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 1037 kg/m2.

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.