Gravitation: Which formula exactly?

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SUMMARY

The discussion centers on calculating the gravitational force acting on a particle 'm' located at various distances from the center of a uniform sphere with mass M and radius a, which contains a concentric cavity of radius a/3. The correct formula to use is Newton's law of universal gravitation, expressed as F = G(m1m2/r^2), where r is the distance from the particle to the center of mass of the sphere. Clarification is provided that the presence of the cavity affects the calculation of the center of mass, which is crucial for determining the correct distance 'r' for the gravitational force calculation.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Knowledge of center of mass calculations
  • Familiarity with the concept of gravitational force
  • Basic algebra for solving equations
NEXT STEPS
  • Study the concept of center of mass in composite bodies
  • Learn how to apply Newton's law of gravitation in different scenarios
  • Explore gravitational force calculations involving cavities in spheres
  • Review examples of gravitational force problems in physics textbooks
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Students studying physics, particularly those focusing on gravitational forces and mechanics, as well as educators seeking to clarify concepts related to gravitational calculations involving irregular shapes.

StingerManB
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I am not looking so much for answers to problems, but I was sick the day of this lecture and need some clarification. I think I understand what to do, but some support would be great.

Homework Statement


What is the gravitational force acting on a sphere on particle 'm' located at distance 'r' from center of sphere, assuming it is a uniform sphere of matter that has mass M, radius a, and a concentric cavity of radius a/3.
Solve for r= a/6, r= 2a/3, r= 3a/2I believe all I need is:

F= G(m1m2/r^2)

I have not attempted to solve, I would like to know it if this is the correct equation to use.
Thanks.
 
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Anyone? Anything at all?
 
yes, that's right. I don't understand why they gave you a/3 and radius of the sphere though, so maybe I'm missing something.
 
Maybe you have to calculate the center of mass of the "sphere with a cavity" which shouldn't be the center of the sphere. Once you've done that, you will have that the distance from the particle and the center of mass is not the same than the distance from the particle to the center of the sphere. Unless I'm misunderstanding what a cavity is.
EDIT : And about "F= G(m1m2/r^2)", yes it is the good equation to use here. Note that r is the distance from the particle to the center of mass of the sphere.
 

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