Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch
ID: 1556595 • 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 14.0 m/s returns to the ground in 7.00 s ; the circumference of Mongo at the equator is 4.00×105 km ; and there is no appreciable atmosphere on Mongo.
A,The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo?
B,If the Aimless Wanderer goes into a circular orbit 3.00×104
km above the surface of Mongo, how many hours will it take the ship to complete one orbit?
Explanation / Answer
time of flight t = 2u/g
where u – the initial velocity and g the acceleration due to gravity of Mongo
t = 2 x 14 /g
g = 28/7
g = 4 m/s2
g= GM/r2
where
G – the universal gravitational constant
M –mass of mongo
r –radius of mongo
radius = circumference/2 = 4.00 x 108/2 x 3.14
r = 6.37 x 107 m
g= GM/r2
4 = 6.67 x 10-11 x M/(6.37 x 107)2
M = 4 x (6.37 x 107)2 /6.67 x 10-11
M = 2.43 x 1026 kg
Period of satellite T =2 {(R+h)3/GM}
T = 2 x 3.14 x {(6.37 x 107 + 3.00 x 107)3/6.67 x 10-11 x 2.43 x 1026 }
T = 6.28 (822.656953 x 1021 / 16.2081 x 1015)
T = 6.28 x 7.124 x 103
T = 44738.72 s
T = 12.43 days
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.