Auroras are produced when charged particles from the sun $($a$.$k$.$a$.$ solar wind$)$ directed toward the Earth are deflected toward the poles. At the poles, the magnetic field is stronger, so it tightens the radius of curvature of the particle's trajectory such that it ionizes the air.

Suppose an alpha particle $($mass of $6\mathrm{.}64{10}^{-27}kg,$ charge of $+2$ e $)$ with a speed of $403k\frac{m}{s}$ becomes trapped by the Earth's magnetic field. Determine the radius of curvature of the particle's trajectory where the Earth's magnetic field is $253T$ and the velocity of the particle makes a $59$ angle with the magnetic field.

Give your answer in units of $m.$

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