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Imagine a solid sphere of radius $R$. From the inside of this sphere we remove a smaller sphere of radius $r$. The sphere can be situated anywhere inside the massive sphere. How does the gravitational field in this hollow sphere look like?

I don´t mean how the field inside a hollow sphere looks like (which is obvious zero everywhere).

I thought it would look like this:

g=-4/3(pi)G(ro)r1-(-4/3(pi)G(ro)r2)=-4/3(pi)G(ro)(r1-r2)=-4/3(pi)G(ro)c

g is the acceleration ro is the (uniform) mass density r1 and r2 are the vectors from the centre of thebig sphere to a random point in the cavity and the vector from the centre of the cavity to the random point. c is the vector from the centre of the big sphere to the centre of the cavity (a constant).

So g is constant, and thus the force.

Deschele Schilder
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    i think superposition hould provide the answer. – Lelouch Jul 26 '16 at 13:15
  • Please see the Homework-and-Exercises policy (http://meta.physics.stackexchange.com/questions/714/). You are expected to ask about a specific physics concept and to demonstrate effort to work though the problem yourself. – sammy gerbil Jul 26 '16 at 13:20
  • Is the inner sphere concentric with the outer sphere? – sammy gerbil Jul 26 '16 at 13:21
  • I was going to answer this question , but then i realized that the link that sammy suggested more then completely explains what going on here. – Haru Fujimura Jul 26 '16 at 13:41
  • My question is certainly not a copy of the quoted question! The gravitational field inside the hollow sphere depends on where in the massive sphere you put it. In the middle it´s clearly zero everywhere, but when you move the hollow sphere to the edge of the massive sphere a gravitational field develops. I ask how that field looks like. – Deschele Schilder Jul 26 '16 at 17:27
  • My guess is that it´s a uniform field, with the direction and the value depending on where the hollow sphere finds itself. The direction is to the centre of the sphere. – Deschele Schilder Jul 26 '16 at 17:30
  • @sammy gerbil As I just wrote, the hollow sphere can be situated anywhere inside the massive sphere. – Deschele Schilder Jul 26 '16 at 17:38
  • @descheleschilder It does not matter where the hollow cavity is inside the sphere; read the post, it is actually some interesting geometrical proofs. Geometry is really useful in the study of physics. – Haru Fujimura Jul 26 '16 at 17:44
  • Non-concentric cavity is different. But you still need to make some effort to solve this problem, and show your working in the question box. A brief description may not be good enough. Follow the hint provided by lelouch. Also see this question : Gravitational field of sphere containing a spherical cavity: http://physics.stackexchange.com/q/24650. – sammy gerbil Jul 26 '16 at 20:53
  • Well, one thing´s for sure. The field inside the cavity dóes depend on where you put the cavity. If you place the cavity in the centre of the massive sphere, the field is zero everywhere. If you put it on the edge, the field inside the edge is uniform, and is directed parallel towards the centre and has it´s maximum value. In this case I trust my feeling, but Ill do the calculation. – Deschele Schilder Jul 27 '16 at 08:20
  • @sammy gerbil The basic strategy is to substract the field produced by a mass (with the same density as the mass of the big sphere) from the field produced by the big sphere without a cavity. They are both lineair functions (the field inside a massive sphere drops from the edge lineair to zero at the centre). – Deschele Schilder Jul 27 '16 at 11:59
  • Please post your calculation attempt in the Question box. Adding comments will not get your Qn reopened. You have to make a change to the Qn and state how this Qn is different from the other. – sammy gerbil Jul 27 '16 at 12:06
  • @sammy gerbil Where can I find the question box to show the calculation? – Deschele Schilder Jul 27 '16 at 13:48
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    I mean : edit your question. Select 'edit' under the topic tags. – sammy gerbil Jul 27 '16 at 14:02
  • Re your edit : 1. You still have not shown any attempt to solve the problem yourself. 2. When you ask "What does the field look like?" what kind of answer are you looking for? A formula, or a method for finding it, or a graph, or a qualitative description? 3. Your question is contradictory : you ask what the field inside the hollow sphere looks like, but in the last sentence you state this will be zero. – sammy gerbil Jul 27 '16 at 15:56
  • @sammy gerbil I stated that in a cavity placed in the centre of the big sphere, the field would be zero. As you can see in the question box, the field is constnt in the sphere and depends on where you put it. – Deschele Schilder Jul 28 '16 at 06:34
  • @sammy gerbil I meant in my last comment that the field is constant in the cavity and depends on where you put the cavity. In my question I made the remark that I don´t mean how big the field is inside a spherical shell (it´s zero). The field in the cavity depends on the vector from the centre of the sphere to the centre of the cavity. – Deschele Schilder Jul 28 '16 at 06:45

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