Gravitational field in a hollow sphere

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Discussion Overview

The discussion revolves around the qualitative justification for the gravitational field inside a uniform hollow sphere being zero. Participants explore this concept from various angles, including theoretical reasoning and analogies, while addressing the understanding of gravitational forces and their cancellation within the sphere.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests a qualitative justification for the gravitational field inside a hollow sphere, indicating confusion about the concept.
  • Another participant mentions an equivalent of Gauss's law for gravitational fields, suggesting that understanding this principle could help clarify the situation.
  • A participant proposes a qualitative analogy involving mass distribution on either side of a point inside the sphere, suggesting that the gravitational effects cancel out due to their distances from the point.
  • One participant describes a method of visualizing gravitational forces using cones extending from a point inside the sphere to the surface, explaining that equal but opposite forces lead to a net gravitational force of zero.
  • A participant expresses a preference for another explanation that incorporates the inverse square dependence of gravitational force more clearly.

Areas of Agreement / Disagreement

Participants present multiple perspectives and analogies regarding the gravitational field inside a hollow sphere, indicating that there is no consensus on a single explanation. The discussion remains exploratory with various interpretations of the concept.

Contextual Notes

Some participants express uncertainty about their level of understanding, and there are references to concepts like Gauss's law that may not be familiar to all contributors. The discussion includes assumptions about the participants' backgrounds in physics.

maddys_daddy
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Can someone please give me a qualitative justification for the gravitational field inside a uniform hollow sphere being zero? I'm having a lot of trouble understanding this. Prof. said (in class) not to worry about the higher order polynomials involved, just be concerned with it "qualitatively" at this point. I'm lost.
Thanks,
m_d
 
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maddys_daddy said:
Can someone please give me a qualitative justification for the gravitational field inside a uniform hollow sphere being zero? I'm having a lot of trouble understanding this. Prof. said (in class) not to worry about the higher order polynomials involved, just be concerned with it "qualitatively" at this point. I'm lost.
Thanks,
m_d

You did not indicate what level of physics you already have. So, I have no idea if what I will say here makes any sense to you.

There is a Gauss's law equivalent for gravitational field. So if you have seen gauss's law applied to electrostatic, you should understand the identical principle applied to gravitational field. So apply that.

http://scienceworld.wolfram.com/physics/GausssLaw.html

Zz.
 
Qualitatively, think of it like this: At any given point inside the sphere, there is x amount of mass to the right in the shape of a bowl, and 1-x amount of mass to the left in the shape of a shperical shell missing a bowl shaped cap. These two complementary portions have centers of mass at let's say rx and r1-x. Then, qualitatively, you can imagine that rx < r1-x by just such an amount that:

x/rx2 = (1-x)/r1-x2.

It would probably help to draw a picture.

Qualitatively, you're supposed to realize that Fgrav is larger for larger amounts of mass and smaller at larger distances away from the mass. So, qualitatively, you can imagine that the effect of more mass (1-x) is canceled by the effect of further away (r1-x).
 

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turin,
Thanks, I think I can understand that. However, when I click on the link to your .gif, I get a "you need to login to view this" message--well, I am! Oh, well, I'll take that up with the admins.
ZapperZ, FWIW, I'm in first year college physics for engineers (PHYS141 @ UoArizona). Next semester is my Electricity and Magnetism. So I have no idea what Gauss' law is, but I guess I'll find out.
Thanks for the help!
 
From any point inside the sphere, imagine a cone extending to a portion of the surface. Now extend that cone back to the opposite side of the sphere. If your point is not exactly at the center, your two cones will not intersect equal areas (and, so, not equal masses) because area is proportional to the square of the distance. HOWEVER, since gravitational force is inversely proportional to the square of the distance, the gravitational force from each of those portions of the surface will be the same. Since they are in opposite directions, the two equal but opposite forces cancel. The total gravitational force is 0.

(The same thing is true of magnetic force as well.)
 
I like HallsofIvy's explanation better than mine. It more clearly incorporates the inverse square dependence.
 

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