by dougettinger » Tue Feb 15, 2011 4:59 pm
Chris Peterson wrote: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 ?
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.
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.
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.(?)
What are the newest assumptions regarding the reason for the measured magnetic field properties for a moon or planet? Is it assumed that the core is mostly ferretic, liquid, and moves with respect to the mantle to produce a magnetic field? Are all these asumptions required similar to the magnetic field produced by the Earth's core ?
Why does Ganymede's core stay heated and liquid for so long, if it was formed almost 4 billion years ago ? I am probably asking too many questions, but this last question is the most important.
Doug Ettinger Pittsburgh, PA 02/15/11
[quote="Chris Peterson"][quote="dougettinger"]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 ?[/quote]
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.
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.[/quote]
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.(?)
What are the newest assumptions regarding the reason for the measured magnetic field properties for a moon or planet? Is it assumed that the core is mostly ferretic, liquid, and moves with respect to the mantle to produce a magnetic field? Are all these asumptions required similar to the magnetic field produced by the Earth's core ?
Why does Ganymede's core stay heated and liquid for so long, if it was formed almost 4 billion years ago ? I am probably asking too many questions, but this last question is the most important.
Doug Ettinger Pittsburgh, PA 02/15/11