Question

What is the expression for the time period of a satellite orbiting Earth at a height \( h \) above the Earth's surface?

• A. \( T = 2\pi \sqrt{\frac{R^3}{GM}} \)
• B. \( T = 2\pi \sqrt{\frac{(R + h)^3}{GM}} \)
• C. \( T = \frac{1}{2\pi} \sqrt{\frac{GM}{(R + h)^3}} \)
• D. \( T = 2\pi \sqrt{\frac{(R^2 + h^2)}{GM}} \)

Hint:

When calculating the time period of a satellite, remember to include both the Earth's radius \( R \) and the satellite's height \( h \) above the surface. Use \( T = 2\pi \sqrt{\frac{(R + h)^3}{GM}} \) for accurate calculations.