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:<math>M_\text{eff} = M \frac{\sinh \lambda r}{\lambda r}</math>.
For an [[ellipsoid]]al shell, the two halves of the shell theorem are generalized by different types of shells. The shell bound by two [[concentric]], [[similarity (geometry)|similar]], and aligned ellipsoids (a [[homoeoid]]) exters no gravitational force on a point inside of it.<ref>[[Michel Chasles]], [http://sites.mathdoc.fr/JMPA/PDF/JMPA_1840_1_5_A41_0.pdf ''Solution nouvelle du problème de l’attraction d’un ellipsoïde hétérogène sur un point exterieur''], Jour. Liouville 5, 465–488 (1840)</ref> Meanwhile, the shell bound by two concentric, [[confocal]] ellipsoids (a [[focaloid]]) has the property that the gravitational force outside of two concentric, confocal focaloids is the same.<ref name="rodrigues">{{cite journal |last1=Rodrigues |first1=Hilário |title=On determining the kinetic content of ellipsoidal configurations |journal=Monthly Notices of the Royal Astronomical Society |date=11 May 2014 |volume=440 |issue=2 |pages=1519–1526 |doi=10.1093/mnras/stu353|doi-access=free |arxiv=1402.6541 }}</ref>
== Newton's proofs ==
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