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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.4 Polar Coordinates and Planetary Motion, #28 · Multivariable Calculus · Curves in space

If a central force is …, explain why

If a central force is $F = - ma (r) u_{r}$ , explain why $d^{2} r / d t^{2} - r (d θ / d t)^{2} = - a (r)$ . What is $a (r)$ for gravity? Equation (12) for $q = 1/ r$ leads to $q_{θ θ} + q = r^{2} a (r)$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.4 Polar Coordinates and Planetary Motion, #28

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