Question

Suppose that the gravitational force is not give by the inverse-square law, and instead is where A and B are real constants. Derive the equations of motion and determine whether

angular momentum is conserved. By using the substitution r =1/u, transform the radial component of the equations of motion into a differential equation for u as a function of the angular coordinate 0. Determine for what values of A, B, and integration constants stationary solutions exist and whether they are stable. \mathbf{F}_{\mathrm{grav}}=\left(\frac{A}{r^{2}}+\frac{B}{r^{4}}\right) \hat{r}

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