Activity 2: Planetary Mass: How Is It
Distributed? | |||

As you can see from Activity 1, different
density models
can have the
correct mass. Mass doesn’t tell us how density varies with depth. We need additional information
to decide which of the three models
are wrong. Fortunately,
each of these
models has a different moment of inertia, a quantity that depends on mass and
the spatial
distribution of that mass.Two bodies can have identical masses but different moments of inertia if they have different internal mass distributions. Consider two spinning tops of equal mass, each with materials of different densities. The tops have identical mass but different mass distributions. One top ( A) has a
dense substance
at its center, whereas
the other (B) has it near the outside. If we spin the tops with the same force and measure
their spinning,
we will find that they spin at different rates. Top A will spin faster than top B because it
has a smaller
moment of inertia.Thus moment of
inertia is directly tied to mass distribution. If two bodies have equal mass, the one whose density
increases with
depth will have a smaller
moment of inertia than
one with uniform
density.Earth’s moment of inertia influences its precession rate. Precession causes Earth’s
rotational axis
to trace a circle against
the backdrop of the stars. The rate of wobble of the rotational axis has been measured relative to the stars and more recently with respect to
satellites orbiting
the Earth. By
measuring precession rate, we know that Earth’s moment of inertia is 8.03 x 10^{37} kg/m^{2}.You will use the Java applet that appears below to create a model of the Earth’s interior that has the correct mass and moment of inertia. By taking into account moment of inertia as well as mass, you can eliminate those models which do not describe the Earth. | |||

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