Shell theorem: Difference between revisions

Revision as of 04:51, 9 June 2022

Revision as of 19:11, 11 November 2022

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The gravitational field <math>E</math> at a position called <math>P</math> at <math>(x,y) = (-p,0)</math> on the ''x''-axis due to a point of mass <math>M</math> at the origin is <math display="block">E_\text{point} = \frac{GM}{p^2}</math>

[[File:Point2.png|frameless|300x300px]]

Suppose that this mass is moved upwards along the ''y''-axis to the point {{nowrap|<math>(0-p,R)</math>.}} The distance between <math>P</math> and the point mass is now longer than before; It becomes the hypotenuse of the right triangle with legs <math>p</math> and <math>R</math> which is {{nowrap|<math display="inline">\sqrt{p^2 + R^2}</math>.}} Hence, the gravitational field of the elevated point is:

<math display="block">E_\text{elevated point} = \frac{GM}{p^2+R^2}</math>

[[File:Pointy2.png|frameless|270x270px]]