
Monster of the Milky Way


Classroom Activity

Activity Summary
In Part I, students use a balloon and aluminum foil ball model to explore
changes in density vs. volume as a massive star evolves into a black hole. In
Part II, students turn to calculations to discover the implications of
increasing density with decreasing size.
Learning Objectives
Students will be able to:
 glass of water
 piece of wood
 aluminum pellet
 iron rod
 piece of gold jewelry
 overhead transparency
 set of differentcolored transparency pens
 copy of the "Dense, Denser, Densest?" student handout
(PDF or
HTML)
 copy of the "Getting Really Dense" student handout
(PDF or
HTML)
 50cmlong piece of aluminum foil (by standard 30.4 cm wide)
 one 22.86 cm (9in) balloon
 44cmlong piece of string
 pan balance
 tape measure
 graph paper
 calculator
Background
A
star spends most of its life fusing hydrogen into helium. During this time, a
balance exists between the energy being released and the gravity of the star.
Once a star uses up all the hydrogen in its core, gravity takes on a bigger
role. Gravity's influence on the core causes it to contract further, setting
off a cascade of fusion of lighter elements into heavier ones. In very massive
stars this cascade continues until only nonfusible iron remains. During this
process, the core releases a far greater amount of energy, which radiates
outward and expands the gas in the outer layers of the star. As a result, the
star swells. Even though the total amount of energy emitted goes up, because of
its large size, the star actually cools off. It becomes red and bloated, so
astronomers call this kind of star a "red giant."
Eventually, gravity once again comes to dominate. If the star is massive enough
(a mass more than about 20 times greater than that of our sun), then it can
fuse iron nuclei. Because iron takes more energy to fuse than it releases, the
core is robbed of the heat it needs to balance gravity. (This process also
absorbs electrons, which help support the core against its own crushing
gravity.) When iron begins to fuse, it's like the legs are kicked out from
under the core. It collapses inward within only a fraction of a second,
releasing a vast amount of energy which flashes outwards, tearing off the outer
layers of the star. The star explodes in an event called a supernova.
What happens to the core when it collapses depends on its mass. If it is
between 1.4 and three to four times as massive as our sun, it will become a
dense neutron star (a neutron star is about 11 kilometers in diameter; a
teaspoonful of it weighs about a billion tons—as much as all the cars on
Earth would weigh). Up to a certain size, a neutron star can resist the inward
pull of gravity. But if it is more than two and a half solar masses, gravity
wins and the neutron star collapses into a black hole. When this happens, the
core digs itself deep into the fabric of spacetime, crushing the matter itself
right out of existence. All that remains is a region of extremely curved
spacetime, the ghost of the collapsed stellar core, the center of which is
called a singularity.
Because black holes are so compact, their gravitational pull is such that once
something ventures too close, it cannot escape. Not even light can break out.
The point of no return is the event horizon surrounding the black hole. Matter
within the horizon falls inexorably down to the very center, where it gets
crushed in the black hole's singularity, an unfathomable place of collapsed
space and time, where the known laws of physics break down.
The radius of this sphereshaped event horizon, known as the Schwarzschild
radius, varies according to the black hole's mass. The expression that
determines the radius of the event horizon is:
R = 2GM/c^{2}
where R is the radius of the event horizon,
M is the mass of the black hole in kg, G is the universal
gravitational constant, and c is the speed of light (G = 6.67 x
10^{11}m^{3}/kgsec^{2} and c = 3 x 10^{8}
m/sec)
Material falling into the black hole forms an accretion disk of gas and dust
outside of the event horizon, which spirals inward toward the black hole. In
addition, the black hole may have jets of hot gas and energy streaming outward
perpendicular to the accretion disk.
Some scientists claim that black holes open onto other universes. No one really
knows. While black holes have been studied mathematically, no one has directly
observed one. Astronomers infer the existence of black holes from the effect
they have on the material around them (i.e., observing Xray emissions
resulting from gas being heated near a black hole due to its strong
gravitational pull). Our Milky Way galaxy has a supermassive black hole in its
with a mass four million times that of the sun. Moreover, every decentsized
galaxy likely has one of these supermassive black holes in its core.
In the first part of this activity, students use aluminum balls to model the
formation of a black hole. Students associate the physical act of crushing
aluminum foil (using mechanical forces) into smaller and smaller spheres with
the gravitational effects on a collapsing star. In the second part of the
activity, students calculate the aluminum ball's density as it becomes smaller
and smaller. They also consider how small it would need to be to become a black
hole.
Key Terms
black
hole: A collapsed star that has a region surrounding it from which nothing
can escape, not even light.
density: A characteristic of matter defined by the amount of mass of
material per unit volume.
event horizon: The boundary of a black hole that marks the region
surrounding the black hole from which nothing can escape. The radius of this
region is known as the Schwarzschild radius.
fusion: The process in which the nuclei of atoms combine to form larger
ones at high pressure and temperature.
gravitational force: The force of attraction between objects that
contain either mass or energy.
mass: The amount of matter a sample of material contains, measured in
grams or kilograms.
neutron star: An extremely small, superdense star formed as a result of
a supernova explosion.
Schwarzschild radius: The radius of the event horizon of a black
hole.
volume: The amount of space matter occupies.
Part I
Prior to the activity, set up the balances at student lab stations. Create
enough 50centimeter sheets of aluminum foil for each team.
To introduce the activity, ask students what they know about black holes.
Ask them how they think black holes form. Use the background information to
review how black holes are formed, what their components are, and where they
are believed to exist.
Explain to students that they will be modeling how a star's interior, called
the core, evolves into a black hole. The balloon students blow up represents a
star 20 times the mass of our sun shining steadily as it converts its interior
reserves of hydrogen to helium, a process known as nuclear fusion. The tension
in the balloon material represents gravity trying to collapse the star's core,
and the pressure from the air inside the balloon represents the heat in the
star's core trying to make it expand. The aluminum foil represents the star's
core. Guide students through what each stage represents prior to or during the
activity:
The first aluminum ball that students form symbolizes the star's core
during most of its lifetime. Ask students to imagine that this core is inside
the balloon and is surrounded by layers of the star as it burns its hydrogen
fuel. The star itself is vastly larger than the aluminum ball.
The first compaction represents what happens after the star burns through
its hydrogen fuel, becomes a red giant, and then cools and begins to fuse
lighter elements into heavier ones, all the while becoming increasingly more
dense. The star alternately heats and cools during this time and gravity takes
on a bigger role each time the star cools. Have students continue to visualize
the core inside the balloon.
The second compaction symbolizes the iron core that is left after the
star has burned through all its lighter elements. When iron fuses, it takes
away energy from the core that is needed to support the star. Once this
happens, gravity takes the upper hand and the star's core collapses under its
own weight. The star goes supernova.
Crushing the aluminum ball down further with the hammer symbolizes the
hot, dense core left behind after the star goes supernova. (Students will pop
the balloon prior to making this compaction to symbolize the supernova
explosion.) At this point, a quantum mechanical effect called neutron
degeneracy pressure prevents further collapse. However, if the neutron star is
more than two and a half solar masses, gravity is so strong that even the
nuclear forces from the neutron star can't stop it—the core will collapse
and become a black hole.
Discuss the limitations of this model with students. (This model is
intended to approximate the stages a star goes through on its way to becoming a
black hole; it does not accurately represent the sizes of the core or the
layers surrounding a star at various times in its life cycle or of the actual
compaction of matter in a star.)
Prior to beginning the activity, discuss density with students. Show
students the glass of water, piece of wood, aluminum pellet, iron rod, and
piece of gold jewelry. Ask students which items they think are most dense. Why?
Discuss density, providing the density of the objects you have shown:
 wood (.5 g/cm^{3})
 water (1 g/cm^{3})
 aluminum (2.7 g/cm^{3})
 iron (8 g/cm^{3})
 gold (19.3 g/cm^{3})
Point out that the average density of the sun is 1.4 g/cm^{3} (note
that the sun is about 1/20^{th} the mass of a star that would become a
black hole). Inform students that as forces are applied to most (nonliquid)
substances and they are squeezed into a smaller space or volume, their density
changes.
Draw a onecentimeter cube on the blackboard. Ask students which of the
following elements would weigh the most (be the most massive) within the box:
water, aluminum, or gold. (Gold, the densest naturally occurring element on
Earth. The box will hold 1 gram of water, 2.7 grams of aluminum, or 19.3 grams
of gold.)
Organize students into teams and distribute the student handouts and
materials to each team. Review activity directions with students.
Have students inflate their balloons until the string goes just around the
widest part of the balloon (about twice the size of a grapefruit) and then tie
the balloons off. Then have students use string or measuring tape to measure,
in centimeters, the balloon's diameter in two directions, at 90degree angles
to each other, to find the average diameter and radius. Help teams through this
process if needed.
Have students follow the directions listed on their "Dense, Denser,
Densest?" student handout. After students have compressed and remeasured their
aluminum ball twice they will bring it to you to hammer down further. Note that
it is fairly difficult to compress the foil to a sphere with a diameter of less
than two centimeters. (See Activity Answer for a typical value.)
Have each team report its data points for you to plot on the overhead (plot
volume on the yaxis and density on the xaxis). Use a different
color for each team's results. This will allow you to discuss reasons for any
data differences and delete any outliers before you draw a final bestfit
curve. The graph will appear to be headed to zero. Ask students whether the
aluminum ball really goes away. (In the case of the creation of a black
hole, for all practical purposes the matter collapses to infinite density, but
mathematically it does not disappear entirely. You may want to note to students
that if you were to continue to magnify the graph, it would come very close to
zero—about 10^{50}—but would not reach it.)
To conclude, hold up the aluminum pellet again. Tell students that the aluminum
pellet demonstrates the maximum density of aluminum obtainable on Earth (2.7
g/cm^{3}). (Forces between the electrons of each atom repel each other
more strongly than any force on Earth that could make the pellet smaller.)
Explain that only in the collapse of massive stars during supernova events can
forces be exerted strongly enough to overcome the repulsion of the electrons in
the atoms. In fact, when very large stars go supernova, even the forces of
repulsion in the nuclei of atoms are overcome, enabling the mass in the core of
the star to be compressed until it virtually disappears and a black hole is
formed.
If you would like, continue to the next part of the activity to have
students work out on paper how much the density of the aluminum would need to
be increased for it to become a black hole.
As an extension, have students create a time line of the theory of black
holes and observational evidence that supports their existence.
Part II
In this part of the activity, students will calculate the increasing density
of their aluminum stars as they get smaller and smaller. Have students perform
the calculations up until their aluminum stars are calculated to be the size of
neutrons (the average radius of a neutron is equal to 10^{15} m).
Once they have completed the neutron calculations, inform students that as
dense as their aluminum star would be if it were the size of a neutron, that is
nothing compared to what happens when a neutron star becomes a black
hole—when the star becomes unimaginably dense in virtually zero volume!
Tell students that this is a very hard model to conceptualize as there is
nothing that exists in our normal experience that it can be compared to.
Have students perform the final calculation of how small the aluminum star
would have to be to become a black hole, and then how large the black hole's
event horizon would be. Discuss with students whether it would be possible to
create a black hole out of a piece of aluminum foil. (It is theoretically
possible, but would take more energy than is currently available.)
As an extension, have students calculate the Schwarzschild radius of the
black hole in the center of our Milky Way galaxy, which is thought to have a
mass of about 4 million suns (mass of our sun = 2 x 10^{30}
kilograms)
R = 2GM/c^{2 }= 2 x 6.67 x
10^{11}m^{3}/kgsec^{2 }x (4 x 10^{6} suns x 2
x 10^{30} kg/sun)/( 3x 10^{8} m/sec)^{2 }= 1.2 x
10^{10} m or 1.2 x 10^{7} km or 7.4 million miles in radius
Sample Data Table and Graph*
Part I
Trial
#

Mass
(g)

R_{1
}(cm)

R_{2
}(cm)

R_{avg
}(cm)

V
(cm^{3})

D
(g/cm^{3})

1 
14.1 
7.6 
6.4 
7.0 
1,432 
0.0098 
2 
14.1 
4.5 
4.7 
4.6 
406 
0.035 
3 
14.1 
2.5 
2.3 
2.4 
58 
0.24 
4 
14.1 
1.7 
1.5 
1.6 
17 
0.83 
* Measurements based on two sheets of foil about 50 centimeters in length and a
balloon about 14 centimeters in diameter. The total mass of aluminum is 14.1
grams in the example.
Part II
Going down to ... one centimeter
V = 4/3πR^{3 }= 1.33 x 3.14 x (1 cm)^{3 }= 4.19 cm^{3
}
D = M/V = 14.1 g/4.19 cm^{3 }= 3.437
g/cm^{3}
And farther down to ... one millimeter
V = 4/3πR^{3 }= 1.33 x 3.14 x (.1 cm)^{3 }=.0019 cm^{3
}
D = M/V = 14.1 g/.0042 cm^{3 }= 3370g/cm^{3}
And farther down to ... a neutron
V = 4/3πR^{3 }= 1.33 x 3.14 x (1 x 10^{13 }cm)^{3
}= 4.0 x 10^{39 }cm^{3 }
D = M/V = 14.1 g/4.2 x 10^{39 }cm^{3 }=
3.4 x 10^{39} g/cm^{3}
And finally down to a ... black hole
V = 4/3πR^{3 }= 1.33 x 3.14 x (approaches 0)^{3 }= 0^{
}cm^{3 }
D = M/V = 14.1 g/0^{ }cm^{3 }= [infinity]
Your black hole's event horizon
R = 2GM/c^{2 }= 2 x 6.67x10^{11}m^{3}/kgsec^{2
}x .0141 kg/(3x10^{8} m/sec)^{2 }
= 2.09x 10^{29}m
The size of the event horizon if our sun were to become a black hole
R = 2GM/c^{2 }= 2 x 6.67x10^{11}m^{3}/kgsec^{2
}x 2 x 10^{30} kg/(3x10^{8} m/sec)^{2 }
= 3,000 m (about 3 km)
What would life be like on Earth if the sun was replaced by a black hole
with the mass of the sun?
There would be no light or warmth because no light could escape the black
hole. Anything falling into the black hole would make Xrays and possibly gamma
rays, sending out lethal amounts of radiation. Nothing could survive. However,
assuming that the black hole was the same mass as the sun, the Earth would
continue to orbit as it does now.
Would Earth be sucked into the black hole?
Earth would not be sucked into the black hole, assuming the black hole had
the same mass as the sun. Since the mass at the center of the solar system
remains the same, Earth's orbital velocity and path would not change.
Web Sites
NOVA—Monster of the Milky Way
www.pbs.org/nova/blackhole
Watch the program online, learn about how black holes form, discover what
little black holes are, look at some of the other marvels of the universe, and
more.
Black Hole Encyclopedia
hubblesite.org/explore_astronomy/black_holes/encyclopedia.html
Explains the nature, formation, and existence of black holes.
Black Holes
glast.sonoma.edu/teachers/blackholes/index.html
Provides information about black holes; an educator's guide of
activities; and links to additional lessons, games, and resources about black
holes.
No Escape: The Truth about Black Holes
amazingspace.stsci.edu/resources/explorations/ blackholes/teacher/sciencebackground.html
Contains background information about black holes, including facts about how
they form, how light can be trapped in them, the kinds of black holes that
exist, and more.
Books
A Nature Company Guide: Skywatching
by David H. Levy. TimeLife Books, 1995.
Provides a general overview and discussion of astronomical objects, including black holes.
The Young Oxford Book of Astronomy
by Jacqueline & Simon Mitton. Oxford University Press, 1995.
Explains many concepts in astronomy from the solar system, galaxies, and the universe, including black holes.
The "Dense, Denser, Densest?" activity aligns with the following National
Science Education Standards (see
books.nap.edu/html/nses).
Grades 58
Science Standard B
Physical Science
Properties and changes of properties of matter
Motions and forces
Grades 912
Science Standard B
Physical Science
Conservation of energy and increase in disorder
Structure of atoms
Motions and forces
Science Standard D
Earth
and Space Science
The origin and evolution of the universe
Classroom Activity Author
Jeff Lockwood taught high school astronomy, physics, and Earth science for 28
years. He has authored numerous curriculum projects and has provided
instruction on curriculum development and science teaching methods for more
than a decade.

How Black Holes Form
Find a description and images related to black hole formation in this NOVA
slide show. 
