A “treetop satellite” moves in a circular orbit just above the surface of a planet, assumed to offer no air resistance. Show that its orbital speed υ and the escape speed from the planet are related by the expression υesc =√2υ.

Classical Dynamics of Particles and Systems
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ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter8: Central-force Motion
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Problem 8.3P
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A “treetop satellite” moves in a circular orbit just above the surface of a planet, assumed to offer no air resistance. Show that its orbital speed υ and the escape speed from the planet are related by the expression υesc =√2υ.

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