A $42\mathrm{.}0$ kg satellite has a circular orbit with a period of $4\mathrm{.}70$ h and a radius of $5\mathrm{.}30{10}^{6}m$ around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is $1\mathrm{.}90\frac{m}{s^2},$ what is the radius of the planet?

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