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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