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Understanding the Gravitational Force Integral
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[QUOTE="Charles Link, post: 5511910, member: 583509"] It's an interesting question. The integral solution you give is in spherical coordinates and the infinitesimal volume ## dv=r^2 \sin{\theta} \ d \theta \ d \phi \ dr ## . It really is not doing it in any kind of shell, but there is a z-axis symmetry. The ## \cos{\theta} ## gives the z-component of the force, since by symmetry any radial components will cancel. ## \rho ## is the density so that ## \rho dv ## gives the elemental mass in volume ## dv ##. The remaining part is just the inverse square law with the universal gravitational constant ## G ##. And you also need to integrate the ## dr ## from ## 0 ## to ## R ##. [/QUOTE]
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Understanding the Gravitational Force Integral
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