Gravity of hollow sphere vs. solid sphere of same mass

In summary, a hollow sphere with the same mass as a solid sphere would measure the same gravitational force externally, but would have different internal stresses and spacetime curvature. Additionally, if you were inside a hollow sphere with uniform density and thickness, you would experience no net gravitational force due to the flat spacetime inside.
  • #1
Andy SV
113
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Would a hollow sphere measure the same gravitationally as a solid sphere if it was the same mass?

Just sharing an interesting question
 
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  • #2
Andy SV said:
Just sharing an interesting question

Which belongs in a separate thread, so I have spun it off into one.
 
  • #3
Andy SV said:
Would a hollow sphere measure the same gravitationally as a solid sphere if it was the same mass?

As far as its external gravity, yes (assuming it also had the same radius). Internally, the stresses and spacetime curvature would be different, but these differences would not show up in the external field.
 
  • #4
Oh yes sorry bout that and thanks
 
  • #5
I've also heard that if you are inside a hollow sphere that has uniform density and thickness, you will experience no net gravitational force from the sphere from anywhere within it. I've never bothered to check if this was true though...
 
  • #6
Arkalius said:
if you are inside a hollow sphere that has uniform density and thickness, you will experience no net gravitational force from the sphere from anywhere within it

That is correct. More precisely, spacetime inside a hollow sphere is flat. (Note that this is true even if the density of the sphere varies, as long as the variation is purely radial, i.e., as long as everything remains spherically symmetric.)
 

Related to Gravity of hollow sphere vs. solid sphere of same mass

1. What is the difference between the gravity of a hollow sphere and a solid sphere of the same mass?

The main difference between the gravity of a hollow sphere and a solid sphere of the same mass is that the hollow sphere has a zero gravity field inside, while the solid sphere has a non-zero gravity field throughout its volume. This means that an object placed inside the hollow sphere will experience no gravitational force, while an object placed inside the solid sphere will experience a gravitational force towards the center of the sphere.

2. How does the distribution of mass affect the gravity of a sphere?

The distribution of mass within a sphere has a significant impact on its gravity. In a solid sphere, the mass is evenly distributed, resulting in a constant gravity field throughout the sphere. In a hollow sphere, the mass is concentrated at the outer surface, resulting in a zero gravity field within the sphere.

3. Is the gravitational force stronger for a solid sphere or a hollow sphere of the same mass?

The gravitational force is stronger for a solid sphere than a hollow sphere of the same mass. This is because the solid sphere has a non-zero gravity field throughout its volume, while the hollow sphere only has a gravity field at its outer surface.

4. How does the radius of a sphere affect its gravitational force?

The radius of a sphere has a direct impact on its gravitational force. As the radius increases, the distance between objects on the surface and the center of the sphere also increases, resulting in a weaker gravitational force. However, for a sphere with a fixed mass, the gravitational force at its surface will remain the same regardless of its radius.

5. Does the shape of a sphere affect its gravitational force?

No, the shape of a sphere does not affect its gravitational force as long as the mass and radius remain constant. This is because the gravitational force is determined by the mass and distance between objects, not the shape of the sphere.

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