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Worksheet #4
Black Holes
For the purposes of this worksheet imagine you are standing on the surface of Earth while
the International Space Station (ISS) orbits 6800 km from the center of the Earth (400 km
above the surface of the Earth as it is now).
1. If the Earth shrunk to half of its size while staying the same mass, what would happen
to the force of gravity you would feel at the surface of the Earrh?
2. If the Earth shrunk to half of its size while staying the same mass, what would happen
to the force of gravity felt by the ISS?
3. Suppose that the Earth shrank even further such that it was 224 km across and had the
density of a write dwarf. How would the gravity you felt standing on its surface compare to
the gravitational force you felt when Earth was at full size or at half size?
4. How force of gravity exerted on the ISS by a 224 km across Earth compare to that exerted
by a full-size or half-size Earth?
5. On which size Earth would you have the highest escape velocity: full-size Earth, half-size
Earth, or 224 km-across Earth? Why?
Astronomy 170
4–1
The Physical Universe
If the Earth were to shrink to have a radius smaller than 9mm, the escape velocity at 9mm
away from its center would exceed the speed of light. At this point, Earth would have become
a black hole and the 9mm radius would define the event horizon.
6. What would happen to the orbit of the ISS after the Earth had become a black hole?
Why?
7. Two students are discussing the answer to problem 6.
Student 1 says: I don’t think anything would happen to the orbit of the ISS. Its mass, the
mass of the Earth, and the distance between it and the center of the Earth are all the same,
so force of gravity it felt would also be the same.
Student 2 says: I disagree. Since Earth became a black hole, it would exert such a strong
gravitational force on the ISS, that it would quickly spiral into it.
In what ways do you agree or disagree with both students?
8. Suppose the mass of the Earth were twice as big. How, if at all, would this increase in
mass change the location of the event horizon (the point where the escape velocity is greater
than the speed of light)?
9. What force, if any, could support the mass of the Earth within its event horizon?
10. What do you suspect would happen to the shape and size of the black hole within the
event horizon?
Astronomy 170
4–2
The Physical Universe