Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch
ID: 1609121 • Letter: Y
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 12.0 m/s returns to the ground in 4.20 s the circumference of Mongo at the equator is 2.60 times 10^5 km; and there is no appreciable atmosphere on Mongo. The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo? Express your answer with the appropriate units. If the Aimless Wanderer goes into a circular orbit 20,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?Explanation / Answer
orbital velocity = sqrt(GM/R) where G is Gravitational constant; M is mass of mongo; R is radius of orbit
G = 6.67 × 10-11 m3/s2 kg.
M = 1.47 x 1026 kg
R = (Ro + 20000)km where Ro is the radius of mongo
R = [circumference/(2*pi) + 20000]km = 260000/(2*3.142) + 20000 = 41374.92 + 20000 = 61,374.920km
= 6.1 x 107 m
Thus orbital velocity = sqrt(6.67 × 10-11 x 1.47 x 1026/6.1 x 107) = 12678m/s
Circumference of orbit = 2*pi*(6.1 x 107 )m
Thus time required = circumference/velocity = 2*3.142*6.1 x 107/12678 = 30235 seconds = 8.4 hours
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