In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,

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In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,200 km with an orbital period of 8 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellites (in days) :-

TestHub · Accepted Answer

Kepler's third law about Pluto: T ∝ r 3/2 , scaled to Charon (19,200 km, 8 days). For the 48,000 km satellite: T = 8 ( 19200 48000 ​ ) 3/2 = 8 ( 2.5 ) 3/2 days; for the 64,000 km one: T = 8 ( 19200 64000 ​ ) 3/2 = 8 ( 3 10 ​ ) 3/2 days. Ans (A)

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