Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch

Question

Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50-kg stone thrown upward from the ground at 11.6 m/s returns to the ground in 8.72 s; the circumference of Mongo at the equator is 2.00 105 km; and there is no appreciable atmosphere on Mongo. The starship commander, Captain Confusion, asks for the following information: (mass of Mongo =4.03e+25 kg) If the Aimless Wanderer goes into circular orbit 29700 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?

Explanation / Answer

freefall acc on mongo     g = 11.9 m/s / 3.84s =    3.098 m/s2

radius of mongo       r = circum/ 2 = 2.00 x 108 meters / 2 =    3.183 x 107 meters

(a) mass of planet is found with.

       g =   GM /R2 M = R2g / G = (3.183 x107)^2 * 3.098 / 6.673 x 10-11 =

                     =   4.7 x 1025 kg

(b) The radius of the orbit would be   height +radius of planet = 28200 + 31830 = 60030km = 6.003 x 107 meters

and using keplers third law

     T2 = (42 / GM) r3   = (42 / 6.673 x 10-11 * 4.7 x1025 ) * (6.003 x 107 )3 =

           = 52.182x10^3 seconds = 14.495 hours

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