Modelling gravitational force vectors

[Aeoliana]

Modelling Density as a Function of Many Objects

Hello,

My question is somewhat difficult to express but this is the best way I can come up with.

Lets say I have a mass of material which has a charge throughout its entirety. This material has a very special property where the density of the material is a function of the magnitude of the charge contained within it.

Something like:
Rho is the density of the material at a point
E is the total charge of the Material
e is the charge of the particle
r is the distance from the particle to the point of measurement
$$\rho = \frac{(E-e)^{-1}}{r^2}$$

I need to consider the scenario in which this charge is separated throughout the volume of the material, but the sum of the charge contained never diminishes. Specifically I need to determine the density of the material at any point and its volume given an array of charges and magnitudes and a mass of the material.

 

[JesseC]

The gravitational force vector at a point in space will simply be the summation of individual gravitational force vectors due to all the objects you are considering.

So long as you treat the objects as stationary point particles...

EDIT... occurred to me a true stationary point particle is basically black hole lol :D - you just need to be careful calculating gravitational forces inside the objects, or very near to objects... if your objects have size? :S

 

[Aeoliana]

Sorry, I realized that my question didn't really pertain to what I was trying to figure out.

I edited the post to reflect more along the lines of what I am trying to figure out.

 

[JesseC]

Haha, now you've confused me! For some reason what you're talking about reminds me of a nucleus, but anyway... If this is some sort of 'problem' you've got to solve, it would help if you could describe exactly what it is you've got to do and how far you've already got, rather than explain through analogy or anecdote. I don't completely understand what you're asking.

When you talk about density can you be more specific. Do you mean charge density? mass density?

What exactly is a 'particle' in this case? are we talking about a discrete set of point charges or a continuous distribution? What do you mean by "the charge is separated throughout the volume"?

I presume your equation is supposed to be an example, but the units don't even make sense so I don't know what to take from it.

I think you ought to put your question in context!

 

[Aeoliana]

Haha ok I will attempt to clarify!

When I say 'determine the density and bounds' of the material I mean mass density and shape of the material. *edit* Oops in this situation the object would be infinitely large, just minimally dense at the extremities.

When I say 'particle' I mean a discrete set of point charges.

I will try to elaborate -

There is an object O with mass M containing a charge C and that the mass density of O relative to a point of charge is given by a specific equation.

The location of a point of charge is not expressed by arbitrary assignment of the person viewing the material, but rather by location within the material itself.

So let us say we have an object with mass 100 and charge 10, this charge is split into 2 points, the points are located at 50% of the Y dimension, 50% of the Z dimension and 25/75% of the X dimension. If the density function was such that density was greater nearest a charge and grew less as you moved further away, your mass density field lines in any plane would have a lemniscus shape to them with the dip centered around the point 50%/50%/50% in all dimensions.

What I need to be able to do is to take a system of discrete point charges with locations given by position within the object, and using that in conjunction with their magnitude of charge, determine the values of mass density anywhere within the object.

My apologies, this isn't a question that is looking for a specific answer, its a conceptual question.

Its similar to finding the magnitude and direction of magnetic field lines with a system of many magnets of varying strength? Maybe?