Building a Scale Model of the Solar System Earth & Sky Name: Introduction Outer space is surprisingly vast and empty. The stars you see in the night sky often burn as bright, or brighter, than the Sun, but the immense distance that the light must travel to reach us helps to dim and shrink the objects to a reasonably small size, distorting our understanding of the distances in space. Furthermore, while light travels extremely fast, nearly 300,000 km/s, light from the nearest stars still takes over 3 years to get to Earth, implying an extremely large amount of empty space. In this lab, you will calculate and design a model solar system and relate it to a map of the RPI campus.
Pre-test 1. How far do you think the Moon is from Earth? How much farther do you think the Sun is from the Earth? The nearest star?
2. How many stars do you think are within 10 light years of Earth?
3. How many times farther do you think the nearest galaxy is, compared to the Sun?
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Making a Model In order to build a scale model, we must first pick a base object. In this lab, we will assume that the Sun is only 8 cm in radius, about the size of a standard CD rotated about an axis through the edges and center. From this size and the size of the Sun itself, you can calculate a scale, and then deduce the relative sizes of the other objects in the solar system. You will then use the scale to determine the relative distances of the planets from the Sun, and, ultimately, the distances of nearby stars and galaxies in your scale.
Creating a Scale 1. If the radius of the Sun is 6.96 × 105 km, what is the scale of this model? (Remember, the radius of our model Sun is 8cm) 1:
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Calculating Scaled Sizes of Planetary Objects 2. Calculate the scaled sizes of the planets according to this scale, and compare them to the sizes of the following everyday things. Object
Average Diameter (mm)
CD
80
Finger
20
Peanut
10
Red Ant
5
Rice
3
Mustard Seed
1
Amoeba
0.5
Average Pixel
0.2
Human Hair
0.08
Planetary Body
Equatorial Diameter (km)
Mercury
4878
Venus
12102
Earth
12756
Earth’s Moon
3476
Mars
6792
Ceres1
941
Jupiter
142984
Saturn
120536
Uranus
51118
Neptune
49528
Pluto2
2306
2
Eris
2400
Sedna3
1500
Scaled Diameter
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Comparable Object
Ceres, a dwarf planet, is the largest asteroid in the asteroid belt between Mars and Jupiter Pluto and Eris are considered dwarf planets, and are the two largest of the Kuiper Belt objects discovered as of 2007. 3 Sedna is the 5th-largest trans-Neptunian object discovered as of 2007, and the only one of these 5 with an aphelion of more than 500AU. 2
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Calculating Scaled Distances from the Sun 3. Now, calculate the distances from the Sun of the planets in this scale, and draw a rough estimate of where the planets are located on the RPI map provided in Figure 1. Don’t forget to mark where your Sun is! One astronomical unit (AU) is about 149.6 × 106 km. You might not be able to plot the locations of all of these objects. Don’t worry if you can’t. Planetary Body
Average Distance from the Sun (AU)
Mercury
0.387
Venus
0.723
Earth
1.000
Mars
1.524
Ceres
2.766
Jupiter
5.204
Saturn
9.582
Uranus
19.229
Neptune
30.104
Pluto
39.482
Eris
67.668
Scaled Distance
Sedna (Perihelion) 76.156 Sedna (Aphelion)
975.56
4. Here are the nearby stars within 10 light years of Earth. Does the number surprise you? What are their distances in this scale? Plot them (roughly) on the map provided in Figure 2. Can you plot Sedna’s aphelion on this map? Remember that a light year is 9.46 × 1012 km. Star
Distance from the Sun (light years) Scaled Distance
Alpha Centauri 4.3649 Barnard’s Star
5.9629
Wolf 359
7.7823
Lalande 21185
8.2903
Sirius
8.5826
Luyten 726-8
8.7278
Ross 154
9.6811
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5. The Andromeda galaxy is 2.5 million light years away. In this scale, how far away is it?
Post-test 1. As you found above, Earth’s Moon is so much smaller than the Sun. Why, then, does it seem almost as large as the Sun in the sky? How much closer do to Earth do you think the Moon is than the Sun?
2. Given that even the fastest trip from Earth to Mars takes 6 months, and the New Horizons mission to Pluto will take nearly 10 years to reach Pluto, how long do you think it would take to reach the nearest star (Alpha Centauri)? Do you think interstellar travel is possible with existing technologies? Why or why not?
3. The nearest exoplanet, or planet outside our Solar System, is 10.5 light years away. Do you think it would be feasible to explore the planet within your lifetime? Why or why not?
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Figure 1: RPI Campus Aerial Photograph
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Figure 2: Equidistant Azumuthal Projection of the World centered on Troy, NY
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