# A Strange Central Force

A small 10 kg sphere is attracted to a central point at the origin by a force $\vec{F}=- \frac{1} {r^{5/3}} \hat{r} ~ \text{ N },$ where $$\text{N}$$ stands for Newtons. At time $$t=0$$ the sphere is at $$r=\SI{10}{ \m}$$ with a tangential velocity of $$0.02 \text{ m/s}$$ and no radial velocity. What is the closest distance the sphere comes to the origin in meters?

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