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There is lots of physical evidence supporting the idea that Ganymede has a liquid iron core, a rocky inner mantle, and an icy outer mantle. The bulk density is about twice that of ice, the moon has a magnetic field, and its moment of inertia has been measured.dougettinger wrote:How can astronomers be much surer of Ganymede with its mantle of ice having a rocky core, then Jupiter having a rocky core with its thick mantle of metallic hydrogen ?
The moment of inertia of a rotating sphere is I = 2/5(m)(R 2). You know m from gravitational laws due to its orbit around Jupiter and you know R. And you know the densities of different materials. But how do you know whether the density is homogeneous or whether the heavier materials are concentrated in an inner core ? The rotation is affected by gravitational locking and should not help in postulating a differentiated core. I am not asking for a complete mathematical explanation; I would appreciate a brief conceptual explanation. Perhaps a tensor treatment (beyond my comprehension) is needed to explain an observed wobble and then its density distribution.Chris Peterson wrote:There is lots of physical evidence supporting the idea that Ganymede has a liquid iron core, a rocky inner mantle, and an icy outer mantle. The bulk density is about twice that of ice, the moon has a magnetic field, and its moment of inertia has been measured.dougettinger wrote:How can astronomers be much surer of Ganymede with its mantle of ice having a rocky core, then Jupiter having a rocky core with its thick mantle of metallic hydrogen ?
The situation with Jupiter is much more complex, because there are fewer measurements to work from, and a good deal of uncertainty about the physical properties of materials at the very high pressures deep inside the planet.
That is the definition of moment of inertia for a sphere of uniform density. Ganymede clearly does not have uniform density, given that its density is twice that of the material observed to make up its surface. Its actual density lies between that of ice and stone. As a spherical solid body, it is certainly differentiated, meaning that denser material is concentrated in the center. There are no known exceptions to this sort of differentiation, and no reason to think that Ganymede wouldn't be differentiated.dougettinger wrote:The moment of inertia of a rotating sphere is I = 2/5(m)(R 2). You know m from gravitational laws due to its orbit around Jupiter and you know R. And you know the densities of different materials. But how do you know whether the density is homogeneous or whether the heavier materials are concentrated in an inner core ?
I am beginning to understand and am excited. If the R is smaller in I = 2/5(m)(R 2), then of course "I" is smaller. And "m" from gravitational equations can also be used to determine the bulk density. And the surface materials are known from other measurements. I could not find the moment of inertia for a hollow sphere with a certain thickness to determine the "I" for the lighter surrounding mantle.(?)Chris Peterson wrote:That is the definition of moment of inertia for a sphere of uniform density. Ganymede clearly does not have uniform density, given that its density is twice that of the material observed to make up its surface. Its actual density lies between that of ice and stone. As a spherical solid body, it is certainly differentiated, meaning that denser material is concentrated in the center. There are no known exceptions to this sort of differentiation, and no reason to think that Ganymede wouldn't be differentiated.dougettinger wrote:The moment of inertia of a rotating sphere is I = 2/5(m)(R 2). You know m from gravitational laws due to its orbit around Jupiter and you know R. And you know the densities of different materials. But how do you know whether the density is homogeneous or whether the heavier materials are concentrated in an inner core ?
The actual moment of inertia was measured by the Galileo spacecraft. It is much too low for a uniform body- the low moment means that much of the total mass is concentrated within a small radius. Knowing the moment of inertia allows for different structural models to be tested. By using the magnetic field properties to estimate the iron core volume, and the moment of inertia and bulk density to predict the depth of the ice/stone boundary, a very reasonable inference can be drawn regarding the moon's interior.
Wikipedia: Ganymede: Origin and evolutiondougettinger wrote:Why does Ganymede's core stay heated and liquid for so long