Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch
ID: 1499747 • 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 5.70 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: what is the mass of Mongo?
If the Aimless Wanderer goes into a circular orbit 30,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?
Explanation / Answer
A. Mass of Mongo
First, find the acceleration on Mongo
a = v / t
v = 14 m/s - (-14m/s) = 28 m/s
t = 5.7 s
a = 28/5.7 m/s^2
a = 4.9 m/s^2
Second, solve for M
radius of Mongo
r = c/(2)
c = 2x10^5 km
r = 2x10^5 km / 2
r = 31,830 km
a = MG/r^2
M = a r^2/G
M = (4.9 m/s^2) (3.183x10^7 m)^2 / (6.67x10^-11)
M = 7.42x10^25 kg
B. Period of Orbit
First, find the acceleration at h = 3x10^4 km
a = g (r/(r+h))
a = (4.9 m/s^2) * ( (3.183x10^4 km / (3.183x10^4 km + 3x10^4 km)))
a = 3.51 m/s^2
Set a = centripetal acceleration and solve for P
a = v^2/r
v = (2r)/P
Sub in for v
a = ((2r)/P)^2 /r
P^2 = (2)^2 r/a
P = 2 (r/a)
P = 2 (3.183x10^7 m / 3.51 m/s^2)
P = 18902 sec
P = 5.250 hours
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