THE NORTHERN LIGHTS
A Grade 7-8 guide to understanding the Aurora Borealis through math, geometry and reading activities.
This booklet was created by the NASA, IMAGE satellite program's Education and Public Outreach Project.
Writers:
Dr. Sten Odenwald (NASA/IMAGE)
Ms. Susan Higley (Cherry Hill School)
Mr. Bill Pine (Chaffey High School)
Students:
Emily Clermont (Holy Redeemer School)
Denali Foldager (Seward Elementary School)
Sonta Hamilton (Mt. Edgecumbe High School)
For more classroom activities about aurora and space weather, visit the IMAGE website at: http://image.gsfc.nasa.gov/poetry
This series of activities will help students understand how the Northern Lights work, what causes them, and how to observe them.
Through a series of math and reading activities, students will learn:
- How aurora are described by scientists and by other students (Reading)
- The geographic locations of aurora based on satellite data (Geography)
- How aurora appear in the sky at different geographic latitudes (Geometry)
- The height of aurora above the ground (Geometry - parallax)
- How to predict when they will appear (Mathematics)
- What Norse Mythology had to say about aurora (symbolic code translation)
Activity 6: Aurora Triangulation from Photographs
Parallax:
Stretch your arm out in front of your face with your thumb extended upwards. Now, close your left eye and note where your thumb appears in relation to objects in the distance. Now close your right eye and open the left. Note that the position of your thumb has shifted slightly to the right compared to where it was when only your left eye was open. This shift is known as parallax, and your brain uses this information to figure out how far things are away from you.
Beginning in 1909, the Norwegian scientist Carl Stormer used a similar technique to find out how high up aurora were located. Although many scientists had attempted to measure auroral heights before 1900, Stormer made the photographic process an exacting science by carefully designing procedures and mathematical techniques to minimize many different sources of experimental error. He used a network of cameras that simultaneously photographed the same auroral feature. The photographs from 10 different stations in Norway were combined in pairs with many different separations. These paired photographs were used to measure the parallax angle shifts. From these shifts, an average distance to different parts of an aurora could be found. Over 12,000 of these measurements were made by Stormer between 1909 and 1944, using specially-designed cameras with no moving parts so that they would not freeze-up during the very cold winter nights! In the days before the invention of modern insulated parkas, they wore thick fur clothing.
Objective:
The students will use real life pictures to determine Parallax angle shifts and use information calculated to determine auroral height.
Benchmarks:
6-8 Technology is essential to science for such purposes as access to outer space, sample collection, measurement, storage and computation.
9-12 Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings.
6-8 Models are often used to think about processes that happen too slowly, too quickly or on too small a scale to observe directly, or that are too vast to be changed deliberately.
9-12 Find answers to problems by substituting numerical values in simple algebraic formulas.
6-8 Understand writing that incorporates circle charts, bar graphs line graphs, tables, diagrams and symbols
Materials:
Procedures:
Step 1: Teacher introduces the vocabulary list to the students. These can be place on the overhead or on the chalkboard.
Step 2: Students work through the steps on the student worksheet. The activity can be completed by the student if the teacher is confident that they can perform the tasks, or the steps can be completed one at a time in pairs or groups. If the teacher opts to do this, it might be good to stop after each step or every two steps and discuss the results prior to completing more steps. The teacher may wish to have a transparency of the student worksheets and the stars to show how and fill in as the activity progresses.
Step 3: Discuss the answers if not already completed.
Vocabulary List:
Perpendicular: two lines are perpendicular if the angle between them is 90 degrees.
Vertical angles: Angles that share only one point. They are on opposite sides of the transversal.
Isosceles triangle: A triangle that has at least two congruent sides.
Parallax: The vertex angle P. Obtained from 180 minus the sum of the two base angles.
Name ________________________________________________________________________ Date ________________
Station 1: This is a photograph taken at one observing station of an aurora that passed through the bowl of the Big Dipper (Ursa Major). The numbered stars are:
1...Dubhe
2...Mirak
3...Phecda
4...Megrez
5...Alioth
6...Mizar
Station 2: This is a photograph of the aurora in the Big Dipper (Ursa Major) taken at the same time from a second observing station 17. 6 kilometers from Station 1. Note that there is a shift in the location of the aurora between the two stations.
Name ________________________________________________________________________ Date ________________
STEP 1: Using the photographs, measure in millimeters the distance between the following points and complete the table.
| Point 1 and 4 | 27 mm |
| Point 1 and 6 | |
| Point 2 and 5 | |
| Point 1 and 5 | |
STEP 2: The points that were measured are really stars in the sky. They make up a constellation known as the Big Dipper. Using the table below, determine the degrees based on the measurement above.
| 1 and 4 | 10 |
| 1 and 6 | 20.5 |
| 2 and 5 | 15.5 |
| 1 and 5 | 14.5 |
For Example:
Point 1 and 4 were measured to be 27 mm. Using the table in step 2, pair of stars 1 and 4 are 10 degrees. This means that the angular distance of these two stars in the sky is 10 degrees.
Step 3: Next it is necessary to calculate the image (pictures) scale based on the above information. In order to do so, use the following formula where S = the scale.
For Example:
S = (Degrees) divided by the (measured millimeters)
S = (10 degrees) / (27mm)
S = 0.37
Identify the degrees for each of the other star pairs.
Use the formula to calculate the scale for the other pairs of stars.
Step 4: Use the formula to calculate the scale for the other pairs of stars and complete the following chart. The first one is completed.
| 1 and 4 -- Dubhe-Mehrez | 0.37 |
| 1 and 6 -- Dubhe-Mizar | |
| 2 and 5 -- Merak-Alioth | |
| 1 and 5 -- Dubhe-Alioth | |
Name ________________________________________________________________________ Date ________________
STEP 5: In this case, the values do not have a significant difference. However, in order to be more accurate in determining the scale, it is a good idea to average the results.
Therefore, average the values in the scale column.
( 0.37 + ____ + ____ + ____ ) / 4 = _______ IMAGE SCALE
STEP 6: Next, pick a feature that is in the aurora and measure the distance to the edge of the aurora in each photo.
For Example:
Select point 4. Measure the horizontal distance to the edge of the photo for this point in each photograph. The edge of the Aurora in photo one is _____ mm away from point 4 and the edge of the Aurora is _____ mm away from the edge of the Aurora in photo two. Now subtract the two measurements in order to obtain the Parallax shift.
Photo two ______ mm - Photo one _____ mm = ________ PARALLAX SHIFT
This value should be typically the same for each point in the photo.
STEP 7: Now that the image scale has been calculated and the Parallax shift is determined, these two values can be multiplied together to obtain the number of degrees in the Parallax angle.
IMAGE SCALE * PARALLAX SHIFT = PARALLAX ANGLE
STEP 8: when all of the above steps are completed, they can be applied to determine the Auroral height. Station 1 and Station 2 are 17.6 kilometers apart. Using the Parallax angle, Pin the diagram below, use properties of vertical angles and the tangent ratio to determine the height, h. (note: the height is perpendicular to the base)
First, divide the Parallax angle in half to determine angle X. Then use the fact that the sum of the angles of a triangle is 180 degrees to find the missing base angle. Last, apply the tangent ratio to determine the height of the Aurora.
The height of the Aurora is __________ km.
Teacher Answer Key
STEP 1: Using the photographs, measure in millimeters the distance between the following points and complete the table.
| Point 1 and 4 | 27 mm |
| Point 1 and 6 | 52 mm |
| Point 2 and 5 | 42 mm |
| Point 1 and 5 | 41 mm |
STEP 2: The points that were measured are really stars in the sky. They make up a constellation known as the Big Dipper. Using the table below, determine the degrees based on the measurement above.
| 1 and 4 | 10 |
| 1 and 6 | 20.5 |
| 2 and 5 | 15.5 |
| 1 and 5 | 14.5 |
For Example:
Point 1 and 4 were measured to be 27 mm. Using the table in step 2, pair of stars 1 and 4 are 10 degrees. This means that the angular distance of these two stars in the sky is 10 degrees.
Step 3: Next it is necessary to calculate the image (pictures) scale based on the above information. In order to do so, use the following formula where S = the scale.
For Example:
S = (Degrees) divided by the (measured millimeters)
S = (10 degrees) / (27mm)
S = 0.37
Identify the degrees for each of the other star pairs.
Use the formula to calculate the scale for the other pairs of stars.
Step 4: Use the formula to calculate the scale for the other pairs of stars and complete the following chart. The first one is completed.
| 1 and 4 -- Dubhe-Mehrez | 0.37 |
| 1 and 6 -- Dubhe-Mizar | 0.39 |
| 2 and 5 -- Merak-Alioth | 0.37 |
| 1 and 5 -- Dubhe-Alioth | 0.35 |
STEP 5: In this case, the values do not have a significant difference. However, in order to be more accurate in determining the scale, it is a good idea to average the results. Therefore, average the values in the scale column.
( 0.37+ 0.39 + 0.37 + 0.35 ) / 4 = 0.37 IMAGE SCALE
STEP 6: Next, pick a feature that is in the aurora and measure the distance to the edge of the
aurora in each photo.
For Example:
Select point 4. Measure the horizontal distance to the edge of the photo for this point in each photograph. The edge of the Aurora in photo one is 2 mm away from point 4 and the edge of the Aurora is 22mm away from the edge of the Aurora in photo two. Now subtract the two measurements in order to obtain the Parallax shift. Photo two 22 mm - Photo one 2 mm = 20 mm PARALLAX SHIFT
This value should be typically the same for each point in the photo.
STEP 7: Now that the image scale has been calculated and the Parallax shift is determined, these two values can be multiplied together to obtain the number of degrees in the Parallax angle.
IMAGE SCALE * PARALLAX SHIFT = PARALLAX ANGLE
0.37degrees per mm * 20 mm = 7.4 degrees
STEP 8: when all of the above steps are completed, they can be applied to determine the Auroral height. Station 1 and Station 2 are 17.6 kilometers apart. Using the Parallax angle, P in the diagram below, use properties of vertical angles and the tangent ratio to determine the height, h. (note: the height is perpendicular to the base)
First, divide the Parallax angle in half to determine angle X. 7.4 / 2 = 3.7 degrees Then use the fact that the sum of the angles of a triangle is 180 degrees to find the missing base angle. 180 - 90 - 3.7 = 86.3 degrees Last, apply the tangent ratio to determine the height of the Aurora.
Tan ( 86.3) = (height)/ 8.8 km
Tan (86.3) (8.8 km) = height
136.08km is the height of the aurora.
The height of the Aurora is approximately 136 km to the nearest km.
Useful Web Resources
Exploratorium "Auroras:Paintings in the Sky"
http://www.exploratorium.edu/learning_studio/auroras/
Archive of aurora photos by Jan Curtis:
http://www.geo.mtu.edu/weather/aurora/images/aurora/jan.curtis/
Archive of aurora photos by Dick Hutchinson:
http://www.ptialaska.net/~hutch/aurora.html
Space Weather Today:
http://www.spaceweather.com/
IMAGE real-time aurora images from space:
http://image.gsfc.nasa.gov/poetry/today/intro.html
http://www.sec.noaa.gov/IMAGE/
http://sprg.ssl.berkeley.edu/image/
NOAA Auroral Activity monitor:
http://www.sec.noaa.gov/pmap/index.html
CANOPUS real-time auroral monitor:
http://www.dan.sp-agency.ca/www/rtoval.htm#TOPOFPAGE
Current solar activity report:
http://www.dxlc.com/solar/
Alaska Science Aurora page for kids:
http://www.alaskascience.com/aurora.htm
Human Impacts of Space Weather:
http://image.gsfc.nasa.gov/poetry/weather01.html
Ask the Space Scientist:
http://image.gsfc.nasa.gov/poetry/ask/askmag.html
More classroom activities:
http://image.gsfc.nasa.gov/poetry/activities.html
The Northern Lights Essay Competition:
http://image.gsfc.nasa.gov/poetry/alaska/alaska.html
