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A satellite moves in a circular orbit just above the surface of a planet (orbital speed v_c). At some instant its speed is suddenly boosted to n*v_c along its direction of motion, and it enters an elliptical orbit. What is the maximum value of n for the orbit to remain elliptical (i.e., the satellite must not escape the planet's gravity)?
- 2
- sqrt(2)
- sqrt(2) + 1
- 1/(sqrt(2) - 1)
Correct answer: sqrt(2)
Solution
Since v_escape = sqrt(2)*v_c, the orbit remains bound (elliptical) only when n*v_c < sqrt(2)*v_c, so the maximum n is sqrt(2).
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