## The Anatomy of Black Holes - Page 13

- Tell students that they are going to attempt to make a black hole with aluminum foil and balloons in this lab. They are going to determine what radius, mass, and density it takes to make this aluminum foil balloon (that will represent a star) into a black hole.
- Before you begin this lab, blow up the balloon until the diameter is about 15 cm, no larger. Tie off the end. Tell students that this is the core of the star. Cover the inflated balloon with several sheets of aluminum foil. These layers of foil represent the outer layers of your "Model Star". Be generous with the foil and cover the balloon thoroughly. It works best if you use several 30-35 cm long sheets and wrap around at least twice. Students should construct their own model stars using the materials. On their worksheets, students record their initial measurements of mass and circumference.
- You are now ready to simulate the enormous mass of the star collapsing inward toward the core. You can tell students that their hands are the "Giant Hands of Gravity". Students will find all sorts of inventive ways to pop their balloons, if a simple squeeze doesn't work for them (the sharp end of a pen or pencil works well). Caution them that they will need to
*gently*shape the aluminum foil back into a "sphere" once they have popped the balloon, however. So they should not stomp on it or do anything that will make it lose its basic round shape. Caution -- This is the first trial measurement of a series of 4, so don't squish it so hard you will not be able to see a change in the data gathered in subsequent trials. Students continue filling their worksheets by making successive measurements of the circumference and mass, and they calculate the radius, volume, and density. - By this time, students should be noticing that the mass is really not changing as they squeeze the ball into a smaller and smaller size.
- Students should notice that as they go to smaller and smaller radii, the densities increase. In most trials seen by the authors, the change in density between the inflated balloon and the smallest size is about a factor of 100.
- Use the equation R=2GM/c
^{2}, where R is the radius of the event horizon, M is the mass of the black hole, G is the universal gravitational constant, and c is the speed of light. G = 6.67x10^{-8}cm^{3}/g-sec^{2}and c = 3x10^{10}cm/sec. This equation gives R, the radius of the event horizon for a black hole of mass M. Think about what this equation says: for ANY mass, it can be a black hole IF it can get small enough. Finding a force to make you small enough is the difficult part! When the authors did this activity, they had a 30 gram star. The radius at which this mass would become a black hole is then about 4 x 10^{-27}cm. At that size, the density would be about 9 x 10^{79}g/cm^{3}! - The densest thing students will probably be able to come with or have any knowledge of is a proton or neutron. Remind them that once you start talking about atoms, they are mostly empty space... with essentially all of the mass in the nucleus. So lead and iron and such are not very dense compared to a proton or neutron. The density of a nucleon (either a proton or neutron) is about 1.5x10
^{15}g/cm^{3}. Comparing this to our collapsed star density as it becomes a black hole, we see that there is no comparison! Our conclusion is this: we may not understand that matter is like inside a black hole, but we know that it is not matter as we know it. It is not protons, neutrons, and electrons - it is not any atom or molecule. We may not be able to conceive of what it may be, but we know what it isn't!