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AstroFloyd (talk | contribs) m →Spherical shell to solid sphere: Use text for non-variable subscripts. |
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It is possible to use this spherical shell result to re-derive the solid sphere result from earlier. This is done by integrating an infinitesimally thin spherical shell with mass of {{nowrap|<math>dM</math>,}} and we can obtain the total gravity contribution of a solid ball to the object outside the ball
:<math>F_\text{total} = \int dF_r = \frac{Gm}{r^2} \int dM.</math>
Uniform density means between the radius of <math>x</math> to {{nowrap|<math>x+dx</math>,}} <math>dM</math> can be expressed as a function of {{nowrap|<math>x</math>,}} i.e.,
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