Lab1_scale_24

Geo Sci 120: Geology of the Planets Spring 2024 Name; LAB DUE: LAB 1: THE SCALE OF THE SOLAR SYSTEM Lab adapted from that of Dr. Devon Burr, U. Tennessee. Thanks, Devon! OBJECTIVES: I. Develop a sense for the relative sizes and distances in the Solar System. II. Learn how to scale distances and sizes. III. Learn proper usage of significant figures and scientific notation. MATERIALS: campus map (provided digitally), calculator (or computer), ruler. INTRODUCTION: The solar system is so vast compared with human scales that it is difficult to imagine the sizes of the planets and the distances between them. (Even so, the solar system is a very tiny part of the observable universe!) In fact, diagrams of the solar system in textbooks generally do not accurately represent both the size of planets and the size of their orbits. In this lab, you will calculate the dimensions of a scale model of the solar system by putting the dimensions of the solar system into familiar units. For all lab exercises through this class, be sure to a) show your work including any calculations you used to generate your results. If you get a wrong answer but we can see that parts of the mathematical reasoning were correct, you can earn partial credit. b ) include units in all answers (where appropriate). In this class we want you to become familiar with the metric system, so answers should be given in metric units. Units may be abbreviated as follows: Units Abbreviation Mass kilograms kg = 1000 g grams g = 1/1000 of a kg Length kilometers km = 1000 m meters m = 1/1000 of a km centimeters cm = 1/100 of a m millimeters mm = 1/1000 of a m astronomical unit* AU *An astronomical unit is the average distance from the Sun to the Earth. c) report your results with the appropriate number of significant figures . For example, 7,930 and 25.4 both have 3 significant (non-zero) digits. If you used those numbers in a calculation, your result should be rounded to show 3 significant figures. The number

of significant figures in your answer indicates the precision of your answer - don’t overstate what you really know . d) use scientific notation for numbers with more than 3 consecutive zeros. That is, represent the number as a coefficient multiplied by base 10 raised to an exponent: coefficient × 10 # The coefficient should be a decimal number (e.g., 1.4) greater than 1 and less than 10. The exponent is equal to the number of spaces the decimal must move, either to the right (+) or to the left (-), in order to write out the number. For example, ● 150 million kilometers (the average distance from the Sun to the Earth, or one AU) is 150,000,000 km or 1.5 x 10 8 km. Since there are only two non-zero digits (1 and 5) before the zeroes, that makes for TWO significant figures. ● The mass of a dust particle is 0.000000000753 kg, or 7.53 × 10 -10 kg. That’s THREE significant figures. Now try one for yourself! The diameter of Jupiter is 143,000 km, or 1.43 × 10 5 km. How many significant figures is that? 3 significant figures.

Thus, the diameter of the Earth in the real world (12,800 km) = 0.182 cm in the model world. How many significant figures is that? 3 significant figures. MODEL PLANETARY DIAMETERS: 1. Now you will do this exercise for each planet in the Solar System. The table below gives planet diameters in km. From these data, calculate their diameters in the model scale solar system as follows. Fill in the table below. Empty column 1 : Use YOUR scaling factor from the pre-lab to calculate the model planet diameter in km. To do this, divide the real diameter by your scaling factor. Remember that this will give you an answer in the same units (if your real diameter was expressed in km, your model diameter will be too). Empty column 2 : Convert to centimeters. We’re including Pluto, though now officially not a planet, to show how small it is compared with the planets. In the last column , name an ordinary household object that has a diameter close to that of your model diameter calculation. Recommended items to consider: grains of salt/sand, ball-shaped candies or gum, pieces of fruit, marbles, etc. Be sure to report your model diameter with the appropriate number of significant figures . Planet Real diameter (km) Model diameter (km) Model diameter (cm) Real world object Mercury 4880 6.97×10 -7 0.0697 Grain of salt/sand Venus 12,100 1.73×10 -6 0.173 Grain of salt/sand Earth 12,800 1.84×10 -6 0.184 Grain of salt/sand Mars 6790 9.72×10 -7 0.0972 Grain of salt/sand Jupiter 143,000 2.05×10 -5 0.205 Peppercorn Saturn 119,000 1.71×10 -5 0.171 Peppercorn Uranus 51,200 7.31×10 -6 0.0731 Grain of salt/sand Neptune 49,600 7.11×10 -6 0.0711 Grain of salt/sand Pluto 2370 3.31×10 -7 0.0331 Grain of salt/sand

Model diameters are 3 significant figures. Show your calculations for AT LEAST ONE PLANET below: Mercury Scale of model = 20.00 / 1.39 * 10 11 = 1: 7 * 10 9 = 1:7,000,000,000 Real Diameter (km) = 4880 Model Diameter (km) = 0.000000697 = 10 -7 = 6.97×10 -7 Model Diameter (cm) = 4880/7,000,000,000 = 0.000000697 Venus Scale of model = 20.00 / 1.39 * 10 11 = 1: 7 * 10 9 = 1:7,000,000,000 Real Diameter (km) = 12100 Model Diameter (km) = 0.000001729 = 10 -6 = 1.73×10 -6 Model Diameter (cm) = 12100/7,000,000,000 = 0.173 Mars Scale of model = 20.00 / 1.39 * 10 11 = 1: 7 * 10 9 = 1:7,000,000,000 Real Diameter (km) = 6790 Model Diameter (km) = 0.00000000972 = 10 -7 = 9.72×10 -7 Model Diameter (cm) = 6790/7,000,000,000 = 0.0972 Jupiter Scale of model = 20.00 / 1.39 * 10 11 = 1: 7 * 10 9 = 1:7,000,000,000 Real Diameter (km) = 143,000 Model Diameter (km) = 0.00000697 = 10 -5

= 0.0331 MODEL PLANETARY DISTANCES FROM THE SUN: 2. Now that we know the sizes of our model planets, using the same scaling factor as before, we’ll calculate their distances from the Sun. Fill in the table below. Note: in this exercise you will be converting from km to m (rather than cm), so make sure you use the appropriate conversion factor. (Reminder to help you imagine your results: 1 meter is a bit more than 1 yard = 3 feet.) Show your calculations for AT LEAST ONE PLANET below: Mercury Average Real Distance (km): Given Mercury = 5.79 × 10 7 Venus = 1.08 × 10 8 Earth = 1.51×10 8 Mars = 2.20 × 10 8 Jupiter = 7.79 × 10 8 Saturn = 1.43 × 10 9 Uranus = 2.87 × 10 9 Neptune = 4.51 × 10 9 Pluto = 5.98 × 10 9 Real Distance (m): Mercury = 5.79 × 10 7 × 1000 = 5.79×10 10 Venus = 1.08 × 10 8 ×1000 = 1.08×10 11 Earth = 1.51×10 8 × 1000 = 1.51×10 11 Mars = 2.20 × 10 8 × 1000 Planet Average real Distance (km) Real Distance (m) Model Distance (m) Mercury 5.79 × 10 7 5.79×10 10 8.28 Venus 1.08 × 10 8 1.08×10 11 15.45 Earth 1.51×10 8 1.51×10 11 21.6 Mars 2.20 × 10 8 2.20×10 11 31.47 Jupiter 7.79 × 10 8 7.79×10 11 111.43 Saturn 1.43 × 10 9 1.43×10 12 204.56 Uranus 2.87 × 10 9 2.87×10 12 410.54 Neptune 4.51 × 10 9 4.51×10 12 645.14 Pluto 5.98 × 10 9 5.98×10 12 855.42

= 2.20×10 11 Jupiter = 7.79 × 10 8 × 1000 = 7.79×10 11 Saturn = 1.43 × 10 9 × 1000 = 1.43×10 12 Uranus = 2.87 × 10 9 × 1000 = 2.87×10 12 Neptune = 4.51 × 10 9 × 1000 = 4.51×10 12 Pluto = 5.98 × 10 9 × 1000 = 5.98×10 12 Model Distance (m): Mercury = 21.6(5.79 × 10 10 /1.51×10 11 ) = 8.28m Venus = 21.6(1.08×10 11 /1.51×10 11 ) = 15.45m Earth = 21.6(1.51×10 11 /1.51×10 11 ) = 21.6m Mars = 21.6(2.20×10 11 /1.51×10 11 ) = 31.47m Jupiter = 21.6(7.79×10 11 /1.51×10 11 ) = 111.43m Saturn =21.6(1.43×10 12 /1.51×10 11 ) = 204.56m Uranus = 21.6(2.87×10 12 /1.51×10 11 ) = 410.54m Neptune = 21.6(4.51×10 12 /1.51×10 11 ) = 645.14m Pluto = 21.6(5.98×10 12 /1.51×10 11 ) = 855.42m 3. Now, to put this into more familiar terms, let’s compare these measurements to a football field (for the sun through Jupiter) and a map of UWM’s campus (for the rest). A standard NFL football is ~27 cm from tip to tip, so we can think of the sun as being roughly football-sized at the scale of our model (though obviously much more spherical). We will use the simplifying assumption that 1 meter is exactly 1 yard (the real conversion factor is 1 meter to 1.09361 yards). If our 20-cm diameter football-sun is sitting on the goal line at one end of the field, where would we see the planets? Scale; 1/7×10 9 = 20/1.391×10 6 = 20/ 1.391×10 6 ×10 3 ×10 2 = 1/7x10 9 Mercury: 9.97 yards from the goal line.

5. Here are a few videos available online that demonstrate this idea using other models. Pick one , then fill in the following: Bill Nye the Science Guy: http://www.youtube.com/watch?v=97Ob0xR0Ut8 It’s Okay to be Smart (PBS): https://www.youtube.com/watch?v=_mD-ia6ng0A a. What video did you pick (url): The video I picked was It’s Okay to be Smart (PBS): https://www.youtube.com/watch?v=_mD-ia6ng0A b. What model did the video present (as in, what types of objects, and what general distances)? Sun = Grapefruit; 110 millimeters in diameter compared to 1.39 million kilometers of actual sun. Mercury = sign; about 4.5 which is the same as 59 million kilometers from the sun Venus = sign; about 8.5 which is the same as 108 million kilometers Earth = sign; about 11.6 meters which is the same as 150 million kilometers Mars = sign; about 18 meters which is the same as 229 million kilometers Asteroid Belt = sign; about 23-46 meters Jupiter = sign; about 61 meters which is the same as 779 million kilometers Saturn = sign; about 112 meters which is the same as 1.4 billion kilometers Uranus = sign; about 226 meters which is the same as 2.9 billion kilometers Neptune = sign; more than 350 meters which is the same as 4.5 billion kilometers Pluto = sign; for 20 out of 250 year orbit it's closer to the sun than Neptune is. c. Did the video do a good job presenting a reasonable model of the solar system? If so, what was good about it? If not, what was wrong, and how could it be improved? The video did do an okay job just because they didn't really use objects to represent the planets not including the sun but they did give good examples of what they could be. I believe they could have shown those examples and while they are outside maybe gluing them down in a white paper or white board because we won't be able to see hair strands on the grass. It would also keep it still in case there was wind that day.