Revision as of 00:45, 4 May 2022 edit Hellacioussatyr (talk \| contribs) Extended confirmed users 10,151 edits →Derivation of gravitational field outside of a solid sphere Tags: Mobile edit Mobile web edit Advanced mobile edit ← Previous edit		Revision as of 04:51, 9 June 2022 edit undo Cewbot (talk \| contribs) Bots 8,375,827 edits m Fixing broken anchor: 2011-02-01 (VERY DIFFERENT 44≥17) #Vector components⇝Euclidean vector#Decomposition Next edit →
Line 64: Applying [[Newton's Universal Law of Gravitation]], the sum of the forces due to the mass elements in the shaded band is :<math>dF = \frac{Gm}{s^2} dM.</math> However, since there is partial cancellation due to the [[Euclidean vector\|vector]] nature of the force in conjunction with the circular band's symmetry, the leftover [[Vector (geometry)#~~Vector components~~Decomposition\|component]] (in the direction pointing towards {{nowrap\|<math>m</math>)}} is given by :<math>dF_r = \frac{Gm}{s^2} \cos(\varphi) \, dM</math> The total force on {{nowrap\|<math>m</math>,}} then, is simply the sum of the force exerted by all the bands. By shrinking the width of each band, and increasing the number of bands, the sum becomes an integral expression:

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