Dusty data dive
Purpose: Students will practice analyzing and graphing data using two data tables from a primary research study about space dust. The activity will help students understand why scientists are rethinking where some of the space dust in the atmosphere comes from.
Procedural overview: After reading the Science News article “Kuiper Belt dust may be sprinkled in our atmosphere” and completing the accompanying Article-Based Observation questions, students will use the data provided to generate graphs and estimate track densities for dust grains traveling various distances.
Approximate class time: 1 class period to complete the activity questions, calculations and graphing.
Supplies:
Dusty Data Dive student activity guide
Calculators
Graph paper or computers with graphing software
Online access to research information about the solar system
A projector for introducing the activity (optional)
Directions for teachers:
To understand the general concepts behind the data being analyzed, students should read the Science News article “Kuiper Belt dust may be sprinkled in our atmosphere” and answer the accompanying Article-Based Observation questions prior to engaging in this activity. Reviewing the answers to the Article-Based Observation questions with students would help them understand the data they are analyzing. If you have time, or some students finish early and need an extra challenge, there is a set of bonus questions about the rate at which dust grains accumulate tracks.
If a projector is available, open “Kuiper Belt dust may be sprinkled in our atmosphere” so students can view the article on the screen, show students where the citations are listed at the end of the article, click on the primary research study “A Kuiper Belt source for solar flare track-rich interplanetary dust particles” and scroll to the data tables on the second page. Students can see that the data they will be working with is directly from the primary research study without having to read the research paper. If a projector is not available, explain and show students the data source.
Discuss the following questions and answers with your students before allowing them to engage with the data on their own.
Based on the Science News article “Kuiper Belt dust may be sprinkled in our atmosphere,” how could the new dust grain findings affect what scientists currently think about the Kuiper Belt?
The track numbers observed on some dust grains collected from Earth’s atmosphere are much higher than expected from grains that originated between Mars and Jupiter. That suggests that these grains must have traveled farther in space, possibly from as far away as the Kuiper Belt, or been exposed to more heavy charged particles in some other way. If the grains are in fact from the Kuiper Belt, that could call into question what scientists thought about the existence of liquid water in the Kuiper Belt.
How does the distance a dust grain travels affect the number of tracks on the grain? What else might affect track grain numbers?
Grains that originated farther away take more time to reach Earth’s atmosphere, so the grains would spend more time exposed to heavy charged particles and thus accumulate more tracks. There are more heavy charged particles from solar flares closer to the sun, so grains that originate closer to the sun would accumulate more tracks faster than grains that originated farther away from the sun.
What data does Table 1 present?
The first column of the table lists 14 samples of dust grains, also called interplanetary dust particles (IDPs), collected from Earth’s atmosphere. The 10 samples without stars are anhydrous. That means they do not contain water. The four samples with stars are hydrated — they do contain water. Information on water content is provided in case it affects the density of tracks an IDP collects over time. The table’s second column gives the measured track density, or the number of tracks per unit area (tracks/centimeter^{2}) for each grain. The table’s third column indicates what type of mineral each grain is made of: “pyx” is pyroxene (often a black mineral like augite), “Ol” is olivine (generally a green mineral like peridot gemstones) and “An” is anorthite (generally a white mineral in the feldspar family).
What data does Table 2 present?
Data presented in Table 2 are based on computer models. Table 2 gives the expected track density, or number of tracks/cm^{2}, for dust grains that have traveled from different initial distances to reach Earth at 1 astronomical unit, or AU. The table gives this information for two models that differ in their assumptions about how the rate at which grains accumulate tracks changes with distance from the sun and their assumptions about how long it takes dust grains from various parts of the solar system to reach Earth.
Directions for students:
After reviewing the general information about the data below with your teacher, look at Tables 1 and 2 and use them to answer the following questions. When needed, use an additional resource to find background information.
Table 1:
IDP # | Track Density Measured (Tracks/cm^{2}) | Type of Mineral |
---|---|---|
1* | 6 x 10^{10} | pyx |
2 | 8 x 10^{10} | Ol |
3 | 6 x 10^{10} | An |
4 | 10 x 10^{10} | pyx |
5 | 7 x 10^{10} | An |
6 | 3 x 10^{10} | pyx |
7 | 8 x 10^{10} | pyx |
8 | 3 x 10^{10} | pyx |
9 | 5 x 10^{10} | pyx |
10* | 7 x 10^{10} | pyx |
11* | 50 x 10^{10} | pyx, Ol |
12 | 6 x 10^{10} | pyx |
13 | 2 x 10^{10} | pyx |
14* | 6 x 10^{10} | pyx |
Table 2:
Initial Distance of IDP from the sun (AU) | Estimated Track Density Computer Model 1 (Tracks/cm^{2}) | Estimated Track Density Computer Model 2 (Tracks/cm^{2}) |
---|---|---|
50 | 6.2 x 10^{9} | 12.6 x 10^{9} |
40 | 5.4 x 10^{9} | 10.6 x 10^{9} |
30 | 4.6 x 10^{9} | 8.4 x 10^{9} |
20 | 3.6 x 10^{9} | 6.0 x 10^{9} |
10 | 2.2 x 10^{9} | 3.2 x 10^{9} |
5 | 1.2 x 10^{9} | 1.6 x 10^{9} |
3 | 0.8 x 10^{9} | 0.8 x 10^{9} |
Background questions
1. Study the first column of Table 2. What does AU stand for and what does it measure? Convert 1 AU to two different units of measurement.
AU stands for astronomical unit. It is a unit of measurement for distance, and is defined as the average distance from sun to Earth. 1 AU is approximately 1.50 x 10^{6} kilometers or 9.30 x 10^{7} miles.
2. What are the approximate distances of the following objects from the sun in AU?
Mercury 0.39 AU
Earth 1.0 AU
Asteroid belt 2.1–3.3 AU
Uranus 19 AU
Kuiper Belt 30–50 AU
3. According to the primary research study, dust from the asteroid belt would reach Earth in about 6 x 10^{4} years, and dust from the Kuiper Belt would reach Earth in about 1 x 10^{7} years. Use this information, Table 2 and your answer to the previous question to answer the following questions.
Approximately how many times further does dust from the asteroid belt need to travel to reach Earth compared with dust from the Kuiper Belt?
Assuming 3 AU as the distance, dust from the asteroid belt travels 2 AU (from 3 AU to 1 AU) to reach Earth. Assuming 30 AU as the distance, dust from the Kuiper Belt travels 29 AU (from 30 AU to 1 AU) to reach Earth, or about 14.5 times as far as dust from the asteroid belt.
Approximately how many times longer does it take for dust from the asteroid belt to travel to Earth compared with dust from the Kuiper Belt?
Dust from the asteroid belt arrives after about 6 x 10^{4} years, or 60,000 years. Dust from the Kuiper Belt arrives after about 1 x 10^{7} years, or 10 million years. Kuiper Belt dust takes roughly 170 times as long to reach Earth as dust from the asteroid belt.
How does the travel time appear to relate to the distance traveled?
Travel time appears to increase roughly like the square of the distance traveled.
4. How does your final answer to question 3 relate to the simple equation for diffusion? In simple diffusion problems, the distance a grain travels (L) depends on a diffusion constant (D) and the time (t) the grain has been traveling: L^{2} = Dt, or t = L^{2}/D.
In this case, dust traveling or diffusing through the solar system seems to obey the equation for simple diffusion — the travel time increases approximately as the square of the distance.
5. What is a benefit and a drawback of applying the simple equation for diffusion to try to understand how space dust travels?
The diffusion equation is much easier to use than other equations that include complicated trajectories and gravitational interactions. But the simple equation might not yield precise results because they ignore those variables.
Data analysis and graphing
6. In Table 1, do you see any obvious outliers in the data? What can you infer about the history of any outliers? Should they be used to draw more general conclusions about the data?
IDP 11 has way more tracks/cm^{2} than any of the other samples. Presumably its history was very different from the histories of the other grains, and it cannot be used to draw more general conclusions.
7. What is the average track density for the 10 anhydrous samples?
5.8 x 10^{10} tracks/cm^{2}
8. What is the average track density for the four hydrated samples?
17.25 x 10^{10} tracks/cm^{2}
9. What is the average track density for the hydrated samples without the outlier?
6.33 x 10^{10} tracks/cm^{2}
10. Does removing the outlier appear to have greatly affected the results? Explain.
Student answers will vary.
11. Use graph paper, a computer or a calculator to graph the data from both computer models shown in Table 2. If both models are represented on the same graph, make sure your graph indicates that Computer Model 1 data is a separate series than Computer Model 2 data. What type of graph might you use?
See example graph. A scatterplot is used as an example.
12. Where would a data point for 1 AU fall on the Table 2 graph?
See example graph. A grain that starts at 1 AU likely originated at or near Earth, so it would arrive at Earth’s atmosphere after zero time. As such, the grain would be unlikely to have a lot of tracks from heavy charged particles.
13. What is a simple, approximate equation that fits most of the data points for the Computer Model 2 data? If you graphed the data on the computer or calculator, use the graphing system to find an equation.
The points are nearly linear with tracks/cm^{2} = (initial distance / 3.5 AU) 0.9 x 10^{9} tracks/cm^{2}
14. If you graphed the data on the computer or calculator, use the graphing system to find an approximate equation for Computer Model 1 data. Why is this equation difficult to predict without graphing software?
tracks/cm^{2} = (initial distance / 3.5 AU)^{0.75} 0.9 x 10^{9} tracks/cm^{2}
The equation is difficult to predict without graphing software because the track data from Computer Model 1 is not linear in nature.
15. Using Computer Model 1 data, estimate the track density for dust grains that originated from the following distances. If you have an equation for Computer Model 2, use it to estimate the track densities.
Distance Computer Model 1 Computer Model 2
100 AU ~11 x 10^{9} tracks/cm^{2} ~26 x 10^{9} tracks/cm^{2}
90 AU ~10 x 10^{9} tracks/cm^{2} ~23 x 10^{9} tracks/cm^{2}
80 AU ~9.4 x 10^{9} tracks/cm^{2} ~21 x 10^{9} tracks/cm^{2}
70 AU ~8.5 x 10^{9} tracks/cm^{2} ~18 x 10^{9} tracks/cm^{2}
60 AU ~7.6 x 10^{9} tracks/cm^{2} ~15 x 10^{9} tracks/cm^{2}
16. Besides travel time and initial distance from the sun, can you think of some other variables that might affect track density?
Other variables that might affect track density include a grain’s mineral type, how much water the grain contains, the time it spent on its parent body or another large body in space, or the sources of track-making heavy charged particles. While particles from solar flares are one source of tracks, another source is cosmic rays.
Bonus questions
17. In order to infer travel time from track density, scientists need to determine a track production rate, referred to as “track-rate estimate” in the Science News article. What is the track production rate and how is it expressed?
The track production rate is the number of heavy charged particle tracks accumulated by dust grains per cross-sectional area per year in space. It is expressed in number of tracks/cm^{2}/year.
18. Scientists had previously estimated the track production rate at 6.5 x 10^{5}/cm^{2}/year. The new estimated rate is 4.4 x 10^{4}/cm^{2}/year. By what multiplicative factor are they different?
The old track production rate is about 15 times the new rate.
19. What would be the effect on the estimated travel time of the dust particles if one used the old track production rate instead of the new track production rate?
The old track production rate is about 15 times the new rate. Assuming the new rate is accurate, using the old rate could overestimate the time it took for a grain to accumulate tracks and thus the time it has been traveling in space by a factor of 15.
20. Based on the answers to question 3, we know that a dust grain’s travel time appears to increase roughly like the square of the distance traveled. Use your answer from question 19 to approximate how much closer a grain’s initial distance may have been to Earth, relative to what previous estimates would suggest.
If the travel time drops by a factor of 15 compared with old estimates, the distance traveled would be shorter by a factor of about (15)^{0.5} or about 3.9. Thus a dust grain would appear to be coming from a location that is roughly one-fourth the distance from Earth.