calculate the accleration of the moon Using an earth-based telescope, you track

Question

calculate the accleration of the moon

Using an earth-based telescope, you track a moon that circles one of the planets of our solar system. You find that the moon completes one rotation every 26.9 hours, and the radius of rotation is 1.177x108 meters. Find the acceleration of this moon. Find the mass of the PLANET that the moon is rotating around. Using Wikipedia, what planet does this moon orbit? (THIS is how the mass of a planet is obtained - by evaluating the orbit of objects around the planet.)

Explanation / Answer

A) a = v2/r for uniform circular motion, and v is distance/time = circumference/period

= (2 * pi * 1.177 * 108 m)/(26.9 hr * 3600 s/hr) = 7636.6 m/s

therefore a = (7636.6 m/s)2/(1.177 * 108 m) = 0.495 m/s2

B) we know v2 = GM/r so M = v2r/G

= (7636.6 m/s)2(1.177 * 108 m)/(6.6738 * 10-11 m3/kg s2) = 1.028 * 1026 kg

C) has to be Neptune

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