Lab1_Scale_Model
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Collin County Community College District *
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Course
1403
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
6
Uploaded by ElderPrairieDogPerson401
Lab 1: Scale Model of
the Solar System -
Worksheet
adapted from NMSU Astronomy lab manual
Equipment
Internet, calculators
Introduction
The Solar System is large, at least when compared to distances we are familiar with on a day-to-day basis. Consider that for those of you who live in McKinney, you travel around 6 kilometers (4 miles) on average to campus each day. If you head to downtown Dallas on weekends, you travel about 53 kilometers (33 miles), and if you travel to South Padre Island for Spring Break, you travel ~1000 kilometers (~600 miles), where the ‘~’ symbol means “approximately.” These are all distances we can mentally comprehend.
Now, how large is the Earth? If you wanted to take a trip to the center of the Earth (the very hot “core”), you would travel 6,378 kilometers (3954 miles) from McKinney down through the Earth to its center. If you then continued going another 6,378 kilometers you would ‘pop out’ on the other side of the Earth in the southern part of the Indian Ocean. Thus, the total distance through the Earth, or the diameter of the Earth, is 12,756 kilometers (~7,900 miles), or nearly 8 times the McKinney – South Padre Island distance. Obviously, such a trip is impossible – to get to the southern Indian Ocean, you would need to travel on the surface of the Earth. How far is that? Since the Earth is a sphere, you would need to travel 20,000 km to go half way around the Earth (remember the equation Circumference = 2πRadius?). This is a large distance, but we’ll go farther still.
Next, we’ll travel to the Moon. The Moon, Earth’s natural satellite, orbits the Earth at a distance of ~400,000 kilometers (~240,000 miles), or about 30 times the diameter of the Earth. This means that you could fit roughly 30 Earths end-to-end between here and the Moon. This Earth-Moon distance is ~60,000 times the distance you travel to campus each day (if you live in McKinney). So, you can see, even though it is located very close to us, it is a long way to the Earth’s nearest neighbor.
Now let’s travel from the Earth to the Sun. The average Earth-to-Sun distance
, ~150 million kilometers (~93 million miles), is referred to as one Astronomical Unit (AU). When we look at the planets in our Solar System, we can see that the planet Mercury, which orbits nearest to the Sun, has an average distance of 0.4 AU and Pluto, the planet almost always the furthest from the Sun has an average distance of 40 AU. Thus, the Earth’s distance from the Sun is only 2.5 percent of the distance between the Sun and planet Pluto!! Pluto is very far away!
The purpose of today’s lab is to allow you to develop a better appreciation for the distances between the largest objects in our solar system, and the physical sizes of these objects relative to each other. You will also gain some practice working with units, unit conversions, and scaling. To achieve this goal we will construct a scale model of the Solar System. A scale model is simply a tool whereby we can use manageable distances to represent larger distances or sizes. We will properly distribute our planets on our model in the same relative way they are distributed in the real Solar System. The longest lengths in our scale models will represent the distance between the Sun and 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?
Enter your answers to each question in the data tables and yellow highlighted areas below. When completed,
please save and upload this file to the assignment submission link in Canvas.
The Distances of the Planets from the Sun
Fill in the first and second columns of Table 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 your textbook.
Table 1: Average Distance from Sun (Round scaled distance to nearest mile.)
Our scale model will fit the Solar System into the state of Texas. On your computer, load Google Maps and search for Texas so that it will show the boundaries of the state. Right click to find the Measure Distance feature
and use that feature to find the longest straight line in Texas. Round this distance to two significant figures (if you are unsure about rounding, ask!) and record it in the bottom row of the third column in Table 1
– this distance will represent the Sun to Pluto distance (40 AU).
Next we need to scale the distances in AU into the unit used by Google Maps to measure distance: the mile. This is called a “scale conversion”. Our scale conversion for this model is based on setting the distance between the Sun and Pluto (40 AU) equivalent to the longest straight-line distance in Texas. Follow the example below and use this relationship to determine how many miles there are in our model per AU. Record this scale factor to the right of the table. Then, determine the scaled distances for each of the planets, using the same scale factor. Round your scaled distances to the nearest mile.
Example: If Texas were found to be 400 miles along the longest straight line (then you should re-check your measurement, but we’re going to run with this distance for the example) then for our scale model,
40 AU = 400 miles.
We want to mathematically rearrange this so that we eventually have a number equal to one with units of miles per AU. Algebraically, there are many paths to get there, here is one:
Divide both sides of the equation by 40:
40 AU / 40 = 400 miles / 40.
This becomes
1 AU = 10 mile.
Planet
Actual Distance
Scaled
Distance
AU
Miles
Mercury
0.387
8
Venus
0.723
15
Earth
1
20
Mars
1.524
31
Jupiter
5.203
105
Saturn
9.54
193
Uranus
19.19
389
Neptune
30.96
627
Pluto
40
810
Scale Factor: 1 AU = 20.25 Miles
Now divide both sides of the equation by 1 AU:
1 AU / 1 AU = 10 mile / 1 AU.
Since anything divided by itself is equal to one, we now have that 1 = 10 mile / 1 AU. Thus, our scale factor is 10 mile / 1 AU, or equivalently, 10 mi / AU
To find the scaled distance between the Sun and the Earth, we would take the actual distance, 1 AU and multiply by our scale factor:
1 AU x (10 mile / AU) = 10 miles.
Note that the unit AU shows up in the numerator and denominator – it is being divided by itself and so it is
equivalent to one and goes
away.
The Sizes of Planets
Now it is time to determine how large (or small) the planet themselves will be on the same scale.
In the introduction it was stated that the diameter of the Earth is 12,756 kilometers, while the distance from the Sun to Earth (1 AU) is equal to 150,000,000 km. We have also determined how many miles 1 AU is represented by in our Texas-sized scale model.
We will start here by using the largest object in the solar system, the Sun, as an example for how we will determine how large the planets will be in our scale model of the solar system. The Sun has a diameter of
~1,400,000 (1.4 million or 1.4 x 10
6
) kilometers, more than 100 times greater than the Earth’s diameter! Since we know in our scaled model 150,000,000 kilometers (1 AU) is worth a certain amount of miles, let’s determine how many meters correspond to 1.4 x 10
6
km (the Sun’s actual diameter).
Our previously determined scale factor scales AU into miles. However, our diameters are in units of kilometers,
not AU. So to use our scale factor, we must first use unit conversion to convert the diameters into units of AU:
This is the conversion between AU and km: 1 AU = 1.5 x 10
8
km:
Sun’s Diameter (AU) = Sun’s Diameter (km) x (1 AU / 1.5 x 10
8
km)
= (1.4 x 10
6
) / (1.5 x 10
8
km/AU)
= 9.33 x 10
-3
AU
Now we can use the scale factor determined for Table 1 to calculate the scaled Sun diameter as follows: Scaled Sun Diameter (miles) = Sun’s Diameter (AU) x Scale Factor (miles / AU)
Now, if the Sun and the objects orbiting it were larger, this might be where we stop, but even the Sun, the largest object in the solar system will scale to much smaller than 1 mile, so let’s convert the Scaled Sun Diameter to a more appropriate unit, the meter. The conversion factor to use here is 1 = 1609 m / mile.
Scaled Sun Diameter (m) = Scaled Sun Diameter (miles) x 1609 (m/mile).
This three-step process (1-convert diameter from km to AU, 2-use scale factor to express AU as miles, 3- convert miles to meters) can be combined into one equation as follows:
Scaled Sun Diameter (m) = Sun’s Actual Diameter (km) x Scale Factor (mile/AU) x 1.072 x 10
-5
(m
AU / mile
km)
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Using this example, fill in the scaled diameters in Table 2. Round your answers to two significant figures.
Table 2: Diameters of Solar System Objects (Round scaled diameter to 2 significant figures.)
Object
Actual Diameter
(km)
Scaled Diameter (m)
Sun
1,390,000
300
Mercury
4,880
1.1
Venus
12,102
2.6
Earth
12,756
2.8
Moon
3,476
0.75
Mars
6,794
1.5
Jupiter
142,984
31
Saturn
120,536
26
Uranus
51,118
11
Neptune
49,528
11
Pluto
2,374
0.52
Create Scale Model Map
Now we have all the information required to create a scale model of the Solar System in Google Maps.
1)
Go to Google My Maps on the computer. You may need to log into your Google account.
2)
Find and click the Menu button (
)and click New Map from the menu options.
3)
Zoom in a bit on Texas, then use the Draw a Line tool to draw the longest straight line through Texas you identified earlier. Label your line and in the description box, give its length in AU and miles.
4)
Starting at one end of your line, zoom in and use the Add Marker tool to place a marker for the Sun. Label your marker as the Sun, and in the description box write its scaled diameter in m. Save your marker.
5)
Use the Measure Distances and Areas tool to measure the distance, along the line you drew, from your Sun marker to the next solar system object on Table 1, Mercury. At the correct distance from the Sun (you may need to zoom in to make the placement accurate) place a marker for Mercury. Label your marker with the object and the object’s distance from the Sun (For example: Mercury, 8 miles from Sun), and in the description
give the object’s scaled diameter in meters (For example: Mercury’s diameter is 1.1 m in this model). Save your label. Repeat this process (step 5) for all objects on Table 1. Include the Moon’s diameter information with Earth’s.
6)
Find the Share button and change Who has access to “On – Anyone with the link” and save. Copy the link to your map.
7)
Log into Canvas and find this lab assignment. Paste the link to the map you created as a submission comment and click Submit.
Questions about Texas Scaled Model
1)
Is this spacing and planet size distribution what you expected when you first began thinking about this lab
today? Why or why not?
The planet size distribution I was expecting because of how much larger the gas giants are than the first four planets. However, I was not expecting the distance distribution to be as spaced out as it was. I did not realize how large the gaps were between the gas giants and using the scale map over Texas helped show the distribution.
Later this semester we will talk about comets, objects that reside on the edge of our Solar System. Most comets are found either in the “Kuiper Belt’, or in the “Oort Cloud”. The Kuiper belt is the region that starts near Pluto’s orbit, and extends to about 100 AU. The Oort cloud, however is enormous: it is estimated to be 40,000 AU in radius! Using your Texas-sized scale model, answer the following questions and show your work:
2)
How many miles away would the edge of the Kuiper belt be from the Sun?
The outer edge of Kuiper belt would be 2025 miles away from the Sun using the same scaling as before (1 AU = 20.25 Mi).
3)
How many Texas’s would you have to line up to represent the radius of the Oort cloud?
You would have to line up about 1000 Texas’s to represent the radius of the Oort Cloud because Texas stretches about 40 AU at its longest point.
Answer the following questions using the information you have gained from this lab and your own intuition:
4)
Which planet would you expect to have the warmest surface temperature? Why?
Using the data from the lab it would be expected that Mercury has the warmest surface temperature because it is the closest planet to the Sun. However, Venus has the hottest surface temperature due to the greenhouse effect trapping gasses in the atmosphere the continuously keep the planet extremely warm, making it even warmer than Mercury although it is further away.
5)
Which planet would you expect to have the coolest surface temperature? Why?
Using the data from the lab it would be expected that Neptune has the coolest surface temperature because it is located the furthest away from the Sun. However, although it is not an official planet, Pluto would have a cooler surface temperature because it is located significantly further away from the Sun than Neptune.
6)
Which planet would you expect to have the greatest mass? Why?
Using the data from the lab it would be expected that Jupiter has the greatest mass because it has the largest scaled diameter out of all the planets. Although Jupiter has the most mass among the planets, it is still about one
tenth the size of the Sun in terms of mass.
7)
Which planet would you expect to have the longest orbital period? Why?
Using the data from the lab it would be expected that Neptune would have the longest orbital period because it is the planet located furthest away from the Sun and therefore takes significantly longer to complete a full orbit. Although Pluto is not an official planet, it does have a longer orbital period than Neptune because it is located further away from the Sun than Neptune.
8)
Which planet would you expect to have the shortest orbital period? Why?
Using the data from the lab it would be expected that Mercury would have the shortest orbital period because it is the planet located closest to the Sun and therefore takes significantly less time to complete a full orbit. Mercury’s orbital period is about one fourth of the Earth’s orbital period, which shows how a year on Mercury is about the equivalent to one of the four seasons on Earth.
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