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A satellite is orbiting the Earth at a height $h = R$ where $R$ is the radius of the Earth. What is the ratio of its orbital speed $v_o$ to the escape velocity $v_e$ from the surface of the Earth?
- A.$1/2$
- B.$1/\sqrt{2}$
- C.$1/2$
- D.$1/\sqrt{8}$
Show correct answer & step-by-step solution
Correct answer: D — $1/\sqrt{8}$
Solution
The orbital speed at height is and the escape velocity from the surface is . The ratio simplifies to .
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