Archived Problems
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Black Holes - VI [PDF] - Grade level: 7-10
Tidal forces are an important gravity phenomenon, but they can be lethal to humans in the vicinity of black holes. This exercise lets students calculate the tidal acceleration between your head and feet while standing on the surface of Earth...and falling into a black hole.
[Skills: scientific notation, working with equations in one variable to first and second power]
Black Holes - V - Chandra/XMM [PDF] - Grade level: 7-10
Students explore how Kepler's Third Law can be used to determine the mass of a black hole, or the mass of the North Star: Polaris.
[Skills: scientific notation, working with equations in one variable to first and second power]
Black Holes - IV - Chandra/XMM [PDF] - Grade level: 7-10
Students explore how much energy is generated by stars and gas falling into black holes. The event horizon radius is calculated from a simple equation, R = 2.83 M, and energy is estimated from E = mc^2.
[Skills: scientific notation, working with equations in one variable to first and second power]
Black Holes - III [PDF] - Grade level: 8-12
Students learn about how gravity distorts time near a black hole and other massive bodies.
[Skills: Simple linear equations, scientific notation]
Black Holes - II [PDF] - Grade level: 8-12
Students learn about how gravity distorts time and causes problems even for the Global Positioning System satellites and their timing signals.
[Skills: Simple linear equations, scientific notation]
Black Holes [PDF] - Grade level: 8-12
Students learn about the most basic component to a black hole - the event horizon. Using a simple formula, and scientific notation, they examine the sizes of various kinds of black holes.
[Skills: Simple linear equations, scientific notation]
GALEX - A Star Sheds a Comet Tail! [PDF] - Grade level: 8-10
The GALEX satellite captured a spectacular
image of the star
Mira shedding a tail of gas and dust nearly 13 light years
long. Students use the GALEX image to determine the speed
of the star, and to translate the tail structures into a
timeline extending to 30,000 years ago.
[Skills: Image Scaling, Unit Conversion, Calculating Speed from Distance and Time]
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.
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