Inside A Shell
For a point inside the shell the difference is that for θ equal to zero φ takes the value π radians and s the value R - r. When then θ increases from 0 to π radians φ decreases from the initial value π radians to zero and s increases from the initial value R - r to the value R + r.
This can all be seen in the following figure
Inserting these bounds in the primitive function
one gets that in this case
saying that the net gravitational forces acting on the point mass from the mass elements of the shell, outside the measurement point, cancel out.
Generalization: If the resultant force inside the shell is:
The above results into being identically zero if and only if
Outside the shell (i.e r>R or r<-R) :
Read more about this topic: Shell Theorem
Famous quotes containing the word shell:
“How then can we account for the persistence of the myth that inside the empty nest lives a shattered and depressed shell of a woman—a woman in constant pain because her children no longer live under her roof? Is it possible that a notion so pervasive is, in fact, just a myth?”
—Lillian Breslow Rubin (20th century)