Intuitive explanation of gravity outside a sphere?

In summary, the gravitational force of a sphere on a distant point is equivalent to if all the mass were concentrated at the center, and this is also true for a disk or a ring and a point in the same plane. This can be understood through symmetry, as the force is directed to the center of the sphere and seen as a point from far away. This theorem holds true for any spherically symmetric distribution.
  • #1
jacobfreeze
6
0
Does anyone have an intuitive explanation why the gravitational force of a sphere on a distant point is the same as if all the sphere's mass were concentrated at the center? The usual integration over spherical shells goes through o.k. but the result is so simple it seems to me that maybe we could get there by insight instead of calculation...or at least part of the way there...
Do we have the same result for a disk or a ring and a point in the same plane? Is the gravitational force of a ring on a point in the same plane equivalent to the force from the same mass concentrated at the center of the ring?
I think this is true...so is there an intuitive way to get this result in the simpler case of a ring and a co-planar point, and does the spherical case then follow?
 
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  • #2
Actually, that's only true if the density is uniform (unless by "distantpoint" the limit as distance goes to infinity). I'm not sure what you would consider "intuitive" but the simplest way to think about it is through symmetry. Take any point outside the uniform, spherical mass. Draw a line from the point to the center of the sphere (I'm going to call that the "center line"). For any point on the sphere, there is a "symmetrically opposite" point (equal distance on other side of the center line). The component of graviational force perpendicular to the center line of the two points are equal and opposite and so cancel. That is, the force is directed to the center of the sphere.

The "very distant" (limit as distance goes to infinity) case is even more "intuitive": any figure, of any density, seen from far enough away looks like a point!
 
  • #3
I don't get your reasoning, Halls. Your argument shows that the force acts along the center line, but does not imply (as far as I can see) that the magnitude of the force is the same as if the mass were at the center.

I can't think of a simple intuitive explanation. Of course, you can apply Gauss's theorem to gravity, but that requires explanation (for those unfamiliar with the Poisson equation for gravity).
 
  • #4
HallsofIvy's response misses the point of my question, but it brings up another aspect...Is the theorem true for any sperically symmetric distribution? The analogy with Gauss' theorem suggests that it is.
But still no insight about why the force operates from the center. I'm not necessarily looking for a complete proof...just a little improvement over watching the result fall out of an integral.
 
  • #5
Originally posted by jacobfreeze
...Is the theorem true for any spherically symmetric distribution?
Yes.
 

1. What is the intuitive explanation for why gravity is weaker outside a sphere?

The intuitive explanation for why gravity is weaker outside a sphere is due to the distribution of mass. When we are inside a sphere, the mass surrounding us is distributed equally in all directions, resulting in a stronger gravitational pull. However, as we move outside the sphere, we are no longer surrounded by mass in all directions, causing the gravitational pull to decrease.

2. Does the shape of an object affect its gravitational pull?

Yes, the shape of an object does affect its gravitational pull. As mentioned earlier, the distribution of mass plays a crucial role in determining the strength of gravity. Objects with a more compact and symmetrical shape, such as a sphere, have a more evenly distributed mass, resulting in a stronger gravitational pull compared to objects with irregular shapes.

3. How does the distance from the center of a sphere affect the strength of gravity?

The strength of gravity is inversely proportional to the square of the distance from the center of a sphere. This means that the farther you are from the center of the sphere, the weaker the gravitational pull will be. This can be observed in planets, where the gravitational pull is stronger at the surface compared to the outer atmosphere.

4. Can gravity exist outside of a sphere?

Yes, gravity can exist outside of a sphere. Gravity is a fundamental force that exists between all objects with mass. As long as there is mass present, gravity will exist regardless of the shape or size of the object.

5. Is the gravitational pull constant throughout the surface of a sphere?

No, the gravitational pull is not constant throughout the surface of a sphere. As we move closer to the center of the sphere, the gravitational pull increases due to the larger amount of mass present. However, as we move towards the outer surface of the sphere, the gravitational pull decreases due to the distribution of mass becoming less dense.

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