PhysicsProblem

Source equations

$\mathbf{F} = - G {m_1 m_2 \over {\lVert \mathbf{r} \rVert}^2} \, \mathbf{\hat{r}}$ (newton's law of universal gravitation)

$\mathbf{F} = m{\mathrm{d}^2\mathbf{p}_t\over\mathrm{d} t^2}$ (newton's second law)

${\mathrm{d}^2\mathbf{p}_t\over\mathrm{d} t^2} = -{C \over \lVert \mathbf{p}_t \rVert^2} \mathbf{\hat{p}}_t$

${\mathrm{d} \mathbf{p}_{t=0}\over\mathrm{d} t} = (0, .1, 0)$

$\mathbf{p}_{t=0} = (1, 0, 0)$

solve for $\mathbf{p}_t$

${\mathrm{d}^2y\over\mathrm{d} x^2} = -{1\over y^2}$