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Lab 1: Collecting and Displaying Data
Purpose of this Lab
All science, including
Lab 1: Collecting and Displaying Data
Purpose of this Lab
All science, including Astronomy, uses the language of mathematics to measure, interpret, and explain information. This lab will enable you to practice how to collect, report, display, and think about scientific data. These are skills that you will be using throughout this course.
Learning Objectives
To successfully complete this lab you will need to:
Input the correct values into an online solar system collider.
Measure lengths on an image with a ruler
Organize your data in a table (discussed in Lecture 1.4).
Create graphs to display the data (Lecture 1.4, including the section on choosing the correct graph).
Answer questions asking you to compare graphs and discuss the reason(s) why they might be similar or different from each other.
Knowledge
Working on this lab will require you to apply existing knowledge and build new knowledge:
Existing knowledge you will be utilizing to complete this lab:
Your understanding of how a piece of ice differs from the same size piece of rock or metal.
Your intuitive knowledge (from experience) that a fast thrown ball will cause more damage than a slow thrown ball and that a heavy ball can cause more damage than a lightweight ball.
Knowledge you will develop by completing this lab:
General background knowledge of how the variables (composition, velocity, size or mass) of an object striking the Earth or Moon do or do not lead to the formation of an impact crater.
Realization that stars are not uniformly distributed across the night sky.
Skills
Completing this lab will require you to apply existing skills and build new skills:
Existing skills you will be utilizing to complete this lab. The ability to:
follow directions, so as to correctly set up the solar system collider
use a ruler to draw a box with sides of a specific length
Skills you will develop by completing this lab. The ability to
create an x-y graph, if this is not already an existing skill
label all the parts on your graph (refer to Lecture 1.4)
choose the correct type of graph to display your data
draw a best fit line through data
determine the slope of a line, if this is not already an existing skill
Materials, Equipment, & Freely Available Software
Google sheets (for graphing) and Google docs (for tables and images) — both are available as part of your PCC email
a metric ruler (either a real one or a correctly scaled online ruler)
Google doc: Star count image and table – you may need to print this out if you can’t measure online
Google doc: Collisions tables
iTools online graphing tool for simple x-y graphs
solar system collider
Link to Lab Quiz
Success Criteria
Answer all of the questions in the lab quiz.
Use complete sentences to answer essay questions.
Provide reasoning and/or examples to support your answers to essay questions.
Turn in all tables and diagrams created to complete the lab.
Show all calculations.
Part 1: Counting Stars
Background
Stars, their colors, and their life cycles will be covered in modules 7 and 8. But we can use an image of a field of stars to start examining how astronomers collect and display data.
How many of you have ever put film into a camera in order to take a picture? The answer is probably very few, if any of you have done this. The “photos” that you take are digital. Most astronomical images taken today are also digital, but there are still telescopes that use film or even glass plates. Why would anyone still use glass plates?
Digital images are composed of individual picture elements (called pixels), which are often square in shape. Anyone who has enlarged a digital image on a computer notices that lines become jagged when enlarged, as shown in the image below.
Section of a digital image enlarged to show square pixels. Image from Wikimedia, authored by “ed g2s • talk”, licensed under CC BY-SA 3.0 DEED.
A web page on astronomic photography by the Australia Telescope National Facility states that one reason to use glass plates is to have better resolution than can be obtained with a digital image: “There are many millions of silver halide crystals on a single plate. A plate has far higher resolution than a CCD chip of the same area. Even a coarse-grained 35mm film has the equivalent of 25 million pixels whilst fine-grained astronomical emulsions have even more.” [CSIRO]
Both film and glass plates have to be “developed”, which produces a negative image. The negative must be “printed” to produce a positive image (which is what your eye sees). The image below shows both a positive (normal) image and the black-and-white negative of this same image.
Top: Hubble Space Telescope image of stars in the part of the sky containing the constellation of Sagittarius. Image from NASA/ESA, public domain. Bottom: Black-and-white negative of the Hubble image. Image created by M. Hutson/PCC.
Astronomers got into the habit of skipping the second step and just working with the negative: “Astronomers tend to work directly with the negative images for several reasons; to reduce chances of further errors, to maximize the image quality and often because it is easier to pick out a faint black object on a clear or white background than vice versa.” [CSIRO].
For this part of the lab, you will be looking at a typical field of stars as seen from a telescope on Earth. The image is inverted, so the sky is white and the stars are black. The original image was digital, so stars will be “squarish” in shape.
The goal of this exercise is to figure out approximately how many stars are in the image without having to count every single one of them. We can estimate the total number of stars by counting the number of stars in a smaller area, and extrapolating to larger areas.
Counting Stars is adapted from Scale Models and Graphing, a paper lab created for GS107 by Sang Park at PCC/Cascade.
Procedure
Part of the answers to the lab are entered into the Lab Quiz. It is recommended that you complete all of the steps of the lab and have the answers on a piece of paper before starting the quiz. The rest of the lab consists of documents that you will upload to assignment boxes. Please read the instructions carefully.
Make a copy of the Star count image and table in Google docs. The page will look like the image below.
A view of the Google doc page that you need to copy for this lab. The image will be 6.5 inches wide, and there will be a table with blank spaces beneath the image.
Use a ruler to outline 6 small squares on the star field, using the widths and heights given in the table. You can choose any part of the star field, as long as the width and height of your boxed squares match the numbers in the table. Important: You need three different squares that each have a length of 2 cm and a width of 2cm.
Calculate the area in each outlined region by multiplying the width times the height, and enter the answer in the correct cell of the table.
Count the number of stars in each outlined region and enter that number in the correct cell of the table.
[10 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – starcount-table
Upload the completed sheet to the correct assignment box. The star field image should have squares showing the areas that you counted, and the table should be completely filled in. Important: the sheet must be saved in a .pdf format. If you work online, you can “Download” from Google Docs choosing “PDF Document (.pdf)”. If you work offline and take an image, you need to insert the image into a Google Doc and download a single document in .pdf format. You will receive 6 points for the completed table and 4 for showing your areas on the image.
Watch the video below to see how to do the next step.
Plot the data from your table using Google Sheets. You should have 7 data points on the graph, including (0,0). Be sure to put area on the x-axis and number of stars (or star count) on the y-axis. Draw a best fit line through the data.
[5 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – star-count-graph-google-sheets
Upload your completed graph to the correct assignment box. Again, this graph needs to be saved as a .pdf document. You will receive 4 points for having all of the data on a correct x-y graph, and 1 point for having a correct best fit line.
Now calculate the slope of the best fit line. The slope of a line is given as . If you need a refresher, please refer back to Lecture 1.4/Graphing Data/Slope of a Line.
[2 points ] Lab 1: Question 1
This question is answered in the Lab Quiz. Please enter the slope that you calculated for the best fit line in the star count graph you created in Google sheets. Please show your calculations. You will receive 1 point for a correct slope and 1 point for showing your calculations.
Notice that you have three regions that have the same area (they all have length of 2 cm and width of 2 cm). You need to average the star counts for those three regions, and treat them as one data point. If you do not remember how to average data, please refer back to Lecture 1.4/Organizing Data/Why Average Data?
Create a plot using iTools online graphing tool instead of Google Sheets. Plot the data from your table, using the average value for the three regions, instead of three separate data points. Your graph should have 5 total data points (including (0,0)). Again, be sure to put area on the x-axis and number of stars (or star count) on the y-axis. Draw a best fit line through the data.
[5 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – star-count-graph-iTools
Upload your completed graph to the correct assignment box. Again, this graph needs to be saved as a .pdf document. You will receive 3 points for having all of the data on a correct x-y graph, 1 point for having the correct axis labels, and 1 point for having a correct best fit line.
Now calculate the slope of the best fit line. The slope of a line is given as . If you need a refresher, please refer back to Lecture 1.4/Graphing Data/Slope of a Line.
[2 points] Lab 1: Question 2
This question is answered in the Lab Quiz. Please enter the slope that you calculated for the best fit line in the star count graph you created using iTools. Please show your calculations. You will receive 1 point for a correct slope and 1 point for showing your calculations.
Take some time to look at both of your graphs and think about creating them.
[4 points] Lab 1: Question 3
This question is answered in the Lab Quiz. Please write a paragraph or two to give your opinions of the two graphs. You can consider such things as which graph you prefer and why, or which graph was easier to create and why, or whether it was easier to create a best fit line with the averaged data or the three individual points or how the slopes for the best fit lines varied? There is no single correct answer, but you need to provide a thoughtful response and include WHY for your opinions. 3 points for your opinions (3=excellent, 2=adequate, 1=needs improvement) and 1 for explaining why.
The slope of the line is equal to the number of stars per centimeters squared (cm2) of area. What this means is that you can estimate the number of stars for any area, as long as the area you are using contains a representative sample of stars. To do his, you use the equation , where m is the slope, x is the area being investigated, bis 0, and y is the number of stars in the area being investigated. In order to estimate the number of stars in the entire star field, you need to measure the area (in centimeters squared) of the entire image and use this value and your average slope to calculate the number of stars in the entire star field.
[2 points] Lab 1: Question 4
This question is answered in the Lab Quiz. Estimate the number of stars in the entire star field. Enter the value in the box provided. Please show your calculations. You will receive 1 point for a correct slope and 1 point for showing your calculations.
Part 2: Exploring Collisions on the Moon and Earth
Background
Comets, asteroids, impacts, and impact craters are covered in Module 3. But we can use an impact collision simulator to examine how astronomers collect and display data.
Impacts happen to all objects in space. It is estimated that around 300 tons of material from space lands on the Earth every day, much of it in the form of fine dust. All of us breath and eat extraterrestrial material every day. Larger sand-sized particles burn up as they enter the Earth’s atmosphere, creating “shooting stars”. Larger rock or boulder sized material might slow down enough to land as a meteorites. Much bigger pieces are dangerous, as they aren’t slowed by the Earth’s atmosphere and hit the Earth’s surface at speeds of 20,000-50,000 miles per hour, with energies similar to or higher than nuclear bombs. These very large pieces will excavate holes in the ground called impact craters. These large pieces are referred to as “projectiles” by people who work on impact processes. In an impact, most of the projectile’s energy goes into excavating a crater, but some of the energy is converted to heat, which vaporizes and melts both the projectile and some of the target material. A small amount of energy may be used for other things, such as causing endothermic reactions (chemical reactions) in the target material. When astronomers talk about the “size” of an impact crater, they are referring to the crater’s diameter (distance across the widest part at the surface).
We’ll be using an online Solar System Collider for this part of the lab. It can be found at https://janus.astro.umd.edu/astro/impact/
This is one of the simpler impact simulations on the web. It looks at an object (called a projectile) coming towards a planet or our Moon. The default approach velocity for the projectile is 20 km/sec, which is a typical velocity for impactors hitting the Earth.
A screen shot of the main page for the collider is shown below.
Things that can be changed are:
the Target. All of the planets in our solar system and our Moon are possible targets. Earth is divided into just “Earth” or “Earth (land only)”. This lab will only use “Earth (land only)” and “the Moon” as targets.
the Projectile Composition. The default is “Rock”. We will also be using “Ice” and and “Iron”.
the Projectile Diameter. This is where you should be careful. The default is “kilometers”, and we will not be using the default. Other options are “microns” (dust), “centimeters” (sand and small pebbles), and “meters”. We will be using meters. For reference, 1 meter is about 39 inches (a bit over 3 feet). The image below shows comparisons of well-known Earth features to the two asteroids visited by the DART mission, for those of you not used to thinking in metric.
ALTERNATE TEXT. Original caption: “The sizes of the two asteroids in the Didymos system relative to objects on Earth. Image credit: NASA/Johns Hopkins APL, public domain.
Procedure
Make a copy of Collisions tables in Google Docs. This is a document with three tables (labeled Table 1, Table 2, and Table 3). You will be filling out these tables as you work through this part of the lab.
For Table 1, we will be using the default Projectile Velocity of 20 km/s. Start with the default Target of Earth (land only) and the default Projectile Composition of “rock”. Change the units for the Projectile Diameter to “meters” using the dropdown menu. To start, enter a Projectile Diameter of 1 meter. Then hit the button that says “KABOOM!” If an impact crater is formed, you will see information including “Crater Diameter” in the lower left of the results screen. If no impact crater is formed, type in the information such as “shooting star” or “explosion over North America” in the table cell. Enter the results for the 5 different sized projectiles for the Earth (land only) in Table 1. Be careful. If you have an impact crater that has a diameter in km, convert the diameter to meters by multiplying by 1000.
Change the Target to “the Moon” and re-run the simulator for the 5 projectile sizes. Enter the results in Table 1. Be careful. If you have an impact crater that has a diameter in km, convert the diameter to meters by multiplying by 1000.
Notice that the Earth’s atmosphere protects us from smaller projectiles. Also notice that for the 100 meter projectile, the Energy Released is 60 Megatons for both the Earth and Moon. But the impact crater that forms on the Moon is larger than the one that forms on the Earth. Why? The answer is that Earth has a higher gravity than the Moon, so it takes more energy to excavate a crater on Earth than on the Moon.
[1 point] Lab 1: Question 5
This question is answered in the Lab Quiz. Both Projectile Diameter and Crater Diameter on the Moon are variables, which means you can plot an x-y graph with this data. Crater Diameter on the Moon is which of the following?
• the independent variable, which should be plotted along the x-axis.
• the dependent variable, which should be plotted along the y-axis.
Create an x-y graph using the Projectile Diameter and the Crater Diameter of the Moon (data from Collisions Table 1). You may use any graphing program that you would like; you can even graph by hand if you want. Be sure to give the graph a title, and label both axes. Also, the final .pdf document that you turn in must have the graph on one page. Please be careful to look at what you turn in. We often see Excel graphs half on one page and half on another.
[4 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – Collisions-graph1-Projectile_Size-Moon
Upload your completed graph to the correct assignment box. Again, this graph needs to be saved as a .pdf document. You will receive 1 point for correctly plotting the data points, 1 point for a meaningful title, 1 point for correctly choosing the x- and y-axes, and 1 point for labeling the axes.
[3 points] Lab 1: Question 6
This question is answered in the Lab Quiz. Look at the graph you just created. Does the data suggest a linear relationship between projectile diameter and crater diameter for smaller projectiles (less than a few hundred meters in diameter) hitting the Moon. Answer yes or no, and then write a couple of sentences discussing whether or not this surprised you and why. You will receive1 point for yes or no; 1 point for whether this was a surprise, and 1 point for why.
We are now going to focus on the effect of the Projectile Composition. Set the collider Target to “the Moon”, the Projectile Diameter to 1 meter, and the Projectile Velocity to 20 km per second. The only thing that will be changed is the Projectile Composition. For each of three compositions (Ice, Rock, Iron), run the collider and copy down the energy (in tons of TNT) and crater diameter (in meters) into Collisions Table 2.
[1 point] Lab 1: Question 7
This question is answered in the Lab Quiz. Go back to Lecture 1.4/Graphing Data/Choosing the Correct Graph. Which is the best graph to display the data in Collisions Table 2? By the way, you won’t be graphing this data.
• X-Y graph
• Bar graph
• Pie chart
[1 point] Lab 1: Question 8
This question is answered in the Lab Quiz. Often, when scientists want to compare two things, they might simply say that one thing is a certain number of times bigger or smaller than another thing by dividing one number into the other.
For example, to compare a 6 foot tall adult to a 3 foot tall child, divide 6 by 3 (). You could say that the adult is 2 times taller than the child.
Look at the numbers for “Ice” and “Iron” in the Collisions Table 2 that you created. The energy released by the collision of a 1-meter piece of iron is approximately _______ times the energy released by the collision of a 1-meter piece of ice on the Moon.
• only about 1.2
• exactly 2
• a bit more than 2
• a bit less than 10
• far more than 10
[1 point] Lab 1: Question 9
This question is answered in the Lab Quiz. Look at the numbers for “Ice” and “Iron” in Collisions Table 2? The crater diameter formed by a 1-meter piece of iron hitting the Moon is approximately _______ times the crater diameter of a 1-meter piece of ice hitting the Moon.
• only about 1.2
• exactly 2
• a bit more than 2
• a bit less than 10
• far more than 10
We’re now going to take a closer look at energy and crater diameter. Set the collider Target to “the Moon”, the Projectile Diameter to 1 meter, and the Projectile Composition to “Rock”. The only thing that will be changed is the Projectile Velocity. Run the collider, and find the Energy Released and the Crater Diameter of the crater that forms and enter these numbers into Collisions Table 3.
[14 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – Collisions Tables 1, 2, 3
At this point, you have completed all three tables on this document. Upload the completed sheet to the correct assignment box. Important: the sheet must be saved in a .pdf format. Be sure to “Download” from Google Docs choosing “PDF Document (.pdf)”. You will receive 5 points for correctly filling in Table 1; 3 points for correctly filling in Table 2, and 6 points for correctly filling in Table 3.
[2 points] Lab 1: Question 10
This question is answered in the Lab Quiz. Now you need to think a bit more about dependent and independent variables. Collisions Table 3 has three columns. The thing that was varying was Velocity. Both the Energy and the Crater Diameter depended on the Velocity. But what if we want to plot Energy and Crater Diameter on an x-y graph? Does one of those two variables depend on the other? Please answer yes or no, and explain why you answered the way you did. You will receive 1 point for yes or no and 1 point for your explanation.
Create an x-y graph using the Energy and the Crater Diameter reported in Collisions Table 3. You may use any graphing program that you would like; you can even graph by hand if you want. Be sure to give the graph a title, and label both axes. Also, the final .pdf document that you turn in must have the graph on one page.
[4 points] UPLOAD TO ASSIGNMENT BOX FOR LAB 1 – Collisions-graph2-Energy-Diameter
Upload your completed graph to the correct assignment box. Again, this graph needs to be saved as a .pdf document. You will receive 1 point for correctly plotting the data points, 1 point for a meaningful title, 1 point for correctly choosing the x- and y-axes, and 1 point for labeling the axes.
[3 points] Lab 1: Question 11
This question is answered in the Lab Quiz. Look at the graph you just created. Does the data suggest a linear relationship between energy and crater diameter for a 1-meter rocky projectile hitting the Moon. Answer yes or no, and then write a couple of sentences discussing whether or not this surprised you and why. You will receive1 point for yes or no; 1 point for whether this was a surprise, and 1 point for why.
Important Information!!!
When you have finished entering all of your lab information into the Lab Quiz, you must hit the SUBMIT button. It is not enough to just save each individual question. d2L/Brightspace will not process the Lab Quiz, or make it available to your instructor for manual grading if you have not hit the SUBMIT button.
Lab 1: Collecting and Displaying Data
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