Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch
ID: 1496957 • Letter: Y
Question
Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a2.50-kg stone thrown upward from the ground at11.0 m/s returns to the ground in 4.20 s ; the circumference of Mongo at the equator is 2.10×105 km ; and there is no appreciable atmosphere on Mongo.
Part A
The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo?
Express your answer with the appropriate units.
Part B
If the Aimless Wanderer goes into a circular orbit 20,000 kmabove the surface of Mongo, how many hours will it take the ship to complete one orbit?
Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a2.50-kg stone thrown upward from the ground at11.0 m/s returns to the ground in 4.20 s ; the circumference of Mongo at the equator is 2.10×105 km ; and there is no appreciable atmosphere on Mongo.
Part A
The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo?
Express your answer with the appropriate units.
Part B
If the Aimless Wanderer goes into a circular orbit 20,000 kmabove the surface of Mongo, how many hours will it take the ship to complete one orbit?
Explanation / Answer
Given,
m = 2.5 kg ; v = 11 m/s ; t = 4.2 s ;
C = 2.1 x 105 km = 2.1 x 108 m
Radius = R = C/2 pi = 2.1 x 108 m/2 pi = 3.34 x 107 m
A)From third equation of motion we know that
S = ut + 1/2 a t2
In our case, S = 0 ; a = - g for the planet
1/2 a t = u
a = 2 u / t = 2 x 11/4.2 = 5.24 m/s2
We know that, g = G M / R2 => M = g x R2/G
M = 5.24 x ( 3.34 x 107 m)2/6.67 x 10-11 = 8.76 x 1025 kg
Hence, M = 8.76 x 1025 kg
B) a = 3.34 x 107 m + 2 x 107 = 5.34 x 107 m
We know from Kepler's law:
T = 2 pi a3/2/sqrt(GM) = 2 x 3.14 x (5.34 x 107 m)3/2/sqrt(6.67 x 10-11 x 8.76 x 1025 kg) = 3.205 x 104 s
Hence, T = 3.205 x 104 s
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