Grav. field of spherical objects

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Discussion Overview

The discussion centers on the gravitational field produced by point masses compared to that of spherical objects with the same mass, particularly focusing on the implications of Newtonian gravity and the conditions under which these gravitational effects are equivalent.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Alex questions whether the gravitational field created by a point mass is the same as that of a spherical object of the same mass when observed from outside the object, seeking an explanation for this equivalence.
  • One participant notes that, according to Newtonian gravity, the net gravitational force from a spherical shell is zero inside the shell and equivalent to that of a point mass at the center when observed from outside.
  • Another participant suggests that this concept is known as the shell theorem and encourages searching for it online.
  • One participant asserts that the gravitational effect would be the same if the mass of the Earth were compressed into a point mass at the same distance, explaining that the distribution of mass results in a balancing effect.
  • A later reply mentions Gauss' theorem as a related concept, although the context of its application is not fully elaborated.

Areas of Agreement / Disagreement

Participants generally agree on the equivalence of gravitational fields from point masses and spherical objects outside their volume, but the discussion includes varying levels of certainty and references to different theorems without a consensus on the proof methods.

Contextual Notes

Some participants express uncertainty about proving these concepts without calculus, and there is mention of the complexity involved in developing calculus as part of the proof.

alexbib
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will the gravitational field created by a point of mass m be the same than that of a spherical object of same mass (outside the volume of the object)? If so, why is this? How does the sum of the grav forces created by all the points in the sphere add up to the same as a point-mass?
Thanks,

Alex
 
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With Newtonian gravity the net gravity from a spherical shell is zero on the inside of the shell, and the same as from a point mass at the center of the shell from the outside. (I'm not sure about the shell itself.)

Proving this wihout calculus (or developing calculus as part of the proof) is pretty daunting.
 
I think it's called the shell theorem, maybe you can find that on google?
 
Yes, it's the same. In other words, if the mass of the Earth were compressed into a single point (ie a black hole) at the same distance from you (about 4000 miles) as the center of the Earth is now, you would feel the same amount of gravity.

The reason is that some of the mass of the Earth is further from you than the center and some of it is closer, and the net effect balances out that way. To prove it requires vector calculus.
 


It is called the Gauss' theorem
 

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