MediumChange of variables

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #32 · Multivariable Calculus · Change of variables

### *33 Compute … to find the force of gravity at …

Problems, on the attraction of a sphere, use Figure 14.18 and the law of cosines $q^{2} = D^{2} - 2 ρ D cos ϕ + ρ^{2} = u$ .

For two solid spheres attracting each other (sun and planet), can we concentrate both spheres into point masses at their centers?

### *33
Compute $∭ cos α d V / q^{3}$ to find the force of gravity at $(0, 0, D)$ from a cylinder $x^{2} + y^{2} \leq a^{2}$ , $0 \leq z \leq h$ . Show from a figure why $q^{2} = r^{2} + (D - z)^{2}$ and $cos α = (D - z) / q$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #32

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