Hydrostatic Equilibrium with a Hoberman Sphere
Introduction
Stars form within dusty cocoons inside of giant molecular clouds in space. They formed by drawing
material in from the cloud until they had sufficient mass to trigger thermonuclear fusion in their cores.
Once fusion of hydrogen atoms into helium atoms began, gravitational collapse was no longer the only
force in operation on the growing star. Now, radiation pressure from the reactions in the core acted to drive
the material outward. This was balanced by inward gravitation force from the mass of the star until a
balance was reached. This balance is called hydrostatic equilibrium and is what defines the size (in terms of
diameter) of a star.
Stars like the sun that are fusing hydrogen atoms to produce energy are on the main sequence branch of the
H-R diagram. While on the main sequence, the sun will essentially remain the same size due to hydrostatic
equilibrium. Some day, billions of years form now, the sun will have used up most of the hydrogen in the
core and thermonuclear fusion will pause. This will result in a loss of equilibrium and the sun will begin to
collapse. As it collapses, the material is compressed and heated until fusion of helium atoms begins. This is
a more energetic process, so radiation pressure is stronger than it was before and the sun inflates into a red
giant. As a red giant hydrostatic equilibrium has been restored.
These processes can be modeled with a common toy known as a Hoberman
sphere.
Procedure
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Start with your sphere expanded fully. This stage will be the protostar
stage of stellar evolution.
Slowly collapse the sphere, simulating gravitational collapse of the
protostar.
When the sphere is almost fully collapsed, state that thermonuclear fusion of hydrogen has begun
and inflate the sphere a little. State that this represents the hydrostatic equilibrium and you now
have a main-sequence star.
Now state that the star has exhausted its supply of hydrogen and fusion has ceased. Collapse the
sphere a bit sharing that equilibrium no longer exists.
Once you have collapsed the sphere a bit state that fusion of helium has begun and now radiation
pressure exceeds gravitational collapse. Inflate the sphere fully, sharing that equilibrium has been
restored and you now have a red giant.
You could continue to the white dwarf stage – but there is no way to model the loss of mass as the
red giant sheds layers of the star’s outer surface.
Questions for Discussion
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How well does this process model what happens in a star to reach hydrostatic equilibrium?
Would this model work for stars more massive than the sun? Why or why not?
Would you want to model a supernova explosion with this model? Why or why not?
MESTA Showstoppers
MSTA 2014
C.L. DeWolf