Question

A satellite is orbiting the Earth at a height of \( 10^4 \, \text{km} \) above the Earth's surface. If the radius of the Earth is \( 6.4 \times 10^6 \, \text{m} \), calculate the orbital speed of the satellite. (Gravitational constant \( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \) and Earth's mass \( M = 6 \times 10^{24} \, \text{kg} \))

• A. \( 7.0 \, \text{km/s} \)
• B. \( 8.0 \, \text{km/s} \)
• C. \( 9.0 \, \text{km/s} \)
• D. \( 10.0 \, \text{km/s} \)

Hint:

Remember: The orbital speed of a satellite depends on the mass of the Earth and the distance from the center of the Earth. A higher orbit results in a lower orbital speed.