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 14.0 m/s returns to the ground in 5.70 s; the circumference of Mongo at the equator is 2.80 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 40,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?

Explanation / Answer

Mass of stone = 2.50 kg

Initial Velocity, U = 14 m/s

time of flight, t = 5.7s

Therefore, acceleration due to gravity of Mongo, g = 2*U/t =2*14/5.7 = 4.92 m/s^2

Circumference of Mongo, C = 2.80*10^8 m

therefore radius of Mongo, r = C/2pi = 44563.38*1000 = 44563380 m

Now, g = Mass of mongo * G/r^2 , where G is universal gravitational constant

Part A

Mass of mongo = 4.92* 44563380^2/6.67408*10^-11 = 1.46*10^26 Kg

Part B

Velocity of Wanderer =sqrt(GM/r) = sqrt(6.67408*10^-11*1.46*10^26/40000000) = 15607.81 m/s

Time = 2*pi*r/V = 2*pi*40000000/15607.81 = 16102.67 s = 4.472 hrs

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