Given below are two statements:
Statement $I$: $A$ satellite is moving around the Earth in an orbit very close to the Earth's surface. The time period of revolution of the satellite depends upon the density of the Earth.
Statement $II$: The time period of revolution of the satellite is $T = 2\pi\sqrt{\frac{R_e}{g}}$ (for a satellite very close to the Earth's surface), where $R_e$ is the radius of the Earth and $g$ is the acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are false
• B
  Both Statement $I$ and Statement $II$ are true
• C
  Statement $I$ is true but Statement $II$ is false
• D
  Statement $I$ is false but Statement $II$ is true