Grav. field of spherical objects

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The gravitational field outside a spherical object of mass m is equivalent to that of a point mass m located at its center, a principle known as the shell theorem. Inside a spherical shell, the net gravitational force is zero, while outside, the gravitational effect is the same as if all mass were concentrated at a point. This equivalence arises because the gravitational forces from different points in the sphere balance each other out due to their varying distances from an external observer. Proving this relationship without calculus is challenging, but it fundamentally relies on Gauss' theorem. Understanding this concept is crucial for grasping gravitational interactions in spherical bodies.
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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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