Lab1Prelab_scale_24
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Milwaukee Area Technical College *
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122
Subject
Geology
Date
Apr 3, 2024
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docx
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Geo Sci 120: Geology of the Planets
Spring 2024
Name ;
PRE-LAB DUE:
LAB 1, PRE-LAB: THE SCALE OF THE SOLAR SYSTEM
Adapted from a lab created by Dr. Devon Burr, U. Tennessee. Thanks, Devon!
OBJECTIVES: •
Develop a sense for the relative sizes and distances in the Solar System.
•
Learn how to scale distances and sizes.
•
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 × 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.
SETTING THE SCALE
To make a scale model of the Solar System, first we have to set the scale. The actual or real-
world diameter of the Sun is 1,391,000 km. For this lab, we will set the model Sun to be just 20.00 cm in diameter. Note that this is FOUR significant figures, since trailing zeroes after the decimal (as in the case of 20.00) count as significant figures. Scale is usually given as a ratio of the real-world distance (i.e., on your ruler) to the equivalent distance in the model world. Note: for the scale to be correct, the units for the real-world distance and the model distance must be the same. Thus, in the example below, you will need to convert between km and cm. Your scale will be expressed as a ratio (below), where the Model value is typically scaled to ‘1’.
• Step 1: convert the diameter of the sun from km to cm, so that the diameters of the sun and your model object are expressed in the same units. If you use the table on the previous page, make sure you consider both the conversion between cm and m (100) and between m and km (1000). Note: you will get a very large number!
• Step 2: Divide both sides by the model diameter (in this case 20.00 cm), so that the Model value is 1.
• Step 3: Express the scale in scientific notation, with significant figures. Note: when we’re expressing our scale as a ratio and both sides have the same units, we can omit the units.
(Model: Real World)
What is the scale of our model? 1:7,000,000,000
Work
diameter of the real world sun's = 1,391,000 km
= 1391000 * 10^3 * 10^2
= 1.39 * 10^11 cm
Model diameter = 20.00
Scale of model = 20.00 / 1.39 * 10^11 = 1: 7 * 10^9
= 1:7,000,000,000
Earth's mode = 12,800 km
= 1.28 * 10^5 / 7000000000
= 0.182cm
This scaling factor can be applied to both the size (diameter) of our model planets and to their distance from the Sun. Real World diameters
Model diameter
Sun
1.391×10
6
km
20.00 cm
Earth
1.28×10
4
km
0.182 cm
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.
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