Table 6.1. In other words, list, in order of increasing distance from the Sun, the planets in our solar system and their average distances from the Sun in Astronomical Units (usually referred to as the semi-major axis of the planet s orbit). You can find these numbers in back of your textbook. (21 points) Next, we need to convert the distance in AU into the unit of a football field: the yard. This is called a scale conversion. Determine the S C A L E D orbital semi-major axes of the planets, based upon the assumption that the Sun-to-Pluto average distance in Astronomical Units (which is already entered into the table, above) is represented by 100 yards, or goal-line to goalline, on the football field. To determine similar scalings for each of the planets, you 80

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7 6.5 Take Home Exercise (35 points total) Now you will work out the numbers for a scale model of the Solar System for which the size of Florida along the turnpike and I-75 will be the scale. The turnpike starts in Miami and continues north through Tampa, Ocala, Gainsville until it leaves Florida, where it then continues to travel to northern Michigan. The total distance of I-75 in Florida is about 455 miles. Using this distance to represent the Sun to Pluto distance (40 AU), and assuming that the Sun is located at the start of I-75 down in Miami and Pluto is located along the Florida- Georgia border, you will determine: the scaled locations of each of the planets in the Solar System; that is, you will determine the city along the highway (I-75) each planet will be located nearest to, and how far north or south of this city the planet will be located. If more than one planet is located within a given city, identify which street or exit the city is nearest to. the size of the Solar system objects (the Sun, each of the planets) on this same scale, for which 455 miles (730 kilometers) corresponds to 40 AU. Determine how large each of these scaled objects will be (probably best to use feet; there are 5280 feet per mile), and suggest a real object which well represents this size. For example, if one of the scaled Solar System objects has a diameter of 1 foot, you might suggest a soccer ball as the object that best represents the relative size of this object. If you have questions, this is a good time to ask" 1. List the planets in our solar system and their average distances from the Sun in units of Astronomical Units (AU). Then, using a scale of 40 AU = 455 miles (1 AU = miles), determine the scaled planet -Sun distances and the city near the location of this planet's scaled average distance from the Sun. Insert these values into Table 6.4, and draw on your map of Florida (on the next page) the locations of the solar system objects. (20 points) 2. Determine the scaled size (diameter) of objects in the Solar System for a scale in which 40 AU = 455 miles, or 1 AU = miles). Insert these values into Table 6.5. (15 points)

8 Table 6.4: Planets' average distances from Sun. Average Distance from Sun Planet in AU in Miles Nearest City Earth Jupiter 5.2 Uranus 19.2 Pluto mi NW of Jennings, FL Table 6.5; Planet s diameters in a Florida Scale Model Object Actual Diameter(km) Scaled Diameter (feet) Object Sun --, 1,400, Mercury 4,878 Venus 12,104 Earth 12, height of 12 year old Mars 6,794 Jupiter 142,800 Saturn 120,540 Uranus 51,200 Neptune 49,500 Pluto 2, soccer ball 86

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10 6.6 P o s s ib le Q u iz Q u e s t io n s 1. W h a t is th e a p p r o x im a te d ia m e te r o f th e E a r t h? 2. W h a t is th e d e fi n i tio n o f a n A s tr o n o m ic a l U n i t? 3. W h a t va lu e is a sca le m o d e l? 6.7 E x t r a C r e d i t L a te r th is sem ester w e w ill ta l k a b o u t co m ets, o b je cts th a t resid e o n th e edge o f o u r S o la r S ystem. M o s t co m ets are fo u n d e ith e r in th e K u ip e r B e l t, o r in th e O o r t C l o u d. T h e K u i p e r b e lt is th e r e g io n th a t s ta r ts n ea r P l u t o s o r b it, a n d e xte n d s to a b o u t 100 A U. T h e O o r t clo u d, h o w e ver, is en orm ous: it is es tim a te d to b e 40,000 A U in ra d iu s! U sin g y o u r fo o tb a ll fi e ld sca le m o d e l t o a nsw er th e fo llo w in g q u estions: 1) H o w m a n y ya r d s a w ay w o u ld th e edge o f th e K u i p e r b e lt b e fr o m th e n o r th er n g o a l lin e a t B i l l S p o o n e S ta d iu m? 2) H o w m a n y fo o t b a ll fi e ld s d oes th e ra d iu s o f th e O o r t clo u d c o rr es p o n d to? I f th e r e a re 1760 ya rd s in a m ile, h o w m a n y m iles aw ay is th e edge o f th e O o r t c lo u d fro m th e n o r th -e r n g o a l lin e a t B i l l S p o o n e S ta d iu m?