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A satellite is launched to orbit the Earth at an altitude of $3\mathrm{.}55{10}^{7}m$ for use in the Global Positioning System $($GPS$).$ Take the mass of the Earth to be $5\mathrm{.}97{10}^{24}kg$ and its radius $6\mathrm{.}38{10}^{6}m.$

$($a$)$ What is the orbital period of this GPS satellite?

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Consider Kepler's Third Law. h