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Scale Model Solar System (with Pluto) Supplemental Teaching Activity (6th-8th) Montana Space Public Outreach Team This activity will allow you to create a scale model of the solar system (and Pluto, which is not considered a planet anymore). Making a model that is accurate in both relative size and distance of planets can be difficult (for an 8’’ Sun, it requires .5 miles, while the solar system that fits in a football field, has planets that are too small to see), so we suggest using one of the two scales on the left to compare relative size, then shifting to the scale where the sun is 1’’ and Pluto is a football field-length away (120 yards) to compare relative distance from the Sun. The more hands-on the activity, the more powerful it is. Try to have physical objects that are roughly the correct size and have students guess which one is Earth, etc. When comparing distances, try letting students represent different planets and stand at the proper place on a football field. Have fun with it! While not necessary, we recommend examining the proportional reasoning used to determine the scale values, as described on the second page. This can go as far as having students create tables similar to those given for a different scale length, or simply investigating how the given tables were made. The scales are rounded, and based off of the values given at the website: http://www.exploratorium.edu/ronh/solar_system/. Some reference charts use slightly different numbers, which would lead to slightly different scale numbers. Remember, Pluto is no longer considered a planet, but is the largest dwarf planet in the Kuiper Belt, which is estimated to contain thousands of objects larger than 62 miles (100 km) in diameter. The distance to Pluto is an approximate distance to the beginning of the Kuiper Belt (1st syllable rhymes with ‘lie’). Distance from the Sun (miles) Sun 0 Mercury .25 mi. (1/4) Venus Diameter (feet and inches) 32’ (about the size of a classroom) Scale Solar System Scale Solar System (scale: diameter of Sun = 8’’) Scale Solar system (scale: diameter of Sun = 32’) Object Distance from the Sun (feet) Diameter (inches) 0 8’’ 1.2’’ (Walnut) 28’ (9 yd) .47 mi. (1/2) 3.3’’ (Apple) Earth .65 mi. (2/3) Mars (scale: Pluto distance= 120 yards {football field with end zones}) Distance from the sun (feet) Diameter 0 1’’ .03’’ (Pinhead) 4’ (1.2 yd) .004’’ 52’ (17 yd) .070’’(Peppercorn) 7’ (2.2 yd) .009” 3.5’’ (Apple) 72’ (24 yd) .073’’(Peppercorn) 9’ (3 yd) .009” .99 mi. (1) 1.9’’ 109’ (37 yd) .04’’ (Pinhead) 14’ (4.5 yd) .005” Jupiter 3.39 mi. 3’ 3’’ 373’ .82’’ 47’ (16 yd) .105” (Peppercorn) Saturn 6.21 mi. 2’ 2’’ 683’ .67’’ (Hazelnut, 87’ (29 yd) Uranus 12.50 mi. 1’ 1’’(Pumpkin, Watermelon) 1375’ (.26mi.) .27’’ 175’ (58 yd) .088” (Peppercorn) .038” (Pinhead) Neptune 19.59 mi. 1’ .5’’(Pumpkin, Watermelon) 2155’ (.41 mi.) .26’’ 274’ (91 yd) .036” (Pinhead) Pluto 25.75 mi. .6’’ (Hazelnut, Acorn, Dime) 2832’ (.54 mi.) .01 360’ (120 yd) .002” (Kuiper Belt) (124 yd, .07 mi.) (228 yd, .13 mi.) (Basketball, Bowling ball, Soccer ball) (Marble, Chestnut, Pecan, Quarter) Acorn, Dime) (Peanut, Coffee Bean, Small Marble,) (Peanut, Coffee Bean, Small Marble) (Pinhead or smaller) (Marble, Chestnut, Pecan, Quarter) It isn’t usually possible to accurately depict the diameter of the planets when the scale distance is small. That’s ok, but it’s important to realize that our common depiction of their size is incorrect. Here is a recent video created by Wylie Overstreet and Alex Gorosh. “To scale: The Solar System” published Sept 16th, 2015. https://www.youtube.com/watch?v=zR3Igc3Rhfg They use a scale where Neptune is 7 miles away. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Now we examine the process of making a scale model: This ratio can be used to make a model of the solar system at any scale: 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Choose any convenient distance from the Sun to Pluto as your starting point, and find the distance from the sun to each planet using the equation. The left ratio determines the scale of the model. Use miles for the actual distances, but you can use miles, yards, feet or inches for the classroom distance. A similar equation can give you the scale diameters of each planet, so you know how large they should be. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡ℎ𝑒𝑒 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐴𝐴𝐴𝐴𝐴𝐴𝑢𝑢𝑢𝑢𝑢𝑢 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Remember that the actual distance is measured in millions of miles (Mercury is 36,000,000 miles from the Sun), and that you may need to do unit conversions to get meaningful answers. There are three feet in a yard. The conversion for feet and inches is: 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 × 5280 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 Object 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 × Actual Mean Distance from the Sun (in millions of miles) 12 𝑖𝑖𝑖𝑖𝑖𝑖ℎ𝑒𝑒𝑒𝑒 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑖𝑖𝑖𝑖𝑖𝑖ℎ𝑒𝑒𝑒𝑒 1 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Actual diameter (in miles) Sun 0 864,938 Mercury 36 3,031 Venus 67.2 7,514 Earth 93 7,921 Mars 141.5 4,215 Jupiter 483.3 88,927 Saturn 886.2 74,520 Uranus 1782.9 32,168 Neptune 2792.6 30,757 Pluto (Kuiper Belt) 3672 1,447