Special Cases for Gravity Force Inside Solid Objects

In summary, the conversation is about the shell theorem in relation to the law of gravity. The conclusion is that the force of gravity due to the mass of a spherical shell is zero inside. The conversation also includes questions about how this conclusion applies to other shapes, such as an ellipsoid or a disk with a shell on the exterior perimeter, and how the gravity force is affected inside a spherical solid with multiple layers and different densities. These questions were posted by a user named Doug Ettinger on the forum Physics Forums, and the moderator has moved the conversation to a new thread.
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dougettinger
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I know about the shell theorem and that the force of gravity due to the mass of the spherical shell is zero inside. I have some questions that may easily be answered for other special cases using the shell theorm and the law of gravity.

1. Does this same conclusion hold for an ellipsoid and/or a disk with the shell on the exterior perimeter ?

2. How is the gravity force inside a spherical solid affected if it has two layers and a central core all with different but homogeneous densities ? Especially inside the middle layer that has the least density and least mass ?

Thoughtfully, Doug Ettinger
 
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What is the concept of "Special Cases for Gravity Force Inside Solid Objects"?

The concept of "Special Cases for Gravity Force Inside Solid Objects" refers to situations in which the force of gravity is not uniform throughout a solid object. This can occur due to variations in density, shape, or orientation of the object.

How does the force of gravity vary inside a solid object?

The force of gravity can vary inside a solid object due to differences in the distribution of mass. For example, an object with a higher density will have a stronger gravitational force towards its center, while an object with a lower density will have a weaker gravitational force.

What are some examples of special cases for gravity force inside solid objects?

Some examples of special cases for gravity force inside solid objects include a non-uniformly shaped object, such as a cone or pyramid, or an object with a hollow or porous interior. Additionally, the force of gravity can vary inside an object due to the presence of other massive objects nearby.

How is the force of gravity calculated in these special cases?

In these special cases, the force of gravity is typically calculated using integration techniques, which take into account the varying distribution of mass within the object. This allows for a more accurate calculation of the force of gravity at any given point inside the object.

Why is understanding special cases for gravity force important for scientists?

Understanding special cases for gravity force is important for scientists because it allows for a more precise understanding of the behavior of objects in gravitational fields. This knowledge can be applied in various fields, such as astronomy, geology, and engineering, to better understand the forces at play in our universe.

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