Shell theorem: Difference between revisions

Revision as of 20:01, 22 January 2022

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{{block indent|Suppose there is a force <math>F</math> between masses ''M'' and ''m'', separated by a distance ''r'' of the form <math>F = M m f(r)</math> such that any spherically symmetric body affects external bodies as if its mass were concentrated at its center. Then what form can the function <math>f</math> take?}}

In fact, this allows exactly one more class of force than the (Newtonian) inverse square.<ref name=Gurzadyan>{{cite journal| last=Gurzadyan |first=Vahe |authorlink=vahe Gurzadyan|title=The cosmological constant in McCrea-Milne cosmological scheme|journal=The Observatory|date= 1985|volume=105|pages=42–43|bibcode=1985Obs...105...42G}} http://adsabs.harvard.edu/full/1985Obs...105...42G</ref><ref name=Arens>{{cite journal| last=Arens| first=Richard| authorlink=Richard Friederich Arens|title=Newton's observations about the field of a uniform thin spherical shell|journal=Note di Matematica|date=January 1, 1990|volume=X|issue=Suppl. n. 1|pages=39–45}}</ref> The most general force as derived by [[Vahe Gurzadyan]] in <ref name="Gurzadyan"/> is:(Gurzadyan

theorem) is:"

:<math> F = -\frac{G M m}{r^2} - \frac{\Lambda M m r}{3} </math>