Archived Problems
Sorted by Category
Aurorae
A
Matter of Perspective. [PDF] - Grade level: 9-11
Why can't we see aurora at lower latitudes on Earth?
This problem will have students examine the geometry of
perspective, and how the altitude of an aurora or other
object, determines how far away you will be able to see
it before it is below the local horizon.
Solar
Storms in the News [PDF] - Grade level: 6-10
Students will use a newspaper archive
to explore how reporters have described the causes of
aurora since the 1850's. They will see how some
explanations were popular for a time, then faded into
oblivion, as better scientific explanations were
created.
Exploring
Earth's Magnetosphere [DOC] Students will examine a NASA website that
discusses Earth's magnetosphere, and identify the
definitions for key phenomena and parts to this
physical system. They will write a short essay that
describes, in their own words, how aurora are produced
based on what they have read at the NASA
site.
Reading
Between the Lines [PDF] Students
solve simple equations for x, (like 2x + 3 = 5) to
discover which words complete an essay on the causes of
aurora, and answer questions after reading the
completed essay.
The
Auroral Oval [PDF] Students learn
that the aurorae are observed as two 'halos' of light
encircling the North and South Poles. Students use
measurements made from two satellite images of the
'auroral ovals' to determine the diameter of the rings,
and their approximate geographic centers - which are
not at the geographic poles!
How
high is an aurora [PDF] Students
use the properties of a triangle to determine how high
up aurora are. They also learn about the parallax
method for finding distances to remote
objects.
The
Life Cycle of an Aurora [PDF] Students examine two eye-witness descriptions of
an aurora and identify the common elements so that they
can extract a common pattern of changes.
Aurora Power! [PDF] Students use
data to estimate the power of an aurora, and compare it
to common things such as the electrical consumption of
a house, a city and a country.
Solar Flares, CME's and Aurora [PDF] Some articles about the Northern Lights imply that
solar flares cause them. Students will use data to
construct a simple Venn Diagram, and answer an
important question about whether solar flares cause
CME's and Aurora.
The November 8, 2004 solar storm [PDF] Students calculate the speed of a CME, and
describe their aurora observations through writing and
drawing.
Sketching the Northern Lights [PDF] Students read an account of an aurora seen by an
observer, and create a drawing or painting based on the
description.
The Sun
General
STEREO
- An Application of the Parallax Effect [PDF] - Grade
level: 8-10
The STEREO mission views the sun from two different
locations in space. By combining these data, the
parallax effect can be used to determine how far above
the solar surface various active regions are located.
Students use the Pythagorean Theorem, a bit of
geometry, and some actual STEREO data to estimate the
height of Active Region AR-978.
[Skills: Pythagorean Theorem, square-root, solving for
variables]
A
Mathematical Model of the Sun [PDF] - Grade level:
8-10
Students will use the formula for a sphere and a shell
to calculate the mass of the sun for various choices of
its density. The goal is to reproduce the measured mass
and radius of the sun by a careful selection of its
density in a core region and a shell region. Students
will manipulate the values for density and shell size
to achieve the correct total mass. This can be done by
hand, or by programming an Excel spreadsheet.
[Skills: scientific notation, volume of a sphere and a
spherical shell, density, mass, and volume]
The
Heliopause...a question of balance [PDF] - Grade level:
8-10
Students will learn about the concept of pressure
equilibrium by studying a simple mathematical model for
the sun's heliopause located beyond the orbit of Pluto.
They will calculate the distance to the heliopause by
solving for 'R' and then using an Excel spreadsheet to
examine how changes in solar wind density, speed and
interstellar gas density relate to the values for
R.
[Skills: Formulas with two variables, scientific
notation, spreadsheet programming]
How
fast does the sun spin?[PDF] - Grade level: 5-9
Students will use two x-ray images of
the sun taken by the Hinode satellite to determine how
fast the sun rotates.
[Skills:calculating map scales, time calculations,
unit conversion]
How
fast does the sun rotate?[PDF] - Grade level: 6-9
Students will analyze consecutive
images taken by the Hinode satellite to determine the
sun's speed of rotation, and the approximate length of
its 'day'.
[Skills: image scales, time
calculations, speed calculations, unit
conversions]
The
Hinode Satellite Views the Sun [PDF] - Grade level:
6-8 Students will use a full-sun
image from the new Hinode satellite to sketch the
locations of magnetic fields on the sun's surface using
information in the introductory article as a guide.
[Skills:image interpretation, eye-hand
coordination, reading to be informed]
Monster
Functions in Space Science I. [PDF] - Grade level:
9-11 This problem has students
employ a pair of complicated algebraic equations to
evaluate the strength of the sun's magnetic field near
Earth's orbit. The equations are a model of the sun's
magnetic field in space based on actual research by a
solar physicist. This introduces students to a
real-world application of mathematical modeling, and
extracting predictions from theoretical models that can
be tested. Students are provided the values for the
relevant variables, and through substitution, calculate
the numerical values for two 'vector' components of the
sun's magnetic field near Earth's orbit.
[Skills: decimals, scientific
notation, significant figures]
Sunspots
Monster
Sunspots![PDF] - Grade level: 5-9 Some sunspots are so big that they can be seen
from Earth without a telescope. In this problem,
students will use images of three super-spots and
calculate their sizes from the image scaling
information. They will then order the images from the
smallest super-spot to the largest super-spot.
[Skills:multiplication, calculating
length from image scale]
Loopy
Sunspots![PDF] - Grade level: 9-11 Students will analyze data from the Hinode
satellite to determine the volume and mass of a
magnetic loop above a sunspot. From the calculated
volume, based on the formula for the volume of a
cylinder, they will use the density of the plasma
determined by the Hinode satellite to determine the
mass in tons of the magnetically trapped material.
[Skills:image scales, cylinder volume
calculation, scientific notation, unit
conversions]
The
Sunspot CYcle - endings and beginnings [PDF] - Grade
level: 6-9 Students will examine a
plot of the sunspot cycle and extract information from
the plotted data about the previous sunspot cycle, and
make predictions about the next one about to start in
2007.
[Skills:graph reading,
extrapolation, time calculations]
Hinode
- Closeup of a Sunspot [PDF] - Grade level: 9-11
Students will determine the sizes of
sunspots and solar granulation cells from a recent
image taken by the Hinode solar observatory.
[Skills:image scales, metric units,
unit conversion]
Moving
Magnetic Filaments Near Sunspots[PDF] - Grade level:
9-11 Students will use two images
from the new, Hinode (Solar-B) solar observatory to
calculate the speed of magnetic filaments near a
sunspot. The images show the locations of magnetic
features at two different times. Students calculate the
image scales in kilometers/mm and determine the time
difference to estimate the speeds of the selected
features.
[Skills: scaling,
estimation, speed calculations, time arithmetic
]
Sunspots
Close-up and Personal [PDF] - Grade level: 9-11
Students will analyze a picture of a
sunspot to learn more about its size, and examine the
sizes of various other features on the surface of the
sun that astronomers study.
Solar
Activity and Tree Rings - What's the connection? [PDF]
- Grade level: 9-11 Trees require
sunlight to grow, and we know that solar activity
varies with the sunspot cycle. Can an average tree
sense solar activity cycles and change the way it grows
from year to year? This activity uses a single tree to
compare its growth rings to the sunspot cycle. This is
also an interesting suggestion for science fair
projects! Here is the accompanying Excel
Spreadsheet Data File.
Super-sized
Sunspots and the Solar Cycle. [PDF] Students compare the dates of the largest sunspots
since 1900 with the year of the peak sunspot cycle.
They check to see if superspots are more common after
sunspot maximum or before. They also compare superspot
sizes with the area of earth.
Solar
Flares and Sunspot Sizes [PDF] Students compare sunspot sizes to the frequency of
solar flares and discover that there is no hard and
fast rule that relates sunspot size to its ability to
produce very large flares.
Observing the Sun's rotation [PDF] Students use a Sunspotter to track sunspots during
the week of November 7, 2004, and calculate the
rotation period of the sun.
Solar Storms
CME
Kinetic Energy and Mass [PDF] - Grade level: 8-10
Coronal Mass Ejections (CMEs) are
giant clouds of plasma released by the sun at millions
of kilometers per hour. In this activity, students
calculate the kinetic energy and mass of several CMEs
to determine typical mass ranges and speeds. Students
will use the formula for kinetic energy to fill-in the
missing entries in a table. They will then use the
completed table to answer some basic questions about
CMEs.
[Skills: time
calculation, Evaluating a simple equation, solving for
variables]
Hinode
Sees Mysterious Solar Micro-Flares![PDF] - Grade level:
6-9 Students will analyze an image
taken by the Hinode solar satellite to determine the
scale of the image in kilometers per millimeter, then
use this to determine the sizes of solar micro-flares.
From the number of micro-flares that they count in the
image, the area of the image in square kilometers, and
the surface area of a spherical sun, they will
calculate the total number of micro-flares on the solar
surface.
[Skills:image scales, area
calculation, unit conversions]
Super-Fast
Solar Flares!![PDF] - Grade level: 6-9 Students will analyze consecutive images taken of
an erupting solar flare, and use the information
provided to calculate the speed of the flare.
[Skills:image scales, time
calculations, speed calculations]
Solar
Flare Reconstruction [PDF] - Grade level: 9-11
Students will use data from a solar
flare to reconstruct its maximum emission using
graphical estimation (pre-algebra), power-law function
fitting (Algebra 2), and will determine the area under
the profile (Calculus).
[Skills:plotting tabular date, fitting functions,
integration]
Solar
Storms: Odds, Fractions and Percentages [PDF] - Grade
level: 9-11 Students will use
actual data on solar storms to learn about the
different kinds of storms and how common they are. This
is a basic science activity that professionals do in
order to look for relationships between different kinds
of events that might lead to clues about what causes
them. Can your students come up with something new that
noone has thought about before? The Venn Diagramming
activity is a key element of the activity and is
reasonably challenging!
[Skills:
Averaging, fractions, percentages, odds, Arithmetic
Operations, Venn Diagrams]
Do
Fast CMEs Produce SPEs? [PDF] - Grade level: 9-11
Recent data on solar proton storms
(SPEs) and coronal mass ejections (CMEs) are compared
using Venn Diagrams to see if the speed of a CME makes
solar proton storms more likely or not.
[Skills: Venn Diagrams, counting, calculating
percentages and odds]
The
Solar Tsunami! [PDF] - Grade level: 9-11
Recent data from the Hinode satellite
is used to measure the speed of a solar explosion on
the surface of the sun using a series of images taken
by the satellite at three different times. Students
calculate the speed of the blast between the first pair
and last pair of images, and determine if the blast
wave was accelerating or decellerating in time.
[Skills: Finding image scale,
calculating time differences, calculating speed from
distance and time]
The
Pressure of a Solar Storm[PDF] - Grade level: 9-11
Students will examine three
mathematical models for determining how much pressure a
solar storm produces as it affects Earth's magnetic
field. They will learn that magnetism produces
pressure, and that this accounts for many of the
details seen in solar storms.
[Skills:
Substituting numbers into equations, filling out
missing table entries, data interpretation,
mathematical models ]
Data
Corruption by High Energy Particles[PDF] - Grade level:
9-11 Students will see how solar
flares can corrupt satellite data, and create a
timeline for a spectacular episode of data loss
recorded by the SOHO satellite using images obtained by
the satellite. Students will also calculate the speed
of the event as particles are ejected from the sun and
streak towards earth.
[Skills: Time
and speed calculations, interpreting scientific data
]
Parametric
Functions and Substitution [PDF] - Grade level:
9-11 The relationship between the
strength of a solar storm and the resulting magnetic
disturbance on Earth is given as a series of equations.
Students are asked to create new formulae based on
these parametric equations using the method of
substitution.
[Skills:
Algebraic manipulation, integer exponents, scientific
notation, significant figures and rounding ]
Solar
Activity and Satellite Mathematics [PDF] - Grade level:
9-11 When solar storms cause
satellite problems, they can also cause satellites to
lose money. The biggest source of revenue from
communications satellites comes from transponders that
relay television programs, ATM transactions and many
other vital forms of information. They are rented to
many different customers and can cost nearly $2 million
a year for each transponder. This activity examines
what happens to a single satellite when space weather
turns bad!
An
Interplanetary Shock Wave [PDF] - Grade level: 6-10
On November 8, 2000 the sun released a
coronal mass ejection that traveled to Earth, and its
effects were detected on Jupiter and Saturn several
weeks later. In this problem, students will use data
from this storm to track its speed and acceleration as
it traveled across the solar system.
Solar
Storm Timeline [PDF] Grade level: 7-9 How long does a solar storm last? How fast does it
travel? Students will examine an event timeline for a
space weather event and use time addition and
subtraction skills to calculate storm durations and
speeds.
Airline
Travel and Space Weather [PDF] Students will read an excerpt from the space
weather book 'The 23rd Cycle' by Dr. Sten Odenwald, and
answer questions about airline travel during solar
storms. They will learn about the natural background
radiation they are exposed to every day, and compare
this to radiation dosages during jet
travel.
The Moon
A
Lunar Transit of the Sun from Space [PDF] - Grade
level: 9-11 One of the STEREO
satellites observed the disk of the moon pass across
the sun. Students will use simple geometry to determine
how far the satellite was from the moon and Earth at
the time the photograph was taken.
[Skills: Geometry, parallax,
arithmetic]
Lunar
Meteorite Impact Risks [PDF] - Grade level: 9-12
In 2006, scientists identified 12
flashes of light on the moon that were probably
meteorite impacts. They estimated that these meteorites
were probably about the size of a grapefruit. How long
would lunar colonists have to wait before seeing such a
flash within their horizon? Students will use an area
and probability calculation to discover the average
waiting time.
[Skills: arithmetic,
unit conversions, surface area of a sphere)
]
Magnetism, Energy, and
Matter
Using
the TV Program CSI to Explore Matter [PDF]
Students will read about how a mass
spectrometer works - the kind used in the TV Series
CSI, and learn how to interpret a simple spectrum to
find out which elements are present in a mystery
sample.
Magnetic
Forces and Kinetic Energy [PDF] Students use the formula for the Kinetic Energy of
a charged particle to calculate particle speeds for
different voltages, and answer simple questions about
lightning, aurora and Earth's radiation
belts.
Kinetic
Energy and Particle Motion [PDF] Students learn about kinetic energy and how this
concept applies to charged particles. They calculate
the speed of a particle for various particle
energies.
Magnetic
Energy From B to V [PDF] Students
will use formulas for the volume of a sphere and
cylinder, and magnetic energy, to calculate the total
magnetic energy of two important 'batteries' for space
weather phenomena- solar prominences and the Earth's
magnetotail. This requires scientific notation, a
calculator, and experience with algebraic equations
with integer powers of 2 and 3.
The
Distance to Earth's Magnetopause [PDF] Students use an algebraic formula and some real
data, to calculate the distance from Earth to the
magnetopause, where solar wind and magnetosphere
pressure are in balance.
An
Application of the Pythagorean Theorem [PDF]
Students learn that the Pythagorean
Theorem is more than a geometric concept. Scientists
use it all the time when calculating lengths, speeds or
other quantities. This problem is an introduction to
magnetism, which is a '3-dimensional vector', and how
to calculate magnetic strengths using the Pythagorean
Theorem.
Magnetic
Forces and Particle Motion [PDF] Students learn about the spiral-shaped
trajectories of charged particles moving in magnetic
fields, and calculate some basic properties of this
'cyclotron' motion.
Magnetic Storms II [PDF] Students
learn about the Kp index using a bar graph. They use
the graph to answer simple questions about maxima and
time.
Magnetic Storms I [PDF] Students
learn about magnetic storms using real data in the form
of a line graph. They answer simple questions about
data range, maximum, and minimum.
The
Wandering Magnetic North Pole [PDF] Mapmakers have known for centuries that Earth's
magnetic North Pole does not stay put. This activity
will have students read a map and calculate the speed
of the 'polar wander' from 300 AD to 2000 AD. They will
use the map scale and a string to measure the distance
traveled by the pole in a set period of time and
calculate the wander speed in km/year. They will answer
questions about this changing speed.
The
Ring Current [PDF] Students use
the formula for a disk to calculate the mass of the
ring current surrounding Earth.
Plasma and the
Plasmasphere
Exploring
the Plasmasphere [PDF] Students
use an image of the plasmasphere obtained by the IMAGE
satellite to calculate how fast it orbits the Earth.
They will use this to determine whether gravity or
Earth's magnetic field provides the forces responsible
for its movement through space.
Exploring
the Plasmasphere [PDF] Students
learn that the Pythagorean Theorem is more than a
geometric concept. Scientists use a photograph taken by
the IMAGE satellite to measure the size of Earth's
plasmasphere region using a ruler and
protractor.
Radio
Plasma Imaging with IMAGE [PDF] Students use the Distance = Velocity x Time
relationship to determine the distances to plasma
clouds seen by the IMAGE satellite.
Plasma
Clouds [PDF] Students use a simple
'square-root' relationship to learn how scientists with
the IMAGE satellite measure the density of clouds of
plasma in space.
Satellites
NASA
Juggles Four Satellites at Once![PDF] - Grade level:
8-10 Students will learn about
NASA's Magnetospheric Multi-Scale (MMS) satellite
mission, and how it will use four satellites flying in
formation to investigate the mysterious process called
Magnetic Reconnection that causes changes in Earth's
magnetic field. These changes lead to the production of
the Northern and Southern Lights and other phenomena.
From the volume formula for a tetrahedron, they will
calculate the volume of several satellite
configurations and estimate the magnetic energy and
travel times for the particles being studied by MMS.
[Skills: Formulas with two variables,
scientific notation]
A
Problem in Satellite Synchrony[PDF] - Grade level:
5-9 The THEMIS program uses five
satellites in five different orbits to study Earth's
magnetic field and its changes during a storm. This
problem asks students to use the periods of the five
satellites to figure out when all 5 satellites will be
lined-up as seen from Earth. They will do this by
finding the Greatest Common Multiple of the five orbit
periods, first for the case of 2 or 3 satellites, which
can be easily diagrammed with concentric circles, then
the case for all five satellites together.
[Skills:multiplication, Greatest Common
Multiple]
Solar
Eclipses and Satellite Power [PDF] From the ground we see total solar eclipses where
the New Moon passes directly between Earth and Sun.
Satellites use solar cells to generate electricity, but
this is only possible when the Earth is not 'eclipsing'
the sun. Students will create a scaled drawing of the
orbits of three satellites around Earth, and calculate
how long each satellite will be in the shadow of Earth.
They will be asked to figure out how to keep the
satellites operating even without sunlight to power
their solar panels.
Solar
Proton Events and Satellite Damage [DOC]
Students will examine the statistics
for Solar Proton Events since 1996 and estimate their
damage to satellite solar power systems.
Satellite
Power and Cosmic Rays [PDF] Most
satellites operate by using solar cells to generate
electricity. But after years in orbit, these solar
cells produce less electricity because of the steady
impact of cosmic rays. In this activity, students read
a graph that shows the electricity produced by a
satellite's solar panels, and learn a valuable lesson
about how to design satellites for long-term operation
in space. Basic math ideas: Area calculation, unit
conversions, extrapolation and interpolation of graph
trends.
Satellite
Failures and the Sunspot Cycle [PDF] There are over 1500 working satellites orbiting
Earth, representing an investment of 160 billion
dollars. Every year, between 10 and 30 of these
re-enter the atmosphere. In this problem, students
compare the sunspot cycle with the record of satellites
re-entering the atmosphere and determine if there is a
correlation. They also investigate how pervasive
satellite technology has become in their daily
lives.
Solar
Power and Satellite Design [PDF] Students perform simple surface area calculations
to determine how much solar power a satellite can
generate, compared to the satellite's needs.
Satellite Surface Area [PDF] Students calculate the surface area of an
octagonal cylinder and calculate the power it would
yield from solar cells covering its surface.
The
Space Station Orbit Decay and Space Weather [PDF]
Students will learn about the
continued decay of the orbit of the International Space
Station by studying a graph of the Station's altitude
versus time. They will calculate the orbit decay rates,
and investigate why this might be happening.
Hinode
Satellite Power [PDF] - Grade level: 9-11
Students will study the design of the
Hinode solar satellite and calculate how much power it
can generate from its solar panels.
[Skills:area of rectangle,area of cylinder, unit
conversion]
Systems
of Equations in Space Science [PDF] - Grade level:
9-11 This problem has students
solve two problems involving three equations in three
unknowns to learn about solar flares, and communication
satellite operating power.
[Skills: decimals, solving systems of equations,
matrix math, algebraic substitution]
Solar
Energy in Space [PDF] Grade level: 7-10
Students will calculate the area of a
satellite's surface being used for solar cells from an
actual photo of the IMAGE satellite. They will
calculate the electrical power provided by this one
panel. Students will have to calculate the area of an
irregular region using nested
rectangles.
Radiation
General
Unit
Conversion Exercises [PDF] - Grade level: 9-11
Radiation dosages and exposure
calculations allow students to compare several
different ways that scientists use to compare how
radiation exposure is delivered and accumulated over
time.Like converting 'centimeters per sec' to
'kilometers per year' ,this activity reinforces student
skills in converting from one set of units to
another.
[Skills: fractions,
decimals, units]
An
Introduction to Space Radiation [PDF] - Grade level:
9-11 Read about your natural
background radiation dosages, learn about Rems and
Rads, and the difference between low-level dosages and
high-level dosages. Students use basic math operations
to calculate total dosages from dosage rates, and
calculating cancer risks.
[Skills: Reading to be Informed, decimals,
fractions, square-roots]
Some
Puzzling Thoughts about Radiation![PDF] - Grade level:
9-11 Students fill-in the blanks
in an essay on radiation risks using a word bank tied
to solving quadratic equations to find the right words
from a pair of possible 'solutions'.
[Skills: Finding the roots of a quadratic
equation, solving for X ]
Correcting
Bad Data Using Partity Bits[PDF] - Grade level:
9-11 Students will see how
computer data is protected from damage by radiation
'glitches' using a simple error-detection method
involving the parity bit. They will reconstruct an
uncorrupted sequence of data by checking the '8th bit'
to see if the transmitted data word has been corrupted.
By comparing copies of the data sent at different
times, they will reconstruct the uncorrupted data.
[Skills: addition, subtraction,
comparing the numbers 1 and 0 ]
Astronauts
A
Study on Astronaut Radiation Dosages in Space [PDF] -
Grade level: 9-11 Students will
examine a graph of the astronaut radiation dosages for
Space Shuttle flights, and estimate the total dosages
for astronauts working on the International Space
Station.
[Skills:Graph analysis,
interpolation, unit conversion]
Are
the Van Allen Belts Really Deadly? [PDF] - Grade level:
9-11 This problem explores the
radiation dosages that astronauts would receive as they
travel through the van Allen Belts enroute to the Moon.
Students will use data to calculate the duration of the
trip through the belts, and the total received dosage,
and compare this to a lethal dosage to confront a
misconception that Apollo astronauts would have
instantly died on their trip to the Moon.
[Skills: decimals, area of rectangle,
graph analysis]
Earth
Radon
Gas in the Basement [PDF] - Grade level: 9-11
This problem introduces students to a
common radiation problem in our homes. From a map of
the United States provided by the US EPA, students
convert radon gas risks into annual dosages.
[Skills: Unit conversion, arithmetic
operations]
Single
Event Upsets in Aircraft Avionics[PDF] - Grade level:
9-11 Radiation is problem for
high-altitude commercial and research aircraft. Showers
of high-energy neutrons cause glitches in computer
electronics and other aircraft systems. This problem
investigates the neutron background radiation at 30,000
to 100,000 feet based on actual flight data, and has
students calculate how many computer memory glitches
will happen over a set amount of flight time.
[Skills: decimals, unit conversions,
graph analysis]
Background
Radiation and Lifestyles [PDF] - Grade level: 9-11
Living on Earth, you will be subjected
to many different radiation environments. This problem
follows one person through four different possible
futures, and compares the cumulative lifetime
dosages.
[Skills: fractions,
decimals, unit conversions]
A
Perspective on Radiation Dosages [PDF] - Grade level:
9-11 Depending on the kind of
career you chose, you will experience different
lifetime radiation dosages. This problem compares the
cumulative dosages for someone living on Earth, an
astronaut career involving travel to the Space Station,
and the lifetime dosage of someone traveling to Mars
and back.
[Skills: decimals,
unit conversions, graphing a timeline, finding areas
under curves using rectangles]
Mars
A
Hot Time on Mars [PDF] - Grade level: 9-11
The NASA Mars Radiation Environment
(MARIE) experiment has created a map of the surface of
mars, and measured the ground-level radiation
background that astronauts would be exposed to. This
math problem lets students examine the total radiation
dosage that these explorers would receive on a series
of 1000 km journeys across the martian surface. The
students will compare this dosage to typical background
conditions on earth and in the International Space
Station to get a sense of perspective
[Skills: decimals, unit conversion,
graphing and analysis ]
Calculating
Total Radiation Dosages at Mars [PDF] - Grade level:
9-11 This problem uses data from
the Mars Radiation Environment Experiment (MARIE) which
is orbiting Mars, and measures the daily radiation
dosage that an astronaut would experience in orbit
around Mars. Students will use actual plotted data to
calculate the total dosage by adding up the areas under
the data curve. This requires knowledge of the area of
a rectangle, and an appreciation of the fact that the
product of a rate (rems per day) times the time
duration (days) gives a total dose (Rems), much like
the product of speed times time gives distance. Both
represent the areas under their appropriate curves.
Students will calculate the dosages for cosmic
radiation and solar proton flares, and decide which
component produces the most severe radiation
problem.
[Skills: decimals,
area of rectangle, graph analysis]
Shielding
An
Introduction to Radiation Shielding [PDF] - Grade
level: 9-11 Students calculate how
much shielding a new satellite needs to replace the ISO
research satellite. Students use a graph of the wall
thickness versus dosage, and determine how thick the
walls of a hollow cubical satellite have to be to
reduce the radiation exposure of its electronics.
Students calculate the mass of the satellite and the
cost savings by using different shielding.
[Skills: Algebra, Volume of a hollow cube, unit
conversion]
Atmospheric Shielding from Radiation- III [PDF] - Grade
level: 9-11 This is Part III of a
3-part problem on atmospheric shielding. Students use
exponential functions to model the density of a
planetary atmosphere, then evaluate a definite integral
to calculate the total radiation shielding in the
zenith (straight overhead) direction for Earth and
Mars.
[Skills: Evaluating an integral,
working with exponential functions]
Atmospheric
Shielding from Radiation- II [PDF] - Grade level:
9-11 This is the second of a
three-part problem dealing with atmospheric shielding.
Students use the formula they derived in Part I, to
calculate the radiation dosage for radiation arriving
from straight overhead, and from the horizon. Students
also calculate the 'zenith' shielding from the surface
of Mars.
[Skills: Algebra I,
evaluating a function for specific
values]
Atmospheric
Shielding from Radiation- I [PDF] - Grade level:
9-11 This is the first part of a
three-part problem series that has students calculate
how much radiation shielding Earth's atmosphere
provides. In this problem, students have to use the
relevant geometry in the diagram to determine the
algebraic formula for the path length through the
atmosphere from a given location and altitude above
Earth's surface.
[Skills: Algebra II,
trigonometry]
The Solar System
The
Comet Encke Tail Disruption Event [PDF] - Grade level:
8-10 On April 20, 2007 NASA's
STEREO satellite captured a rare impact between a comet
and the fast-moving gas in a solar coronal mass
ejection. In this problem, students analyze a STEREO
satellite image to determine the speed of the tail
disruption event.
[Skills: time
calculation, finding image scale, calculating speed
from distance and time]
The
Transit of Mercury[PDF] - Grade level: 9-11
As seen from Earth, the planet Mercury
occasionally passes across the face of the sun, an
event that astronomers call a transit. From images
taken by the Hinode satellite, students will create a
model of the solar disk to the same scale as the image,
and calculate the distance to the sun.
[Skills:image scales, angular measure, degrees,
minutes and seconds]
When
is a planet not a planet? [PDF] - Grade level: 9-11
In 2003, Dr. Michael Brown and his
colleagues at CalTech discovered an object nearly 30%
larger than Pluto, which is designated as 2003UB313. It
is also known unofficially as Xenia, after the famous
Tv Warrior Princess! Is 2003UB313 really a planet? In
this activity, students will examine this topic by
surveying various internet resources that attempt to
define the astronomical term 'planet'. How do
astronomers actually assign names to astronomical
objects? Does 2003UB313 deserve to be called a planet,
or should it be classified as something else? What
would the new classification mean for asteroids such as
Ceres, or objects such as Sedna, Quaoar and
Varuna?
Getting
A Round in the Solar System! [PDF] - Grade level:
9-11 How big does a body have to
be before it becomes round? In this activity, students
examine images of asteroids and planetary moons to
determine the critical size for an object to become
round under the action of its own gravitational field.
Thanks to many Internet image archives this activity
can be expanded to include dozens of small bodies in
the solar system to enlarge the research data for this
problem. Only a few example images are provided, but
these are enough for the student to get a rough
answer!
Asteroids
and comets and meteors - Oh My! [PDF] - Grade level:
9-11 Astronomers have determined
the orbits for over 30,000 minor planets in the solar
system, with hundreds of new ones discovered every
year. Working from a map of the locations of these
bodies within the orbit of Mars, students will
calculate the scale of the map, and answer questions
about the distances between these objects, and the
number that cross earth's orbit. A great, hands-on
introduction to asteroids in the inner solar system!
Links to online data bases for further inquiry are also
provided.
Beyond
the Blue Horizon [PDF] - Grade level: 9-11
How far is it to the horizon? Students
use geometry, and the Pythagorean Theorem, to determine
the formula for the distance to the horizon on any
planet with a radius, R, from a height, h, above its
surface. Additional problems added that involve
calculus to determine the rate-of-change of the horizon
distance as you change your height. [Skills: Algebra, Pythagorean Theorem, Experts:
DIfferential calculus) ]
Making a Model Planet [PDF] Students use the formula for a sphere, and the
concept of density, to make a mathematical model of a
planet based on its mass, radius and the density of
several possible materials (ice, silicate rock, iron,
basalt).
Galaxies
The
Sombrero Galaxy Close-up [PDF] - Grade level: 9-11
The Sombrero Galaxy in Virgo is a
dazzling galaxy through the telescope, and has been
observed in detail by both the Hubble Space Telescope
and the Spitzer Infrared Observatory. This exercise
lets students explore the dimensions of this galaxy as
well as its finest details, using simple image scaling
calculations.
Exploring
Distant Galaxies [PDF] - Grade level: 9-11
Astronomers determine the redshifts of
distant galaxies by using spectra and measuring the
wavelength shifts for familiar atomic lines. The larger
the redshift, denoted by the letter Z, the more distant
the galaxy. In this activity, students will use an
actual image of a distant corner of the universe, with
the redshifts of galaxies identified. After
histogramming the redshift distribution, they will use
an on-line cosmology calculator to determine the
'look-back' times for the galaxies and find the one
that is the most ancient galaxy in the field. Can
students find a galaxy formed only 500 million years
after the Big Bang?
Measuring
the Speed of a Galaxy. [PDF] - Grade level: 9-11
Astronomers can measure the speed of a
galaxy by using the Doppler Shift. By studying the
spectrum of the light from a distant galaxy, the shift
in the wavelength of certain spectral lines from
elements such as hydrogen, can be decoded to give the
speed of the galaxy either towards the Milky Way or
away from it. In this activity, students will use the
formula for the Doppler Shift to analyze the spectrum
of the Seyfert galaxy Q2125-431 and determine its
speed.
A
Spiral Galaxy Up Close. [PDF] - Grade level: 9-11
Astronomers can learn a lot from
studying photographs of galaxies. In this activity,
students will compute the image scale (light years per
millimeter) in a photograph of a nearby spiral galaxy,
and explore the sizes of the features found in the
image. They will also use the internet or other
resources to fill-in the missing background information
about this galaxy.
Stars
Star
light...Star bright - A question of magnitude! [PDF] -
Grade level: 9-11 Since the time
of the ancient Greek astronomer Hipparchus, astronomers
have measured and cataloged the brightness of stars
according to the 'apparent magnitude scale'. This
activity lets students experience this peculiar
numbering system where bright stars have small numbers
(even negative: our sun is a -26 magnitude!) and faint
stars have large numbers (faintest stars are +29
magnitudes). Students will calculate the brightness
differences between stars using multiplication and
division. Working with the number line will be a big
help and math review!
How
many stars are there? [PDF] - Grade level: 9-11
For thousands of years, astronomers
have counted the stars to determine just how vast the
heavens are. Since the 19th century, 'star gauging' has
been an important tool for astronomers to assess how
the various populations of stars are distributed within
the Milky Way. In fact, this was such an important
aspect of astronomy between 1800-1920 that many
cartoons often show a frazzled astronomer looking
through a telescope, with a long ledger at his knee -
literally counting the stars through the eyepiece! In
this activity, students will get their first taste of
star counting by using a star atlas reproduction and
bar-graph the numbers of stars in each magnitude
interval. They will then calculate the number of
similar stars in the sky by scaling up their counts to
the full sky area.
Measuring
the size of a Star Cluster[PDF] - Grade level: 9-11
Astronomers often use a photograph to
determine the size of astronomical objects. The
Pleiades is a famous cluster of hundreds of bright
stars. In this activity, students will determine the
photographic scale, and use this to estimate the
projected (2-D) distances between the stars in this
cluster. They will also use internet and library
resources to learn more about this cluster.
Discovering
the Milky Way by Counting Stars. [PDF] - Grade level:
9-11 It is common to say that
there are about 8,000 stars visible to the naked eye in
both hemispheres of the sky, although from a typical
urban setting, fewer than 500 stars are actually
visible. Students will use data from a deep-integration
image of a region of the sky in Hercules, observed by
the 2MASS sky survey project to estimate the number of
stars in the sky. This number is a lower-limit to the
roughly 250 to 500 billion stars that may actually
exist in the Milky Way.
Interstellar
Distances with the Pythagorean Theorem [PDF] - Grade
level: 9-11 If you select any two
stars in the sky and calculate how far apart they are,
you may discover that even stars that appear to be far
apart are actually close neighbors in space. This
activity lets students use the Pythagorean distance
formula in 3-dimensions to explore stellar distances
for a collection of bright stars, first as seen from
Earth and then as seen from a planet orbiting the star
Polaris. Requires a calculator and some familiarity
with algebra and square-roots.
Why
do stars rise in the East? [PDF] Grade level 9-10
Students will follow a step-by-step
geometric construction procedure to create a figure,
and then use basic Euclidean postulates to prove that,
because Earth rotates from west to east, stars must
rise in the east and set in the west, and that the
angle turned by the Earth equals the amount of apparent
sky position change by a fixed star in the
sky.
Work and Economy in Space
Science
Compound
Interest [PDF] - Grade level: 9-11 Students use the 'compound interest' formula to
examine rates of growth for space mission costs, and
the salaries of astronomers, with allowance for
inflation.
[Skills: Algebra
II]
A
Career in Astronomy [PDF] - Grade level: 9-11
This problem looks at some of the
statistics of working in a field like astronomy.
Students will read graphs and answer questions about
the number of astronomers in this job area, and the
rate of increase in the population size and number of
advanced degrees.
[Skills: graph
reading, percentages,
interpolation]
Other Teasers
STEREO-An
Application of the Parallax Effect[PDF] - Grade level:
8-10 The STEREO mission views the
sun from two different locations in space. By combining
this data, the parallax effect can be used to determine
how far above the solar surface various active regions
are located. Students use the Pythagorean Theorem, a
bit of geometry, and some actual STEREO data to
estimate the height of Active Region AR-978.
[Skills:Pythagorean Theorem,
square-root, solving for variables]
Scientific
Notation II[PDF] - Grade level: 5-9 In this continuation of the review of Scientific
Notation, students will perform simple addition and
subtraction problems.
[Skills:Scientific notation - addition and
subtraction]
Scientific
Notation I[PDF] - Grade level: 5-9 Scientists use scientific notation to represent
very big and very small numbers. In this exercise,
students will convert some 'astronomical' numbers into
SN form.
[Skills:Scientific notation -
conversion from decimal to SN]
Oscillating
Spheres[PDF] - Grade level: 9-11 Many astronomical bodies have a natural period of
oscillation. In this problem, students will use a
simple mathematical model to calculate the period of
oscillation of a star, a planet, and a neutron star
from the estimated densities of these bodies.
[Skills:Algebra, calculating with a
formula]
Are
U nuts? [PDF] - Grade level: 9-11 Students will use a number of obscure English
units measures to convert from metric to English units
and back, and answer some unusual questions!
[Skills: arithmetic, unit conversions
involving 1 to 5 steps) ]
Drake's
Equation and the Search for Life...sort of! [PDF] -
Grade level: 9-11 Way back in the
1960's Astronomer Frank Drake invented an equation that
helps us estimate how much life, especially the
intelligent kind, might exist in our Milky Way. It has
been a lively topic of discussion in thousands of
college astronomy courses for the last 30 years. In
this simplified version, your students will get to
review what we now know about the planetary universe,
and come up with their own estimates. The real fun is
in doing the research to track down plausible values
(or their ranges) for the factors that enter into the
equation, and then write a defense for the values that
they choose. Lots of opportunity to summarize basic
astronomical knowledge towards the end of an astronomy
course, or chapter.
Essays
by Starlight [PDF] - Grade level: 9-11 Being an astronomer is far more than just knowing
facts and measurements. Sometimes you can learn
important things about the universe by listening to
your own feelings. Song lyrics are often a great
stimulus for thinking about space in a different way.
Students will select three song lyric fragments from
popular Rock songs and write a short essay for each of
them. The challenge is to explain what the songs make
you think of, from both a human and an astronomical
point of view!
Astronomy:
A Moving Experience! [PDF] - Grade level: 9-11
Objects in space move. To figure out
how fast they move, astronomers use many different
techniques depending on what they are investigating. In
this activity, you will measure the speed of
astronomical phenomena using the scaling clues and the
time intervals between photographs of three phenomena:
A supernova explosion, a coronal mass ejection, and a
solar flare shock wave.
Scientific
Notation - An Astronomical Perspective. [PDF] - Grade
level: 9-11 Astronomers use
scientific notation because the numbers they work with
are usually.. astronomical in size. This collection of
problems will have students reviewing how to perform
multiplication and division with large and small
numbers, while learning about some interesting
astronomical applications. They will learn about the
planet Osiris, how long it takes to download all of
NASA's data archive, the time lag for radio signals to
Pluto, and many more real-world
applications.
Theories,
Facts, Beliefs...Oh My! [PDF] - Grade level: 9-11
It is very common to confuse the
definitions for Theory, Hypothesis, Fact, Law and
Belief. This causes all sorts of problems when
scientists and non-scientists speak to each other, or
when reporters try to explain the latest discoveries.
This activity presents 36 statements which the student
is to evaluate as either a theory, law, fact,
hypothesis or belief. Be prepared for some lively
discussions!!
Time
Zone Mathematics [PDF] Students
will learn about the time zones around the world, and
why it is important to keep track of where you are when
you see an astronomical phenomenon. A series of simple
time calculations teaches students about converting
from one time zone to another.
A
Space Science Crossword Puzzle [PDF] Students work with positive and negative numbers
to solve a crossword puzzle. The theme is 'Scientists
use math to explore Nature'. Good exercise for
pre-algebra review of adding and subtracting positive
and negative numbers.
|
