Even gravity wants me

A satellite is in a circular orbit very close to the surface of a planet of uniform density ρ\rho. What is the period (in hours) of the satellite's orbit around the planet?

Details and Assumptions

  • G=6.67×1011Nm2/kg2G = 6.67 \times {10}^{-11} N\cdot{m}^{2}/{kg}^{2}
  • ρ=4.5gcm3\rho = 4.5 \frac{g}{{cm}^{3}}
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